Cambridge IGCSE Physics CB
Cambridge IGCSE Physics CB
Cambridge IGCSE Physics CB
Physics
Fourth Edition
Physics
Fourth Edition
Heather Kennett
Tom Duncan
Revision checklist
At the end of each topic, a revision checklist will Going further
allow you to recap what you have learnt in each
These boxes take your learning further than is
topic and double check that you understand the key required by the Cambridge syllabus so that you have
concepts before moving on. the opportunity to stretch yourself.
vi
vii
★ Understand the difference between scalar and vector quantities, and give examples of each.
★ Calculate or determine graphically the resultant of two perpendicular vectors.
This topic introduces the concept of describing space and time in terms of numbers together with
some of the basic units used in physics. You will learn how to use simple devices to measure or
calculate the quantities of length, area and volume. Accurate measurements of time will be needed
frequently in the practical work in later topics and you will discover how to choose the appropriate
clock or timer for the measurement of a time interval. Any single measurement will not be entirely
accurate and will have an error associated with it. Taking the average of several measurements, or
measuring multiples, reduces the size of the error.
The small figures 1, 2, 3, etc. are called powers of To obtain an average value for a small distance,
ten. The power shows how many times the number multiples can be measured. For example, in ripple
has to be multiplied by 10 if the power is greater tank experiments (Topic 3.1), measure the distance
than 0 or divided by 10 if the power is less than 0. occupied by five waves, then divide by 5 to obtain
Note that 1 is written as 100. the average wavelength.
This way of writing numbers is called standard
notation.
Significant figures
Every measurement of a quantity is an attempt
Length to find its true value and is subject to errors
The unit of length is the metre (m) and is the arising from limitations of the apparatus and
distance travelled by light in a vacuum during the experimenter. The number of figures, called
a specific time interval. At one time it was the significant figures, given for a measurement
distance between two marks on a certain metal bar. indicates how accurate we think it is and more
Submultiples are: figures should not be given than are justified.
1 decimetre (dm) = 10 −1 m
For example, a value of 4.5 for a measurement
has two significant figures; 0.0385 has three
1 centimetre (cm) = 10 −2 m significant figures, 3 being the most significant and
1 millimetre (mm) = 10 −3 m 5 the least, i.e. it is the one we are least sure about
since it might be 4 or it might be 6. Perhaps it had
1 micrometre (µm) = 10 −6 m to be estimated by the experimenter because the
1 nanometre (nm) = 10 −9 m
reading was between two marks on a scale.
When doing a calculation your answer should
A multiple for large distances is have the same number of significant figures as the
5 measurements used in the calculation. For example,
1 kilometre (km) = 103 m ( mile approx.) if your calculator gave an answer of 3.4185062, this
8
would be written as 3.4 if the measurements had
1 gigametre (Gm) = 109 m = 1 billion metres two significant figures. It would be written as 3.42
for three significant figures. Note that in deciding
Many length measurements are made with rulers; the least significant figure you look at the next
the correct way to read one is shown in Figure 1.1.2. figure to the right. If it is less than 5, you leave the
The reading is 76 mm or 7.6 cm. Your eye must be least significant figure as it is (hence 3.41 becomes
directly over the mark on the scale or the thickness 3.4), but if it equals or is greater than 5 you increase
of the ruler causes a parallax error. the least significant figure by 1 (round it up) (hence
3.418 becomes 3.42).
If a number is expressed in standard notation,
correct wrong
the number of significant figures is the number of
digits before the power of ten. For example,
2.73 × 103 has three significant figures.
70 80
object
b 4 cm
▲ Figure 1.1.3
5 cm
meniscus
3 cm
4 cm
Worked example
a Calculate the volume of a block of wood which is 40 cm
long, 12 cm wide and 5 cm high in cubic metres.
volume V = length × breadth × height
= 40 cm × 12 cm × 5 cm
= 2400 cm3
= 2400 × 10 −6 m3
= 2.4 × 10 −3 m3
3 4 5 cubes
b Calculate the volume of a cylinder of radius 10 mm and
▲ Figure 1.1.5 height 5.0 cm in cubic metres.
volume of cylinder V = πr 2h
The volume of a cylinder of radius r and height
h is πr 2h. r = 10 mm = 1.0 cm and h = 5.0 cm
The volume of a liquid may be obtained by so V = πr 2h
pouring it into a measuring cylinder (Figure 1.1.6). = π × (1.0 cm)2 × 5.0 cm
When making a reading the cylinder must be
= 16 cm3 = 16 × 10 −6 m3 = 1.6 × 10 −5 m3
upright and your eye must be level with the bottom
of the curved liquid surface, i.e. the meniscus. Now put this into practice
The meniscus formed by mercury is curved
1 Calculate the volume of a rectangular box which is 30 cm
oppositely to that of other liquids and the top long, 25 cm wide and 15 cm high in cubic metres.
is read. 2 Calculate the volume of a cylinder of radius 50 mm and
Measuring cylinders are often marked in millilitres height 25 cm in cubic metres.
(ml) where 1 ml = 1 cm3; note that 1000 cm3 = 1 dm3
(= 1 litre).
Practical work
metal plates
By itself the scale reading is not equal to the
height. It is too small by the value of x.
This type of error is known as a systematic error.
The error is introduced by the system. A half-metre
string ruler has the zero at the end of the ruler and so can
support
be used without introducing a systematic error.
stand When using a ruler to determine a height, the ruler
must be held so that it is vertical. If the ruler is at an
angle to the vertical, a systematic error is introduced.
8
7
pendulum
bob
P
6
B O A
5
▲ Figure 1.1.7
4
3
Systematic errors
2
x
is shown as the length x. The height of the point P
bench
▲ Figure 1.1.8
Going further
Vernier scales and micrometers
Lengths can be measured with a ruler to a precision of
about 0.5 mm. Some investigations may need a more
precise measurement of length, which can be achieved
by using vernier calipers (Figure 1.1.9) or a micrometer
screw gauge.
1 2
mm
b
O object A B
5 10
1 2
mm
Worked example
Calculate the resultant of two forces of 3.0 N and 4.0 N Graphical method
acting at right angles to each other. The values for F and θ can be found graphically by drawing
Let FX = 3.0 N and FY = 4.0 N as shown in Figure 1.1.12. the vectors to scale on a piece of graph paper as shown in
Figure 1.1.12.
scale 1 cm = 1 N F First choose a scale to represent the size of the vectors
(1 cm could be used to represent 1.0 N).
Draw the vectors at right angles to each other. Complete the
rectangle as shown in Figure 1.1.12 and draw the diagonal
from the origin as shown. The diagonal then represents the
4.0 N resultant force, F. Measure the length of F with a ruler and
use the scale you have chosen to determine its size. Measure
the angle θ, the direction of the resultant, with a protractor.
Check that the values for F and θ you obtain are the same
θ as those found using the algebraic method.
Revision checklist
After studying Topic 1.1 you should know and After studying Topic 1.1 you should be able to:
understand the following: ✓ write a number in powers of ten (standard
✓ how to make measurements of length and time notation) and recall the meaning of standard
intervals, minimise the associated errors and use prefixes
multiple measurements to obtain average values ✓ measure and calculate lengths, areas and
volumes of regular objects and give a result with
✓ the difference between scalars and vectors and the correct units and an appropriate number of
recall examples of each. significant figures
10
Exam-style questions
1 A chocolate bar measures 10 cm long by 2 cm c Write down expressions for
wide and is 2 cm thick. i the area of a circle [1]
a Calculate the volume of one bar. [3] ii the circumference of a circle [1]
b How many bars each 2 cm long, 2 cm iii the volume of a cylinder. [2]
wide and 2 cm thick have the same total [Total: 7]
volume? [3]
c A pendulum makes 10 complete oscillations
in 8 seconds. Calculate the time period of Going further
the pendulum. [2]
5 What are the readings on the micrometer screw
[Total: 8] gauges in Figures 1.1.14a and 1.1.14b?
2 a A pile of 60 sheets of paper is 6 mm high.
Calculate the average thickness of a sheet a
11
★ Describe the motion of objects falling with and without air/liquid resistance.
The concepts of speed and acceleration are encountered every day, whether it be television
monitoring of the speed of a cricket or tennis ball as it soars towards the opposition or the
acceleration achieved by an athlete or racing car. In this topic you will learn how to define speed
in terms of distance and time. Graphs of distance against time will enable you to calculate speed
and determine how it changes with time; graphs of speed against time allow acceleration to be
studied. Acceleration is also experienced by falling objects as a result of gravitational attraction.
All objects near the Earth’s surface experience the force of gravity, which produces a constant
acceleration directed towards the centre of the Earth.
12
13
Speed–time graphs Values for the speed of the object at 1 s intervals
can be read from the graph and are given in Table
If the speed of an object is plotted against the 1.2.2. The data shows that the speed increases by
time, the graph obtained is a speed–time graph. the same amount (4 m/s) every second.
It provides a way of solving motion problems.
▼ Table 1.2.2
In Figure 1.2.2, AB is the speed–time graph
for an object moving with a constant speed of Speed/m/s 20 24 28 32 36 40
20 m/s. Time/s 0 1 2 3 4 5
Values for the speed of the object at 1 s intervals
can be read from the graph and are given in You can use the data to plot the speed–time graph.
Table 1.2.1. The data shows that the speed is Join up the data points on the graph paper with
constant over the 5 s time interval. the best straight line to give the line PQ shown in
▼ Table 1.2.1
Figure 1.2.3a. (Details for how to plot a graph are
given on pp. 297–8 in the Mathematics for physics
Speed/m/s 20 20 20 20 20 20 section.)
Time/s 0 1 2 3 4 5 Figure 1.2.3b shows the shape of a speed–time
graph for an object accelerating from rest over time
interval OA, travelling at a constant speed over time
30 interval AB and then decelerating (when the speed
is decreasing) over the time interval BC. The steeper
A B
speed/m/s
tio
cel
ce
shown in Figure 1.2.3a means that the gradient, and ac
tio
n
14
10 L
40
Y
O 1 2 3 4 5 30
distance/m
time/s
10
Using the gradient of M
a speed–time graph to O
1 2 3 4
decreasing. constant
speed
Distance–time graphs O
at rest
A B C D
An object travelling with constant speed covers equal
time/s
distances in equal times. Its distance–time graph is
a straight line, like OL in Figure 1.2.4a for a constant ▲ Figure 1.2.4b Constant speed
speed of 10 m/s. The gradient of the graph is
15
The speed of the object is higher when the gradient At the start of the timing the speed is 20 m/s,
of the graph is steeper. The object is travelling but it increases steadily to 40 m/s after 5 s.
faster in time interval AB than it is in time interval If the distance covered equals the area under PQ,
CD; it is at rest in time intervals OA and BC when i.e. the shaded area OPQS, then
the distance does not change. distance = area of rectangle OPRS + area of triangle PQR
When the speed of the object is changing, the 1
gradient of the distance–time graph varies, as in = OP × OS + 2 × PR × QR
Figure 1.2.5, where the upward curve of increasing 1
(area of a triangle = 2 base × height)
gradient of the solid green line shows the object 1
accelerating. The opposite, upward curve of = 20 m/s × 5 s + 2 × 5 s × 20 m/s
decreasing gradient (indicated by the dashed green = 100 m + 50 m = 150 m
line) shows an object decelerating above T.
Note that when calculating the area from the graph,
40 A the unit of time must be the same on both axes.
accelerating The rule for finding distances travelled is true
30
even if the acceleration is not constant. In Figure
decelerating
1.2.3c, the distance travelled equals the shaded
distance/m
20
area OXY.
T
10 accelerating
Test yourself
C B 5 The speeds of a bus travelling on a straight road are
O given below at successive intervals of 1 second.
1 2 3 4 5
time/s Time/s 0 1 2 3 4
▲ Figure 1.2.5 Non-constant speed Speed/m/s 0 4 8 12 16
16
17
Falling bodies
In air, a coin falls faster than a small piece of paper.
In a vacuum they fall at the same rate, as may
be shown with the apparatus of Figure 1.2.6.
The difference in air is due to air resistance having
a greater effect on light bodies than on heavy
bodies. The air resistance to a light body is large
when compared with the body’s weight. With a
dense piece of metal, the resistance is negligible
at low speeds.
There is a story, untrue we now think, that in the
sixteenth century the Italian scientist Galileo Galilei
dropped a small iron ball and a large cannonball ten
times heavier from the top of the Leaning Tower
of Pisa (Figure 1.2.7). And we are told that, to the
surprise of onlookers who expected the cannonball
to arrive first, they reached the ground almost
simultaneously.
rubber
stopper
Perspex or
Pyrex tube
paper
1.5 m coin
pressure
tubing
to vacuum
pump
screw clip
▲ Figure 1.2.6 A coin and a piece of paper fall at the same ▲ Figure 1.2.7 The Leaning Tower of Pisa, where Galileo is
rate in a vacuum. said to have experimented with falling objects
18
Practical work
▲ Figure 1.2.8
19
Going further
Measuring g
Using the arrangement in Figure 1.2.9, the time for a A rough estimate for g can be made by timing the fall of
steel ball-bearing to fall a known distance is measured a rubber ball from the top of a building. It will only take
by an electronic timer. a second to reach the ground from a height of 5 m, so
you will need fast reactions if you use a stopwatch for
When the two-way switch is changed to the ‘down’
the measurement. Watch out that you do not hit anybody
position, the electromagnet releases the ball and
below!
simultaneously the clock starts. At the end of its fall the
ball opens the ‘trap-door’ on the impact switch and the
clock stops.
Distance–time graphs for a falling object
For an object falling freely from rest in a uniform
The result is found from the third equation of motion gravitational field without air resistance, there will be
s = ut + 12 at2 , where s is the distance fallen (in m), t is the constant acceleration g, so we have
time taken (in s), u = 0 (the ball starts from rest) and
1
a = g (in m/s2). s = gt2
2
Hence A graph of distance s against time t is shown in Figure
1 1.2.10a. The gradually increasing slope indicates the
s = gt2 speed of the object increases steadily. A graph of s
2
or against t2 is shown in Figure 1.2.10b; it is a straight line
through the origin since s ∝ t2 ( g being constant at one
g = 2s/t2 place).
Air resistance is negligible for a dense object such as a
steel ball-bearing falling a short distance.
80
electromagnet
60
distance/m
40
ball-
bearing 20
0 1 2 3 4
time/s
EXT
two-way
COM 80
switch
CLOCK
OPERATING 60
distance/m
40
magnet 12 V a.c.
adjustable 20
terminal
0 4 8 12 16
hinge trap-door of
impact switch (time)2/s2
▲ Figure 1.2.9
20
Test yourself
7 An object falls from a hovering helicopter and hits
the ground at a speed of 30 m/s. How long does it
take the object to reach the ground and how far
does it fall? Sketch a speed–time graph for the
object (ignore air resistance).
8 A stone falls from rest from the top of a high
tower. Ignore air resistance and take g = 9.8 m/s2.
Calculate
a the speed of the stone after 2 seconds
b how far the stone has fallen after 2 seconds.
9 At a certain instant a ball has a horizontal velocity
of 12 m/s and a vertical velocity of 5 m/s.
Calculate the resultant velocity of the ball at that
instant.
Going further
Projectiles
The photograph in Figure 1.2.11 was taken while a For example, if a ball is thrown horizontally from the
lamp emitted regular flashes of light. One ball was top of a cliff and takes 3 s to reach the beach below, we
dropped from rest and the other, a projectile, was thrown can calculate the height of the cliff by considering the
sideways at the same time. Their vertical accelerations vertical motion only. We have u = 0 (since the ball has no
(due to gravity) are equal, showing that a projectile falls vertical velocity initially), a = g = +9.8 m/s2 and t = 3 s.
like a body which is dropped from rest. Its horizontal The height s of the cliff is given by
velocity does not affect its vertical motion. 1
s = ut + at2
The horizontal and vertical motions of a body are 2
independent and can be treated separately. 1
= 0 × 3 s + (+9.8 m/s2)32 s2
2
= 44 m
Projectiles such as cricket balls and explosive shells
are projected from near ground level and at an angle.
The horizontal distance they travel, i.e. their range,
depends on
• the speed of projection – the greater this is, the
greater the range, and
• the angle of projection – it can be shown that,
neglecting air resistance, the range is a maximum
when the angle is 45° (Figure 1.2.12).
45°
21
Revision checklist
After studying Topic 1.2 you should know and ✓ define and calculate acceleration and use
understand the following: the fact that deceleration is a negative
acceleration in calculations
✓ that a negative acceleration is a deceleration
or retardation. ✓ state that the acceleration of free fall, g, for an
object near to the Earth is constant and use the
After studying Topic 1.2 you should be able to:
given value of 9.8 m/s2
✓ define speed and velocity, and calculate average
speed from total distance/total time; sketch, plot, ✓ describe the motion of objects falling in a
interpret and use speed–time and distance–time uniform gravitational field.
graphs to solve problems
22
Exam-style questions
1 The speeds of a car travelling on a straight 4 The graph in Figure 1.2.15 represents the
road are given below at successive intervals of distance travelled by a car plotted against time.
1 second. a State how far the car has travelled at the
end of 5 seconds. [1]
Time/s 0 1 2 3 4 b Calculate the speed of the car during the
Speed/m/s 0 2 4 6 8 first 5 seconds. [1]
c State what has happened to the car after A.[2]
Calculate d Draw a graph showing the speed of the car
a the average speed of the car in m/s [2] plotted against time during the first
b the distance the car travels in 4 s [3] 5 seconds. [3]
c the constant acceleration of the car. [2] [Total: 7]
[Total: 7]
2 If a train travelling at 10 m/s starts to 120
A
accelerate at 1 m/s2 for 15 s on a straight track, 100
calculate its final speed in m/s.
distance/m
80
[Total: 4] 60
40
3 The distance–time graph for a girl on a cycle ride 20
is shown in Figure 1.2.14.
a Calculate 0 1 2 3 4 5 6
i how far the girl travelled [1] time/s
30 B C
7.5
speed/m/s
20 A 5.0
2.5
10
0 time of 0 2 4 6 8 10 12 14 16 18 20 22
1pm 2pm 3pm 4pm 5pm 6pm day
time/s
▲ Figure 1.2.14 ▲ Figure 1.2.16
23
100
C D a i A is the force which causes the raindrop
A B to fall. Give the name of this force. [1]
80
ii B is the total force opposing the motion
speed/km/h
600
500
400
distance/m
300
200
100
time/s
0 10 20 30
▲ Figure 1.2.18
24
Images of astronauts walking on the surface of the Moon show them walking with bouncing steps.
The force of gravity is less on the Moon than it is on the Earth and this accounts for their different
movements. In the previous topics you have encountered measurements of space and time, and the
rates of change that define speed and acceleration. You will now encounter a further fundamental
property, the mass of an object. Mass measures the quantity of matter in a body. In the presence of
gravity, mass acquires weight in proportion to its mass and the strength of the gravitational force.
Although the mass of an object on the Moon is the same as it is on the Earth, its weight is less on the
Moon because the force of gravity there is less.
Key definitions
Mass a measure of the quantity of matter in an object at Weight
rest relative to an observer We all constantly experience the force of gravity,
Weight a gravitational force on an object that has mass in other words, the pull of the Earth. It causes an
unsupported body to fall from rest to the ground.
There are several kinds of balance used to measure Weight is a gravitational force on an object that
mass. In the beam balance the unknown mass in has mass.
25
For an object above or on the Earth’s surface, the the same wherever it is and, unlike weight, does not
nearer it is to the centre of the Earth, the more the depend on the presence of the Earth.
Earth attracts it. Since the Earth is not a perfect
sphere but is flatter at the poles, the weight of a
body varies over the Earth’s surface. It is greater at Test yourself
the poles than at the equator. 1 An object of mass 1 kg has weight of 10 N at a
Gravity is a force that can act through space, that certain place. What is the weight of
a 100 g
is there does not need to be contact between the b 5 kg
Earth and the object on which it acts as there does c 50 g?
when we push or pull something. Other action-at- 2 The force of gravity on the Moon is said to be one-
a-distance forces which, like gravity, decrease with sixth of that on the Earth. What would a mass of
distance are 12 kg weigh
(i) magnetic forces between magnets and a on the Earth
b on the Moon?
(ii) electric forces between electric charges.
When a mass experiences a gravitational force we
say it is in a gravitational field. Weight is the result
of a gravitational field acting on a mass: weight is a Weight and gravity
vector quantity and is measured in newtons (N). The weight W of an object is the force of gravity
acting on it which gives it an acceleration g when
The newton it is falling freely near the Earth’s surface. If the
The unit of force is the newton. It will be defined object has mass m, then W can be calculated from
later (Topic 1.5); the definition is based on the change F = ma (Newton’s second law, see p. 39). We put
of speed a force can produce in a body. Weight is a F = W and a = g to give
force and therefore should be measured in newtons. W = mg
The weight of an object can be measured by
Taking g = 9.8 m/s2 and m = 1 kg, this gives W = 9.8 N,
hanging it on a spring balance marked in newtons
that is an object of mass 1 kg has weight 9.8 N, or
(Figure 1.3.2) and letting the pull of gravity stretch
near enough 10 N. Similarly, an object of mass 2 kg
the spring in the balance. The greater the pull, the
has weight of about 20 N, and so on.
more the spring stretches.
Gravitational field
0
The force of gravity acts through space and can
1
2
1 newton cause an object, not in contact with the Earth,
3
4
5
to fall to the ground. It is an invisible, action-at-
6
7
spring balance
a-distance force. We try to explain its existence
8
9
10
by saying that the Earth is surrounded by a
gravitational field which exerts a force on any
object in the field. Later, magnetic and electric
fields will be considered.
The gravitational field strength is defined as
the force acting per unit mass.
Rearranging the equation W = mg gives g = W m.
▲ Figure 1.3.2 The weight of an average-sized apple is
about 1 newton. Key definition
Gravitational field strength force per unit mass
On most of the Earth’s surface:
The weight of an object of mass 1 kg is 9.8 N.
Gravitational field strength is a vector and has
Often this is taken as 10 N. A mass of 2 kg has a both magnitude and direction.
weight of 20 N, and so on. The mass of an object is
26
Revision checklist
After studying Topic 1.3 you should know and After studying Topic 1.3 you should be able to:
understand the following: ✓ state the units of mass and weight and recall that
✓ what is meant by the mass of a body the weight of an object is the force of gravity on it
✓ the difference between mass and weight and that W
✓ recall and use the equation g =
weights (and masses) may be compared using a m
balance. ✓ describe and use the concept of weight as the
effect of a gravitational field on a mass.
27
Exam-style questions
1 a i Explain what is meant by the mass of an 2 a Define gravitational field strength. [2]
object. b On the Earth the acceleration of free fall is
ii Explain what is meant by the weight of about 9.8 m/s2. On Mars the acceleration of
an object. free fall is about 3.7 m/s2.
iii Describe how weights may be The weight of the Mars Rover Opportunity on
compared. [4] the Earth was 1850 N.
b State which of the following definitions for i Calculate the mass of the Rover. [2]
weight W is correct. ii Calculate the weight of the Rover
A W = g/mass on Mars. [2]
B W = mass/g [Total: 6]
C W = mass × g 3 a Explain what is meant by a gravitational
D W = force × g [1] field. [2]
c Which of the following properties is the same
for an object on the Earth and on the Moon? b State the effect of a gravitational field
A weight on a mass. [1]
B mass
C acceleration of free fall c Define gravitational field strength. [2]
D gravitational field strength [1] d The gravitational field strength on Venus
d State the SI units of is 8.8 N/kg. The mass of a rock is 200 kg.
i weight Calculate the weight of the rock on Venus. [2]
ii acceleration of free fall [Total: 7]
iii gravitational field strength. [3]
[Total: 9]
28
★ Use density data to determine whether one liquid will float on another liquid.
A pebble thrown into a pond will sink to the bottom of the pond, but a wooden object will float.
Objects of the same shape and size but made from different materials have different masses. In this
topic you will see how you can quantify such differences with the idea of density. Density specifies the
amount of mass in a unit volume. To measure the density of a material you will need to know both its
mass and its volume. The mass can be found using a balance, and the volume by measurement. If the
density of an object is greater than that of a liquid it will sink, but if the density of the object is less
than that of the liquid it will float.
In everyday language, lead is said to be heavier The approximate densities of some common
than wood. By this it is meant that a certain volume substances are given in Table 1.4.1.
of lead is heavier than the same volume of wood. ▼ Table 1.4.1 Densities of some common substances
In science such comparisons are made by using the
term density. This is the mass per unit volume of a Solids Density/g/cm3 Liquids Density/g/cm3
substance and is calculated from aluminium 2.7 paraffin 0.80
copper 8.9 petrol 0.80
density = mass
volume iron 7.9 pure water 1.0
For a mass m of volume V, the density ρ = m/V. gold 19.3 mercury 13.6
glass 2.5 Gases Density/kg/m3
Key definition wood (teak) 0.80 air 1.3
Density mass per unit volume ice 0.92 hydrogen 0.09
polythene 0.90 carbon dioxide 2.0
The density of lead is 11 grams per cubic centimetre
(11 g/cm3) and this means that a piece of lead of
volume 1 cm3 has mass 11 g. A volume of 5 cm3
of lead would have mass 55 g. If the density of a
Calculations
Using the symbols ρ (rho) for density, m for mass
substance is known, the mass of any volume of it
and V for volume, the expression for density is
can be calculated. This enables engineers to work
out the weight of a structure if they know from the ρ=m
plans the volumes of the materials to be used and V
their densities. Strong enough foundations can then Rearranging the expression gives
be made.
The SI unit of density is the kilogram per cubic m = V × ρ and V = m
ρ
metre. To convert a density from g/cm3, normally
the most suitable unit for the size of sample we These are useful if ρ is known and m or V have to be
use, to kg/m3, we multiply by 103. For example, the calculated. If you do not see how they are obtained
density of water is 1.0 g/cm3 or 1.0 × 103 kg/m3. refer to the Mathematics for physics section on p. 295.
29
measuring cylinder
m
ρV
2nd reading
▲ Figure 1.4.1
1st reading
Worked example
Taking the density of copper as 9 g/cm3, find a the mass of water
5 cm3 and b the volume of 63 g.
a ρ = 9 g/cm3, V = 5 cm3 and m is to be found.
m = V × ρ = 5 cm3 × 9 g/cm3 = 45 g solid
b ρ = 9 g/cm3, m = 63 g and V is to be found.
m 63g
∴V = = = 7 cm3
ρ 9 g/cm3
Now put this into practice ▲ Figure 1.4.2a Measuring the volume of an irregular solid:
1 A sheet of aluminium has a mass of 200 g and a volume method 1
of 73 cm3. Calculate the density of aluminium.
2 Taking the density of lead as 11 g/cm3, find water
a the mass of 4 cm3
b the volume of 55 g.
measurements
flowing before
solid inserted)
displacement
Use one of these methods to find the volume of
a pebble or glass stopper, for example. The mass
of the solid is found on a balance. Its volume is water
measured by one of the displacement methods
shown in Figure 1.4.2. In Figure 1.4.2a the volume
is the difference between the first and second
readings. In Figure 1.4.2b it is the volume of water ▲ Figure 1.4.2b Measuring the volume of an irregular solid:
collected in the measuring cylinder. method 2
30
31
Exam-style questions
1 a Choose which of the following definitions 3 a A block of wood has dimensions of
for density is correct. 10 cm × 8 cm × 20 cm.
A mass/volume i Calculate the volume of the block in
B mass × volume cubic metres. [2]
C volume/mass ii The block is placed on a balance and
D weight/area [1] found to weigh 1.2 kg. Calculate the
b Calculate density of the block in kg/m3. [3]
i the mass of 5 m3 of cement of density b When a golf ball is lowered into a
3000 kg/m3 [3] measuring cylinder of water, the water level
ii the mass of air in a room measuring rises by 30 cm3 when the ball is completely
10 m × 5.0 m × 2.0 m if the density of submerged. If the ball weighs 33 g in air,
air is 1.3 kg/m3. [3] calculate its density in kg/m3. [3]
[Total: 7] [Total: 8]
2 a Describe how you could determine the
density of a liquid. [4]
b An empty beaker is weighed and found to
have a mass of 130 g. A measuring cylinder
contains 50 cm3 of an unknown liquid.
All the liquid is poured into the beaker
which is again weighed and found to have
a mass of 170 g. Calculate the density of
the liquid. [4]
c Explain why ice floats on water. [1]
[Total: 10]
32
★ Define the spring constant and the limit of proportionality on a load–extension graph.
★ Apply the equation F = ma to calculate force and acceleration.
★ Describe motion in a circular path and understand the effect on force if speed, radius or mass change.
A gravitational force causes a freely falling object to accelerate and keeps a satellite moving in a
circular path. Clearly a force can change the speed or direction of travel of an object. A force can
also change the shape or size of an object. If you stand on an empty paper carton it will change its
shape and if you pull on a spiral spring it will stretch. Several forces may act on an object at once and
it is useful to calculate a resultant force to predict their combined effect; both the size and direction
of the forces are needed for this. Friction between a moving object and its surroundings is also
important as it acts to reduce the speed of the object and produce heat. You have already learnt how
to quantify some of these changes and in this topic you will encounter more ways to do so.
Force
A force is a push or a pull. It can cause an object A force can also change a body’s shape or size.
at rest to move, or if the body is already moving For example, a spring (or wire) will stretch when
it can change its speed or direction of motion. loaded with a weight.
▲ Figure 1.5.1 A weightlifter in action exerts first a pull and then a push.
33
Practical work
Safety steel
spring
l Eye protection must be worn (in case the
spring snaps).
Arrange a steel spring as in Figure 1.5.2.
Read the scale opposite the bottom of the hanger.
10
Add 100 g loads one at a time (thereby increasing
the stretching force by steps of 1 N) and take hanger
20
Stretching force/N Scale reading/mm Total extension/mm 1 What is the shape of the graph you plotted?
2 Do the results suggest any rule about how the
spring behaves when it is stretched?
Sometimes it is easier to discover laws by 3 What precautions could you take to improve
displaying the results on a graph. Do this on the accuracy of the results of this experiment?
graph paper by plotting total extension readings 4 How could you test if the extension of the
along the x-axis (horizontal axis) and stretching spring is proportional to the stretching force?
Key definition
Limit of proportionality the point at which the load-
extension graph becomes non-linear
O S
The graph of Figure 1.5.3 is for a spring stretched total extension/mm
34
Spring constant
The spring constant, k, is defined as force per
unit extension. It is the force which must be
applied to a spring to cause an extension of 1 m. Test yourself
If a force F produces extension x then 2 State two effects which a force may have on an
object.
k= F 3 Make a sketch of a load–extension graph for a
x
spring and indicate the region over which the
Rearranging the equation gives extension is proportional to the stretching force.
F = kx 4 Calculate the spring constant of a spring which
is stretched 4 cm by a mass of 200 g.
Key definition 5 Define the limit of proportionality for a
stretched spring.
Spring constant force per unit extension
1N 2N
1N
2N 3N
▲ Figure 1.5.5 The design of an offshore oil platform ▲ Figure 1.5.6 The resultant of forces acting in the same
requires an understanding of the combination of many straight line is found by addition or subtraction.
forces.
Practical work
36
Test yourself
6 Jo, Daniel and Helen are pulling a metal ring.
Jo pulls with a force of 100 N in one direction
and Daniel with a force of 140 N in the opposite
direction. If the ring does not move, what force does
Helen exert if she pulls in the same direction as Jo?
7 A boy drags a suitcase along the ground with a
force of 100 N. If the frictional force opposing the
motion of the suitcase is 50 N, what is the resultant
forward force on the suitcase?
8 A picture is supported by two vertical strings.
If the weight of the picture is 50 N, what is the
force exerted by each string?
9 Using a scale of 1 cm to represent 10 N, find ▲ Figure 1.5.8 Friction is much reduced for a hover scooter.
the size and direction of the resultant of forces
of 30 N and 40 N acting at right angles to each
other. Going further
Mass and inertia
Newton’s first law is another way of saying that all
Newton’s first law matter has a built-in opposition to being moved if it is
Friction and air resistance cause a car to come to at rest or, if it is moving, to having its motion changed.
This property of matter is called inertia (from the
rest when the engine is switched off. If these forces Latin word for laziness).
were absent, we believe that an object, once set in
Its effect is evident on the occupants of a car that
motion, would go on moving forever with a constant
stops suddenly: they lurch forwards in an attempt to
speed in a straight line. That is, force is not needed continue moving, and this is why seat belts are needed.
to keep a body moving with uniform velocity The reluctance of a stationary object to move can be
provided that no opposing forces act on it. shown by placing a large coin on a piece of card on
This idea was proposed by Galileo and is summed your finger (Figure 1.5.9). If the card is flicked sharply
up in Isaac Newton’s first law of motion: the coin stays where it is while the card flies off.
coin
An object stays at rest, or continues to move in a
straight line at constant speed, unless acted on by a
resultant force.
It seems that the question we should ask about a card
moving body is not what keeps it moving but what
changes or stops its motion.
The smaller the external forces opposing a
moving body, the smaller is the force needed to
keep it moving with constant velocity. A hover
scooter, which is supported by a cushion of air
(Figure 1.5.8), can skim across the ground with little
frictional opposition, so that relatively little power
is needed to maintain motion.
A resultant force may change the velocity of an ▲ Figure 1.5.9 Flick the card sharply
object by changing its direction of motion or speed. The larger the mass of a body, the greater is its inertia,
i.e. the more difficult it is to move it when at rest and to
Key definitions stop it when in motion. Because of this we consider that
the mass of a body measures its inertia. This is a better
Resultant force may change the velocity of an object by definition of mass than the one given earlier (Topic 1.3) in
changing its direction of motion or its speed which it was stated to be the amount of matter in a body.
37
Practical work
Effect of force and mass on acceleration Repeat using first two and then three identical
For safe experiments/demonstrations related pieces of elastic, stretched side by side by the
to this topic, please refer to the Cambridge same amount, to give two and three units of
IGCSE Physics Practical Skills Workbook that is force.
also part of this series. If you are using tickertape, make a tape chart
for each force and use it to find the acceleration
Safety produced in cm/ten-tick2. Ignore the start of the
l Take care when rolling the trolley down the tape (where the dots are too close) and the end
ramp. Ensure it is clear at the bottom of (where the force may not be steady). If you use a
the ramp and use a side barrier to prevent motion sensor and computer to plot a speed–time
the trolley from falling onto the floor. graph, the acceleration can be obtained in m/s2
The apparatus consists of a trolley to which a from the slope of the graph (Topic 1.2).
force is applied by a stretched length of elastic Put the results in a table.
(Figure 1.5.10). The velocity of the trolley is
found from a tickertape timer or a motion sensor, Force (F)/(no. of pieces of elastic) 1 2 3
datalogger and computer. Acceleration (a)/cm/ten-tick2 or m/s2
First compensate the runway for friction: raise
one end until the trolley runs down with constant (b) Mass and acceleration (force constant)
velocity when given a push. The dots on the Do the experiment as in part (a) using two
tickertape should be equally spaced, or a pieces of elastic (i.e. constant F ) to accelerate
horizontal trace obtained on a speed–time graph. first one trolley, then two (stacked one above
There is now no resultant force on the trolley and the other) and finally three. Check the friction
any acceleration produced later will be due only compensation of the runway each time.
to the force caused by the stretched elastic. Find the accelerations from the tape charts or
computer plots and tabulate the results.
tickertape timer trolley stretched elastic
(or motion sensor)
Mass (m)/(no. of trolleys) 1 2 3
Acceleration (a)/cm/ten-tick2 or m/s2
38
▲ Figure 1.5.12
39
Going further
Newton’s third law
If a body A exerts a force on body B, then body B exerts Note that the pair of equal and opposite forces do not act
an equal but opposite force on body A. on the same body; if they did, there could never be any
resultant forces and acceleration would be impossible.
This is Newton’s third law of motion and states that
For a book resting on a table, the book exerts a
forces never occur singly but always in pairs as a
downward force on the table and the table exerts an
result of the action between two bodies. For example,
equal and opposite upward force on the book; this pair
when you step forwards from rest your foot pushes
of forces act on different objects and are represented by
backwards on the Earth, and the Earth exerts an equal
the red arrows in Figure 1.5.14. The weight of the book
and opposite force forward on you. Two bodies and two
(blue arrow) does not form a pair with the upward force
forces are involved. The small force you exert on the
on the book (although they are equal numerically) as
large mass of the Earth gives no noticeable acceleration
these two forces act on the same body.
to the Earth but the equal force it exerts on your very
much smaller mass causes you to accelerate.
40
push of table
contact on book
force pair pull of Earth
push of book
on book
on table
gravitational
force pair
pull of book
on Earth
NE
WT
O N I II
▲ Figure 1.5.17
41
Satellites
For a satellite of mass m orbiting the Earth at
radius r with orbital speed v, the centripetal force,
F, is the Earth’s gravitational force on the mass.
To put an artificial satellite in orbit at a certain
height above the Earth it must enter the orbit
at the correct speed. If it does not, the force of
gravity, which decreases as height above the Earth
increases, will not be equal to the centripetal force
needed for the orbit.
42
Test yourself
14 a Explain the conditions under which friction
16 An apple is whirled round in a horizontal circle on
occurs.
the end of a string which is tied to the stalk. It is
b Name two effects resulting from solid friction.
whirled faster and faster and at a certain speed
15 A car is moving at a constant speed along a straight
the apple is torn from the stalk. Explain why this
road. Describe how the forces acting on the car
happens.
influence the speed of the car. How is a constant
17 Is the gravitational force on a satellite greater or
speed achieved?
less when it is in a high orbit than when it is in a
low orbit?
★ Apply the principle of moments to situations involving more than two forces about a pivot.
★ Be familiar with an experiment showing that an object in equilibrium has no resultant moment.
A seesaw in a children’s playground can be balanced if the two children have similar weights or if
the lighter child sits further from the pivot than the heavier child. Each child exerts a turning effect
on the seesaw, either clockwise or anticlockwise, which depends not only on their weight but also on
their distance from the pivot. Forces act in different ways depending on their orientation. In this topic
you will discover that the turning effect of a force (its moment) depends on both its magnitude and
the perpendicular distance from the pivot point. This means that a small force at a large distance can
balance a much larger force applied closer to the pivot. When the combination of all the forces acting
on a body is such that there is no net force or turning effect, the body is in equilibrium (the seesaw is
level) and will not move unless additional forces are applied.
43
a
Balancing a beam
3m
To balance a beam about a pivot, like the ruler
hinge (fulcrum)
O in Figure 1.5.20, the weights must be moved
so that the clockwise turning effect equals the
gate
anticlockwise turning effect and the net moment on
F 5N the beam becomes zero. If the beam tends to swing
clockwise, m1 can be moved further from the pivot
b
to increase its turning effect; alternatively, m2 can
be moved nearer to the pivot to reduce its turning
O
1.5 m 1.5 m effect. What adjustment would you make to the
position of m2 to balance the beam if it is tending
F 5 N
to swing anticlockwise?
▲ Figure 1.5.19
Practical work
▲ Figure 1.5.20
F1 is trying to turn the ruler anticlockwise and 12 Name the variables you will need to measure
F1 × d1 is its moment. F2 is trying to cause in this experiment.
clockwise turning and its moment is F2 × d2. 13 Calculate the moments of a force of 5 N acting
When the ruler is balanced or, as we say, at a perpendicular distance from the pivot of
in equilibrium, the results should show that a 10 cm
the anticlockwise moment F1 × d1 equals the b 15 cm
clockwise moment F2 × d2. c 30 cm.
44
Test yourself
18 A seesaw has a weight of 40 N placed 1 m from the
pivot and a weight of 20 N is placed on the opposite
side of the pivot at a distance of 2 m from the pivot. fulcrum
load
Is the seesaw balanced?
19 A half-metre ruler is pivoted at its mid-point and
balances when a weight of 20 N is placed at the ▲ Figure 1.5.23a Wheelbarrow
10 cm mark and a weight W is placed at the 45 cm
mark on the ruler. Calculate the weight W.
45
▲ Figure 1.5.24
effort Moments can be taken about any point but if we
take them about C, the moment due to force Q is
zero.
load clockwise moment = P × 5 m
anticlockwise moment =
400 N × 2 m
= 800 N m
▲ Figure 1.5.23c Scissors
Since the plank is in equilibrium we have from (ii)
fulcrum
above
P × 5 m = 800 N m
800 Nm
∴ P = = 160 N
effort 5m
From equation (1)
load
Q = 240 N
▲ Figure 1.5.23d Spanner
Equilibrium experiment
When the concept of moments was introduced,
Conditions for equilibrium we described an experiment to balance a beam
Sometimes a number of parallel forces act on an (see Practical work, p. 44). In this experiment
object so that it is in equilibrium. We can then say: different weights (F) are suspended either
(i) The sum of the forces in one direction equals the side of the central pivot and the distance (d)
sum of the forces in the opposite direction. of each from the pivot is measured when the
(ii) The law of moments must apply. beam is balanced (in equilibrium). The clockwise
When there is no resultant force and no resultant and anticlockwise moments (F × d) are then
moment, an object is in equilibrium. calculated for each weight. It is found that when
the beam is in equilibrium, the clockwise and
Key definition anticlockwise moments are equal in magnitude
Equilibrium when there is no resultant force and no and there is no resultant moment (i.e. no net
resultant moment turning effect) on the beam.
46
Test yourself
20 The metre ruler in Figure 1.5.25 is pivoted at
22 The beam shown in Figure 1.5.26 is balanced with
its centre. If it balances, which of the following
weights of 160 N, 120 N and W in the positions
equations gives the mass of M?
shown. Calculate the value of W.
A M + 50 = 40 + 100
B M × 40 = 100 × 50 3m 3m
C M × 50 = 100 × 40 A B O C
D M/50 = 40/100
1m pivot
50 cm 40 cm
160 N 120 N W
Why are tall vehicles more likely to topple over on a slope than less tall ones? The answer lies in
the position of the centre of gravity. In the presence of gravity an object behaves as if its entire
mass is concentrated at a single point, the centre of gravity. The object’s weight appears to act at
this point. For a symmetrical object, such as a ball, the centre of gravity will be at its centre. In this
topic, you will learn that when an object is suspended so that it can swing freely, it comes to rest with
its centre of gravity vertically below the point of suspension. This enables the centre of gravity of
unsymmetrical objects to be located. You will discover that it is the position of the centre of gravity
that controls stability against toppling. If the centre of gravity remains within the footprint of the
base of the object, it remains stable.
Centre of gravity any other point it topples because the moment of its
weight W about the point of support is not zero, as
An object behaves as if its whole mass were in Figure 1.5.27b. The centre of gravity is sometimes
concentrated at one point, called its centre of also termed the centre of mass.
gravity even though the Earth attracts every part of
it. The object’s weight can be considered to act at
Key definition
this point. The centre of gravity of a uniform ruler
Centre of gravity the point through which all of an
is at its centre and when supported there it can be
object’s weight can be considered to act
balanced, as in Figure 1.5.27a. If it is supported at
47
Practical work
Centre of gravity of an irregularly shaped of gravity lies on CD and must be at the point
lamina of intersection of AB and CD. Check this by
For safe experiments/demonstrations related hanging the lamina from a third hole. Also try
to this topic, please refer to the Cambridge balancing it at its centre of gravity on the tip of
IGCSE Physics Practical Skills Workbook that your forefinger.
is also part of this series. A
hole nail clamped
Suppose we have to find the centre of gravity in stand
C
of an irregularly shaped lamina (a thin sheet) of lamina
centre of gravity
cardboard.
D B
Make a hole A in the lamina and hang it so that
it can swing freely on a nail clamped in a stand. plumb line
It will come to rest with its centre of gravity
vertically below A. To locate the vertical line ▲ Figure 1.5.30
through A, tie a plumb line (a thread and a
weight) to the nail (Figure 1.5.30), and mark its 14 a How could you make a plumb line?
position AB on the lamina. The centre of gravity b Explain the purpose and use of a plumb
lies somewhere on AB. line.
15 When an object is suspended and allowed to
Hang the lamina from another position, C, and swing freely, where does its centre of gravity
mark the plumb line position CD. The centre lie when it comes to rest?
48
centre of
mass
base
▲ Figure 1.5.31
49
centre weight
of mass
card cork
b centre of mass
thick
point of wire
contact
matchsticks
weight
iron nut
bar
c
▲ Figure 1.5.34 Balancing tricks
50
Test yourself
24 Where does the centre of gravity lie for
a a uniform ruler
b a sphere of uniform density? A B C
25 a When does an object topple?
b How can the stability of an object be increased?
26 Figure 1.5.36 shows a Bunsen burner in three
different positions. State the type of equilibrium
when it is in position ▲ Figure 1.5.36
i A
ii B
iii C
Revision checklist
After studying Topic 1.5 you should know and ✓ combine forces acting along the same straight line
understand: to find their resultant
✓ the significance of the term limit of ✓ recall the equation F = ma and use it to solve
proportionality problems
✓ describe qualitatively motion in a circular path
✓ Newton’s first law of motion due to a perpendicular force and recall that
✓ friction as the force between two surfaces that the force required to maintain circular motion
impedes motion and results in heating and that changes when the speed, radius of orbit or
friction also acts on an object moving through mass changes
the air
✓ the conditions for equilibrium ✓ define the moment of a force about a pivot and give
✓ that an object’s weight acts through the centre of everyday examples; recall the law of moments and
gravity. use it to solve problems, including the balancing of
a beam
After studying Topic 1.5 you should be able to:
✓ recall that a force can cause a change in the ✓ apply the principle of moments to balance
motion, size or shape of a body multiple moments (more than two) about a pivot
✓ describe an experiment to study the relation ✓ describe an experiment to verify that there is no
between force and extension for springs; plot and resultant moment on an object in equilibrium
draw conclusions from load–extension graphs
✓ recall that an object behaves as if its whole mass
✓ define the spring constant and use the equation
acts through its centre of gravity
k = F/x to solve problems ✓ describe an experiment to find the centre of gravity
of an object and connect the stability of an object
to the position of its centre of gravity.
51
Exam-style questions
1 a Describe how you would investigate the 3 Two forces of 5 N and 12 N act at a point.
variation of the extension of a spring when a The two forces first act in opposite directions.
different loads are applied. Mention two i Make a sketch showing the direction
precautions you would take to obtain of the forces. [2]
accurate results. [6] ii Calculate the resultant of the forces
b The table below shows the results obtained and mark its direction on your sketch. [2]
in an experiment to study the stretching
of a spring. Copy the table and fill in the b The two forces then act at 90° to each other.
missing values. What can you say about the Calculate the magnitude and direction of the
relationship between the extension of the resultant force by calculation. [6]
spring and the stretching force? [4]
[Total: 10]
Stretching Scale Extension/
Mass/g force/N reading/mm mm
4 Starting from rest on a level road a girl can
0 20.0 0 reach a speed of 5 m/s in 10 s on her bicycle.
100 20.2 a Find the acceleration. [2]
b Find the average speed during the 10 s. [2]
200 20.4
c Find the distance she travels in 10 s. [2]
300 20.6 d Eventually, even though she still pedals as
400 20.8
fast as she can, she stops accelerating and
her speed reaches a maximum value.
500 21.0 Explain in terms of the forces acting why
this happens. [2]
[Total: 10]
[Total: 8]
2 The spring in Figure 1.5.37 stretches from 5 Explain the following using F = ma.
10 cm to 22 cm when a force of 4 N is applied. a A racing car has a powerful engine and is
a Calculate the spring constant of the made of strong but lightweight material.[3]
spring. [3] b A car with a small engine can still
b If the extension is proportional to the accelerate rapidly. [3]
stretching force when a force of [Total: 6]
6 N is applied, calculate
i the new extension length of the 6 A rocket has a mass of 500 kg.
spring [2] a Write down the weight of the rocket
ii the final length in cm of the spring. [1] on Earth where g = 9.8 N/kg. [1]
[Total: 6] b At lift-off the rocket engine exerts an
upward force of 25 000 N.
i Calculate the resultant force on the
rocket. [2]
10 cm
22 cm ii Calculate the initial acceleration of
the rocket. [3]
[Total: 6]
4N
▲ Figure 1.5.37
52
force
chain
crank
A B
▲ Figure 1.5.38
53
Alternative to Practical
12 A physics class is asked to investigate the 14 In an experiment to investigate the law of
extension of a stretched spring. moments, a half-metre ruler is balanced at its
You will be supplied with a spring, a clamp stand, centre as shown in Figure 1.5.40.
a half-metre ruler, a set square and a hanger with
d1 d2
100 g weights and sticky tape.
a Describe how you would carry out the
experiment. [5]
b Mention any precautions you would take to
fulcrum (nail through
achieve good results. [3] m1 hole in ruler) m2
[Total: 8]
▲ Figure 1.5.40
13 a The table below shows the extension of a
Masses of 50 g, 100 g and 150 g are placed in turn
spring for increasing stretching forces.
at the positions given in the table below.
Stretching force/N 0 1 2 3 4 5 a Complete the table, filling in values for
Extension/mm 0 2 4 6 8.5 12 i the units at the head of each column [1]
ii force (F) [2]
i Plot a graph with extension/mm along iii distance from pivot (d) [2]
the x-axis and stretching force/N on iv moment about pivot (F × d). [2]
the y-axis. [4] b State which combinations of two different
ii Draw the best line through the points; masses could be used to balance the beam. [3]
mark the region over which
proportionality holds. [2] Mass/g Force/ Ruler reading/cm d/ F × d/
50 5 A
iii Indicate the limit of proportionality. [1] 50 10 B
b Calculate the gradient of the graph. [2]
50 15 C
c Determine the spring constant k. [1]
50 20 D
[Total: 10] 100 30 E
100 35 F
100 40 G
150 20 H
150 35 I
[Total: 10]
54
FOCUS POINTS
★ Define momentum, impulse and resultant force and use the correct equations to calculate them.
★ Solve simple one-dimensional problems using the principle of the conservation of momentum.
When a tennis ball is struck by a racket or a gas molecule rebounds from the side of its container,
their behaviour can be understood by introducing the concept of momentum. Momentum is defined
as the product of mass and velocity. In a collision, momentum is conserved unless there are
external forces acting such as friction. You can demonstrate conservation of momentum with a
Newton’s cradle (Figure 1.7.10, p. 66); the last ball in the line moves off with the same velocity as
the first. Collisions generally occur over a very short interval of time; the shorter the time interval
the greater the force on the bodies involved in the collision. Crumple zones at the front and rear of
a car help to prolong the collision time and reduce the force of an impact.
Momentum is a useful quantity to consider when A 2 kg mass moving at 10 m/s has momentum
bodies are involved in collisions and explosions. 20 kg m/s, the same as the momentum of a 5 kg
It is defined as the mass of the body multiplied by mass moving at 4 m/s.
its velocity and is measured in kilogram metre per
second (kg m/s) or newton second (N s). Key definition
momentum = mass × velocity Momentum mass × velocity
Practical work
Collisions and momentum will record the time taken for the passage of a
trolley.
Safety trolley with
‘interrupt card’
l Take care when rolling the trolley down the photogate 2
photogate 1
ramp. Ensure it is clear at the bottom of the
ramp and use a side barrier to prevent the sloping to timer
runway
trolley from falling onto the floor.
Figure 1.6.1 shows an arrangement which can
be used to find the velocity of a trolley before
and after a collision. If a trolley of length l takes
time t to pass through a photogate, then its
velocity = distance/time = l/t. ▲ Figure 1.6.1
Two photogates are needed, placed each side A tickertape timer or motion sensor, placed at
of the collision point, to find the velocities before the top end of the runway, could be used instead
and after the collision. Set them up so that they of the photogates if preferred.
55
Conservation of momentum
When two or more bodies act on one another, as in a This statement is called the principle of
collision, the total momentum of the bodies remains conservation of momentum. Experiments like
constant, provided no external forces act (e.g. those in the Practical work section show that it is
friction). true for all types of collisions.
Worked example
Suppose a truck of mass 60 kg moving with velocity 3 m/s a b
3 m /s v
collides and couples with a stationary truck of mass 30 kg at rest
(Figure 1.6.2a). The two move off together with the same
60 kg 30 kg 60 kg 30 kg
velocity v which we can find as follows (Figure 1.6.2b).
Total momentum before collision is
▲ Figure 1.6.2
(60 kg × 3 m/s) + (30 kg × 0 m/s) = 180 kg m/s
Total momentum after collision is
Now put this into practice
1 A trolley of mass 3 kg moving with velocity 5 m/s collides
(60 kg + 30 kg) × v = 90 kg × v and couples with a stationary trolley of mass 2 kg and the
Since momentum is not lost two move off together with the same velocity v. Assuming
momentum is not lost in the collision, calculate the value of v.
90 kg × v = 180 kg m/s or v = 2 m/s 2 A trolley of mass 5 kg moving with velocity 5 m/s collides
with a stationary trolley of mass 2 kg.
The 5 kg trolley stops and the 2 kg trolley moves off
with velocity v. Assuming momentum is not lost in the
collision, calculate the value of v.
56
57
Test yourself
5 A force of 5 N is applied to a cricket ball for
0.02 s. Calculate
a the impulse on the ball
b the change in momentum of the ball.
6 In a collision, a car of mass 1000 kg travelling at
24 m/s comes to rest in 1.2 s.
▲ Figure 1.6.4a This cricketer is ‘following through’ after Calculate
hitting the ball. a the change in momentum of the car
b the steady stopping force applied to the car.
58
Revision checklist
After studying Topic 1.6 you should know and After studying Topic 1.6 you should be able to:
understand the following: ✔ define momentum and apply the principle of
✔ the relationship between force and rate of change conservation of momentum to solve problems
of momentum and use it to solve problems. ✔ recall that in a collision, impulse = FΔt and use the
definition to explain how the time of impact affects
the force acting in a collision.
Exam-style questions
1 A truck A of mass 500 kg moving at 4 m/s collides 3 A rocket of mass 10 000 kg uses 5.0 kg of fuel
with another truck B of mass 1500 kg moving in and oxygen to produce exhaust gases ejected
the same direction at 2 m/s. at 5000 m/s.
a Write down an expression for momentum. [1] a Define momentum. [1]
b Calculate the momentum of truck A before b Calculate the backward momentum of
the collision. [2] the ejected gas. [2]
c Calculate the momentum of truck B before c Explain what is meant by the principle of
the collision. [2] conservation of momentum. [2]
d Determine the common velocity of the trucks d Calculate the increase in velocity of
after the collision. [4] the rocket. [3]
[Total: 9] [Total: 8]
2 The velocity of an object of mass 10 kg increases 4 A boy hits a stationary billiard ball of mass 30 g
from 4 m/s to 8 m/s when a force acts on it for head on with a cue. The cue is in contact with
2 s. Write down the the ball for a time of 0.001 s and exerts a force
a initial momentum of the object [2] of 50 N on it.
b final momentum of the object [2] a Calculate the acceleration of the ball during
c momentum gained in 2 s [2] the time it is in contact with the cue. [2]
d value of the force [2] b Work out the impulse on the ball in the
e impulse of the force. [2] direction of the force. [2]
[Total: 10] c Calculate the velocity of the ball just after
it is struck. [2]
d Give two ways by which the velocity of the
ball could be increased. [2]
[Total: 8]
59
★ Use the correct equations for kinetic energy and change in gravitational potential energy.
★ Apply the principle of the conservation of energy to simple examples and use it to interpret flow diagrams.
★ Apply the principle of the conservation of energy to complex examples represented by Sankey diagrams.
Energy is a theme that appears in all branches of science. It links a wide range of phenomena and
enables us to explain them. There are different ways in which energy can be stored and, when
something happens, it is likely to be due to energy being transferred from one store to another.
Energy transfer is needed to enable people, computers, machines and other devices to work and to
enable processes and changes to occur. For example, in Figure 1.7.1, the water skier can be pulled
along by the boat only if energy is transferred from the burning petrol to its rotating propeller.
Although energy can be transferred to different stores, the total energy of a system remains
constant. In this topic you will learn in detail about the potential energy associated with the position
of an object in a gravitational field and the kinetic energy which is associated with its motion.
60
Electrostatic energy
weight
Energy can be stored by charged objects (see Topic (500 g)
4.2.1) as electrostatic energy. This energy can be
▲ Figure 1.7.2 Demonstrating energy transfers
transferred by an electric current.
Nuclear energy Other examples
The energy stored in the nucleus of an atom is known In addition to electrical working, mechanical
as nuclear energy. It can be transferred to other working, electromagnetic waves and heating, energy
energy stores in nuclear reactions such as fission and can be transferred between stores by other types of
fusion (Topic 5.1.2). waves, such as sound waves. Sound waves transfer
energy from a vibrating source to our eardrums or
61
to a microphone. Heating water in a boiler transfers Some energy transfers are shown in Figures 1.7.3a to d:
chemical energy stored in a fuel to internal energy a Potential energy is transferred to kinetic energy by
stored in the water. mechanical working (action of a gravitational force).
In summary, energy can be transferred between b Thermal energy stored in an electric fire element
stores in the following ways: is transferred by electromagnetic waves and by
• mechanical working – by the action of a force heating to the environment.
(Topic 1.5) c Chemical energy (stored in muscles in the arm)
• electrical working – by an electric current (Topic 4.2.2) is transferred to elastic energy in the bow by
• waves – electromagnetic, sound and other waves mechanical working.
(Topic 3.3) d Gravitational potential energy stored in the water
• heating – by conduction, convection or radiation in the upper reservoir is transferred to the kinetic
(Topic 2.3). energy of a turbine by mechanical working.
a c
b d
63
Calculate the kinetic energy of a football of mass 0.4 kg Transfer of gravitational potential energy to
(400 g) moving with a speed of 20 m/s.
1
kinetic energy
Ek = mv2
2 Safety
1 ● Place something soft on the floor to absorb
= × 0.4 kg × (20 m/s)2
2 the impact of the masses.
= 0.2 × 400 kg m 2/s2 ● Take care to keep feet well away from the
= 80 N m = 80 J falling masses.
Friction-compensate a runway by raising the
Now put this into practice start point slightly so that the trolley maintains
1 Calculate the kinetic energy of a ball of mass 0.4 kg a constant speed on the slope when no weight
moving with a speed of 80 m/s.
2 Calculate the kinetic energy of a ball of mass 50 g
is attached. Arrange the apparatus as in Figure
moving with a speed of 40 m/s. 1.7.7 with the bottom of the 0.1 kg (100 g) mass
0.5 m from the floor.
Start the timer and release the trolley. It will
Potential energy (Ep) accelerate until the falling mass reaches the
Potential energy is the energy an object has floor; after that it moves with constant velocity v.
because of its position or condition. to tickertape
trolley
friction-compensated
timer (or runway
An object above the Earth’s surface is motion sensor) thread pulley
considered to have gained an amount of
gravitational potential energy equal to the work
that has been done against gravity by the force
used to raise it. To lift an object of mass m
through a vertical height Δh at a place where the
Earth’s gravitational field strength is g needs a
force equal and opposite to the weight mg of the 100 g
body. Hence
0.5 m
work done by force =
force × vertical height
= mg × Δh floor
64
Ep Ep
Ep Ek Ep Ek
Ek
65
Going further
Elastic and inelastic collisions it is longer when the road is wet or icy, when friction
between the tyres and the road is low, than when
In all collisions (where no external force acts) some
conditions are dry. Efficient brakes and deep tyre tread
kinetic energy is usually transferred to thermal energy
help to reduce the braking distance.
and, to a small extent, to sound. The greater the
proportion of kinetic energy transferred, the less elastic Car design and safety
is the collision, i.e. the more inelastic it is. In a perfectly
When a car stops rapidly in a collision, large forces
elastic collision, kinetic energy is conserved.
are produced on the car and its passengers, and their
kinetic energy has to be dissipated.
Crumple zones at the front and rear collapse in such
a way that the kinetic energy is absorbed gradually
(Figure 1.7.11). As we saw in Topic 1.6, this extends the
collision time and reduces the decelerating force and
hence the potential for injury to the passengers.
Braking distance/metres 6 24 54 96 All these are secondary safety devices which aid survival
in the event of an accident. Primary safety factors
Total stopping distance/metres 12 36 72 120 help to prevent accidents and depend on the car’s
roadholding, brakes, steering, handling and above all on
Thinking distance depends on the driver’s reaction the driver since most accidents are due to driver error.
time – this will vary with factors such as the driver’s
degree of tiredness, use of alcohol or drugs, eyesight The chance of being killed in an accident is about five
and the visibility of the hazard. Braking distance varies times less if seat belts are worn and head restraints are
with both the road conditions and the state of the car; installed.
66
Test yourself
1 Name the way by which energy is transferred in the
3 Calculate the kinetic energy of a
following processes
a 1 kg trolley travelling at 2 m/s
a a battery is used to light a lamp
b 2 g (0.002 kg) bullet travelling at 400 m/s
b a ball is thrown upwards
c 500 kg car travelling at 72 km/h.
c water is heated in a boiler.
4 a What is the velocity of an object of mass 1 kg
2 State how energy is stored in the following
which has 200 J of kinetic energy?
a fossil fuels
b Calculate the potential energy of a 5 kg mass
b hot water
when it is i 3 m and ii 6 m, above the ground.
c a rotating turbine
(g = 9.8 N/kg)
d a stretched spring.
5 It is estimated that 7 × 106 kg of water pours over
the Niagara Falls every second.
If the falls are 50 m high, and if all the energy of
the falling water could be harnessed, what power
would be available? (g = 9.8 N/kg)
1.7.2 Work
FOCUS POINTS
★ Understand that when mechanical or electrical work is done, energy is transferred.
★ Use the correct equation to calculate mechanical work.
In science the word work has a different meaning from its everyday use. Here work is associated
with the motion of a force. When you lift and move a heavy box upstairs you will have done work in
either sense! In the absence of heat being generated, the work done is a measure of the amount of
energy transferred. When moving the heavy box, chemical energy from your muscles is transferred
to gravitational potential energy. If an electric motor is used to move the box, an equal amount of
electrical work will be done. In this topic you will learn how to calculate the mechanical work done in
different situations.
67
▲ Figure 1.7.12b
Test yourself
50 N 6 How much work is done when a mass of 3 kg
(g = 9.8 N/kg) is lifted vertically through 6 m?
3m
7 A hiker climbs a hill 300 m high. If she has a mass
of 51 kg, calculate the work she does in lifting her
body to the top of the hill.
▲ Figure 1.7.12a 8 An electric motor does 80 J of work in lifting
a box vertically upwards through 5 m.
Calculate the weight of the box.
★ Know that energy is released by nuclear fusion in the Sun and that research is being carried out into
how energy released from nuclear fusion could produce large-scale electrical energy.
★ Define efficiency and use the correct equations to calculate it.
Energy is needed to heat buildings, to make cars move, to provide artificial light, to make computers
work, and so on. The list is endless. This useful energy needs to be produced in controllable energy
transfers. For example, in power stations a supply of useful energy is transferred by electric
currents to different energy stores required by electricity customers. The raw materials for energy
production are energy sources. These may be non-renewable or renewable.
In this topic you will learn that, apart from nuclear, geothermal, hydroelectric or tidal energy,
energy released by nuclear fusion in the Sun (Topic 5.1) is the source for all our energy resources.
Although energy cannot be destroyed, as you learnt in the previous section, it can be transferred
into non-useful stores, such as internal energy. The efficiency of a device measures the useful
energy as a percentage of the total energy supplied.
68
69
70
Geothermal energy
If cold water is pumped down a shaft into hot
rocks below the Earth’s surface, it may be forced up
another shaft as steam. This can be used to drive a
turbine and generate electricity or to heat buildings.
The geothermal energy that heats the rocks is
constantly being released by radioactive elements
deep in the Earth as they decay (Topic 5.2).
Geothermal power stations are in operation in the
USA, New Zealand and Iceland. A disadvantage is
that they can only be built in very specific locations
where the underlying rocks are hot enough for the ▲ Figure 1.7.18 Methane generator in India
process to be viable.
Biofuels (vegetable fuels) The Sun as an energy source
Biomass includes cultivated crops (e.g. oilseed rape), The Sun is the main source of energy for many
crop residues (e.g. cereal straw), natural vegetation of the energy sources described above. The
(e.g. gorse), trees grown for their wood (e.g. spruce), exceptions are geothermal, nuclear and tidal
animal dung and sewage. Chemical energy can sources. Fossil fuels such as oil, coal and gas
be stored in biofuels such as alcohol (ethanol) are derived from plants which grew millions of
and methane gas can be obtained from them by years ago in biological processes requiring light
fermentation using enzymes or by decomposition from the Sun. Sunlight is also needed by the
by bacterial action in the absence of air. Liquid plants used in biomass energy production today.
biofuels can replace petrol (Figure 1.7.17); although Energy from the Sun drives the weather systems
they have up to 50% less energy per litre, they which enable wind and hydroelectric power to be
are lead- and sulfur-free and so do not pollute the harnessed. Solar energy is used directly in solar
atmosphere with lead or sulfur dioxide when they cells for electricity generation.
are burned. Biogas is a mix of methane and carbon The source of the Sun’s energy is nuclear
dioxide with an energy content about two-thirds fusion in the Sun. You will learn more about the
that of natural gas. It is produced from animal and fusion process which produces large amounts of
human waste in digesters (Figure 1.7.18) and used for energy in Topic 5.1. At present it is not possible
heating and cooking. Biogas is cheap to produce on to reproduce the fusion process on Earth for the
a small scale but not economically viable for large- large-scale production of electricity but much
scale production. It reduces landfills but due to its research is being directed towards that goal.
methane content it is unstable and may explode.
71
Power stations are not released into the atmosphere but used to
produce steam in a boiler. The steam is then used
The processes involved in the production of to generate more electricity from a steam turbine
electricity at power stations depend on the energy driving another generator. The efficiency is claimed
source being used. to be over 50% without any extra fuel consumption.
Non-renewable sources Furthermore, the gas turbines have a near 100%
Fossil fuels and nuclear fuels are used in thermal combustion efficiency, so very little harmful exhaust
power stations to provide thermal energy that turns gas (i.e. unburnt methane) is produced, and natural
water into steam. The steam drives turbines which in gas is almost sulfur-free, so the environmental
turn drive the generators that produce electricity as pollution caused is much less than for coal.
described in Topic 4.5. If fossil fuels are the energy Renewable sources
source (usually coal but natural gas is favoured in new In most cases the renewable energy source is used
stations), the steam is obtained from a boiler. If nuclear to drive turbines directly, as explained earlier in
fuel is used, such as uranium or plutonium, the steam is the cases of hydroelectric, wind, wave, tidal and
produced in a heat exchanger as explained in Topic 5.1. geothermal schemes.
The action of a steam turbine resembles that of The efficiency of a large installation can be as
a water wheel but moving steam, not moving water, high as 85–90% since many of the causes of loss in
causes the motion. Steam enters the turbine and is thermal power stations (e.g. water-cooling towers)
directed by the stator or diaphragm (sets of fixed are absent. In some cases, the generating costs are
blades) onto the rotor (sets of blades on a shaft that half those of thermal stations.
can rotate) (Figure 1.7.19). The rotor revolves and A feature of some hydroelectric stations is pumped
drives the electrical generator. The steam expands storage. Electricity cannot be stored on a large scale
as it passes through the turbine and the size of the but must be used as it is generated. The demand
blades increases along the turbine to allow for this. varies with the time of day and the season (Figure
1.7.20), so in a pumped-storage system electricity
generated at off-peak periods is used to pump water
back up from a low-level reservoir to a higher-level
one. It is easier to do this than to reduce the output
of the generator. At peak times the potential energy of
the water in the high-level reservoir is converted back
into electricity; three-quarters of the electricity that
was used to pump the water is generated.
5
winter
4
demand/W 1010
In gas-fired power stations, natural gas is burnt 0 4h 8h 12h 16h 20h 24h
in a gas turbine linked directly to an electricity time of day
generator. The hot exhaust gases from the turbine ▲ Figure 1.7.20 Variation in power demand
72
Economic, environmental and varies. Natural gas power stations have a short
start-up time, while coal and then oil power stations
social issues take successively longer to start up; nuclear power
When considering the large-scale generation of stations take longest. They are all reliable in that
electricity, the economic and environmental costs they can produce electricity at any time of day
of using various energy sources have to be weighed and in any season of the year as long as fuel is
against the benefits that electricity brings to available. Hydroelectric power stations are also very
society as a clean, convenient and fairly cheap reliable and have a very short start-up time, which
energy supply. means they can be switched on when the demand
Environmental problems such as polluting for electricity peaks. The electricity output of a
emissions that arise with different energy sources tidal power station, although predictable, is not as
were outlined when each was discussed previously. reliable because it depends on the height of the tide
Apart from people using less energy, how far which varies over daily, monthly and seasonal time
pollution can be reduced by, for example, installing scales. The wind and the Sun are even less reliable
desulfurisation processes in coal-fired power sources of energy since the output of a wind turbine
stations, is often a matter of cost. changes with the strength of the wind and that of
Although there are no fuel costs associated a solar cell with the intensity of light falling on it;
with electricity generation from renewable energy the output may not be able to match the demand for
sources such as wind power, the energy is so dilute electricity at a particular time.
that the capital costs of setting up the generating Renewable sources are still only being used
installation are high. Similarly, although fuel costs on a small scale globally. The contribution of the
for nuclear power stations are relatively low, the main energy sources to the world’s total energy
costs of building the stations and of dismantling consumption at present is given in Table 1.7.2.
them at the end of their useful lives is higher than (The use of biofuels is not well documented.)
for gas- or coal-fired stations. The great dependence on fossil fuels worldwide is
It has been estimated that currently it costs evident. It is clear the world has an energy problem
between 9 USc and 22 USc to produce a unit of and new solutions to energy production need to be
electricity in a gas- or coal-fired power station in found.
the UK. Wind energy costs vary, depending upon ▼ Table 1.7.2 World use of energy sources
location, but are in the range 7 USc to 16 USc
per unit. In the most favourable locations wind Oil Coal Gas Nuclear Hydroelectric
competes with coal and gas generation. The cost 34% 27% 24% 4% 7%
for a nuclear power station is in excess of 10 USc
per unit. After the Tohoku earthquake and tsunami Consumption varies from one country to another;
disaster which led to the damage and closure of North America and Europe are responsible for about
the Fukushima nuclear reactor in Japan, several 42% of the world’s energy consumption each year.
countries have reduced their dependence on nuclear Table 1.7.3 shows approximate values for the annual
energy and Germany plans to phase out nuclear consumption per head of population for different
power completely by 2022. areas. These figures include the hidden consumption
The reliability of a source has also to be in the manufacturing and transporting of goods.
considered, as well as how easily production can be The world average consumption is 76 × 109 J per
started up and shut down as demand for electricity head per year.
▼ Table 1.7.3 Energy consumption per head per year/J × 109
73
74
1.7.4 Power
FOCUS POINT
★ Define power and use the correct equations to calculate power in terms of the rate at which work is done
or energy transferred.
To heat up a frozen dinner in a microwave oven you need to know the power of the oven, if over- or
under-cooking is to be avoided. Similarly, one needs to check the power rating of a light bulb before
inserting it into a socket to ensure over-heating does not occur. Most electrical appliances have their
power rating marked on them, usually at the rear or base of the device. The power of a device is the
rate at which it does work and so is equal to the rate at which it transfers energy to different stores.
also P = ΔE Safety
t l You should only volunteer for this if you feel
where ΔE is the energy transferred in time t. able to. No one should pressure you into
taking part.
Key definition Get someone with a stopwatch to time you
Power the work done per unit time and the energy running up a flight of stairs; the more steps the
transferred per unit time
better. Find your weight (in newtons). Calculate
the total vertical height (in metres) you have
The unit of power is the watt (W) and is a rate of
climbed by measuring the height of one step
working of 1 joule per second, i.e. 1 W = 1 J/s. Larger
and counting the number of steps.
units are the kilowatt (kW) and the megawatt (MW):
The work you do (in joules) in lifting your weight
1 kW = 1000 W = 103 W
to the top of the stairs is (your weight) × (vertical
1 MW = 1 000 000 W = 106 W height of stairs). Calculate your power (in watts).
If a machine does 500 J of work in 10 s, its power 5 Name the stores between which energy is
is 500 J/10 s = 50 J/s = 50 W. A small car develops a transferred as you run up the stairs.
maximum power of about 25 kW. 6 How is energy transferred when you run up
the stairs?
75
Revision checklist
After studying Topic 1.7 you should know and After studying Topic 1.7 you should be able to:
understand the following: ✓ recall different stores of energy and describe
✓ work is done when energy is transferred energy transfers in given examples
✓ recall the principle of conservation of energy
✓ the Sun is the main source of energy for all our and apply it to simple systems including the
energy resources except geothermal, nuclear interpretation of flow diagrams
and tidal
✓ energy is released by nuclear fusion in the Sun ✓ define kinetic energy and perform calculations
1
using Ek = mv2
✓ the different ways of harnessing solar, wind, wave,
2
tidal, hydroelectric, geothermal and biofuel energy ✓ define gravitational potential energy and
✓ the difference between renewable and non- perform calculations using ΔEp = mgh
renewable energy sources ✓ apply the principle of conservation of energy
✓ how nuclear fuel and the chemical energy stored to complex systems and interpret Sankey
in fuel are used to generate electricity in power diagrams
stations ✓ relate work done to the magnitude of a force and
✓ the meaning of efficiency in energy transfers and
the distance moved, and recall the units of work,
that power is the rate of energy transfer. energy and power
✓ recall and use the equation W = F × d = ΔE to
calculate energy transfer
✓ compare and contrast the advantages and
disadvantages of using different energy sources to
generate electricity
76
Exam-style questions
1 State how energy is transferred from 5 The pie chart in Figure 1.7.21 shows the
a a toaster [2] percentages of the main energy sources used
b a refrigerator [2] by a certain country.
c an audio system. [2]
[Total: 6]
natural
gas
2 A 100 g steel ball falls from a height of 1.8 m oil 25%
onto a metal plate and rebounds to a height 40%
hydroelectric 2%
of 1.25 m. Calculate the nuclear 8%
coal
a potential energy of the ball before the fall 25%
(g = 9.8 m/s2) [2]
b kinetic energy of the ball as it hits the
plate [1] ▲ Figure 1.7.21
c velocity of the ball on hitting the plate [3] a Give the percentage supplied by water. [1]
d kinetic energy of the ball as it leaves the b Name any of the sources that are
plate on the rebound [2] renewable. [1]
e velocity of rebound. [3] c Explain what is meant by a renewable
[Total: 11] source. [1]
3 A ball of mass 0.5 kg is thrown vertically d Name two other renewable sources. [2]
upwards with a kinetic energy of 100 J. e If energy is always conserved, explain the
Neglecting air resistance calculate importance of developing renewable
a the initial speed of the ball [3] sources. [2]
b the potential energy of the ball at its [Total: 7]
highest point [1] 6 a Give
c the maximum height to which the ball i two advantages and
rises. [3] ii two disadvantages
[Total: 7] of using fossil fuels in electricity
generating stations. [4]
4 In loading a lorry a man lifts boxes each of b Give
weight 100 N through a height of 1.5 m. i two advantages and
a Calculate the work done in lifting one box. [2] ii two disadvantages
b Calculate how much energy is transferred of using solar energy in electricity
when one box is lifted. [1] generating stations. [4]
c If he lifts four boxes per minute, at what [Total: 8]
power is he working? [3]
[Total: 6] 7 When the energy input to a gas-fired power
station is 1000 MJ, the energy output
is 300 MJ.
a Calculate the efficiency of the power
station. [3]
b Calculate how much energy is lost and
name the energy store to which it is
moved. [2]
c Describe where the lost energy goes. [2]
[Total: 7]
77
★ Calculate the change in pressure beneath the surface of a liquid using the correct equation.
The large flat feet of an Arabian camel prevent it sinking into the soft sand of the desert. This is
because the weight of the camel is spread over the area of its four large feet. It appears that the
effect of a force depends on the area over which it acts. The effect can be quantified by introducing
the concept of pressure. In this topic you will learn that pressure increases as the force increases
and the area over which the force acts becomes less. Pressure in a liquid is found to increase with
both density and depth. If a deep-sea diver surfaces too quickly, the pressure changes can lead to
a condition called the bends. The properties of liquid pressure are utilised in applications ranging
from ≈zwater supply systems and dam construction to hydraulic lifts.
Pressure large when the area is small and this is why nails are
made with sharp points. Walnuts can be broken in
To make sense of some effects in which a force acts the hand by squeezing two together, rather than one
on an object we have to consider not only the force alone, because the area of contact is smaller leading
but also the area on which it acts. For example, to a higher pressure on the shells (Figure 1.8.1).
wearing skis prevents you sinking into soft snow
because your weight is spread over a greater area.
We say the pressure is less.
Pressure is defined as the force per unit area
(i.e. 1 m2) and is calculated from
pressure = force
area
p= F
A
Key definition
Pressure the force per unit area
78
Worked example
Figure 1.8.2 shows the pressure exerted on the floor by weight 24 N
the same box standing on end (Figure 1.8.2a) and lying flat
(Figure 1.8.2b). If the box has a weight of 24 N, calculate the
pressure on the floor when the box is 2m
a standing on end as in Figure 1.8.2a
b lying flat as in Figure 1.8.2b. 3m
4m
a area = 3 m × 2 m = 6 m 2
▲ Figure 1.8.2b
force 24 N
pressure = = = 4 Pa
area 6 m 2 Now put this into practice
b area = 3 m × 4 m = 12 m 2 1 A rectangular box has a width of 2 m, a height of 5 m and a
depth of 2 m.
force 24 N a Calculate the area of
pressure = = = 2 Pa
area 12 m 2 i the base of the box and
ii one of the sides of the box.
b If the box has a weight of 80 N, calculate the pressure on
i the base of the box
weight 24 N ii one of the sides of the box.
4m 2 a Calculate the pressure on a surface when a force of
50 N acts on an area of
i 2.0 m2
ii 100 m2
iii 0.50 m2.
3m 2m b A pressure of 10 Pa acts on an area of 3.0 m2. What is
the force acting on the area?
▲ Figure 1.8.2a
Liquid pressure 3 A liquid finds its own level. In the U-tube of Figure
1.8.4a the liquid pressure at the foot of P is
1 Pressure in a liquid increases with depth. This is greater than at the foot of Q because the left-hand
because the further down you go, the greater the column is higher than the right-hand one. When
weight of liquid above. In Figure 1.8.3a water spurts the clip is opened, the liquid flows from P to Q
out fastest and furthest from the lowest hole. until the pressure and the levels are the same, i.e.
2 Pressure at one depth acts equally in all directions. the liquid ‘finds its own level’. Although the weight
The can of water in Figure 1.8.3b has similar of liquid in Q is now greater than in P, it acts over
holes all round it at the same level. Water comes a greater area because tube Q is wider.
out equally fast and spurts equally far from each In Figure 1.8.4b the liquid is at the same level in
hole. Hence the pressure exerted by the water at each tube and confirms that the pressure at the foot
this depth is the same in all directions. of a liquid column depends only on the vertical depth
a b of the liquid and not on the tube width or shape.
can a b
water
liquid
clip
▲ Figure 1.8.3 P Q
▲ Figure 1.8.4
79
Worked example
A hydraulic jack is used to lift a heavy load. A force of A force of 1 N could lift a load of 50 N; the hydraulic system
1 N is applied to a piston of area 0.01 m2 and pressure is multiplies the force 50 times.
transmitted through the liquid to a second piston of area of
0.5 m2. Calculate the load which can be lifted. Now put this into practice
Taking f = 1 N, a = 0.01 m 2 and A = 0.5 m 2 then 1 In a hydraulic jack a force of 20 N is applied to a piston of
area 0.1 m2. Calculate the load which can be lifted by a
F= f × A second piston of area 1.5 m2.
a 2 In a hydraulic jack a load of 70 N is required to be lifted on
so an area of 1.0 m2. Calculate the force that must be applied
0.5m 2 to a piston of area 0.1 m2 to lift the load.
F = 1N × = 50 N 3 Name the property of a liquid on which a hydraulic jack relies.
0.01m 2
80
REAR WHEEL
brake drum
pistons
brake shoe
return
spring
pad
pistons
master
cylinder
disc
81
liquid
density ρ
depth
∆h
area
A
▲ Figure 1.8.10
Going further
Pressure gauges
These measure the pressure exerted by a fluid, in other
words by a liquid or a gas.
Bourdon gauge
This works like the toy shown in Figure 1.8.11, where
the harder you blow into the paper tube, the more it
uncurls. In a Bourdon gauge (Figure 1.8.12), when a
fluid pressure is applied, the curved metal tube tries to
straighten out and rotates a pointer over a scale.
Car oil-pressure gauges and the gauges on gas
cylinders are of this type.
▲ Figure 1.8.11
82
fluid Y
pressure
mercury
▲ Figure 1.8.12 A Bourdon gauge
U-tube manometer
In Figure 1.8.13a each surface of the liquid is acted on
760 mm
equally by atmospheric pressure and the levels are the
same. If one side is connected to, for example, the gas
supply (Figure 1.8.13b), the gas exerts a pressure on atmospheric
surface A and level B rises until pressure
atmospheric
pressure atmospheric
pressure to gas supply
B
h
gas pressure
C A
a b
Revision checklist
After studying Topic 1.8 you should know and After studying Topic 1.8 you should be able to:
understand: ✓ define pressure from the equation p = F/A and give
✓ that the pressure beneath a liquid surface everyday examples of its use; recall the units of
increases with depth and density and that pressure pressure
is transmitted through a liquid.
✓ calculate the change in pressure below the
surface of a liquid.
83
Exam-style questions
1 The following statements relate to definitions 4 a The pressure in a liquid varies with depth
of pressure. In each case write down if the and density.
statement is true or false. State whether the following statements are
A Pressure is the force acting on unit area. [1] true or false.
B Pressure is calculated from force/area. [1] A The pressure in a liquid increases with
C The SI unit of pressure is the pascal (Pa) depth. [1]
which equals 1 newton per square metre B The pressure in a liquid increases with
(1 N/m2). [1] density. [1]
D The greater the area over which a force C The pressure in a liquid is greater
acts, the greater the pressure. [1] vertically than horizontally. [1]
E Force = pressure × area. [1]
F The SI unit of pressure is the pascal (Pa) b Calculate the increase in pressure at a
which equals 1 newton per metre (1 N/m). [1] depth of 100 m below the surface of sea
[Total: 6] water of density 1150 kg/m3. [4]
2 a Calculate the pressure exerted on a
wood-block floor by each of the following. [Total: 7]
i A box weighing 2000 kN standing on an
area of 2 m2. [2] 5 a State the equation which relates the
ii An elephant weighing 200 kN standing change in pressure in a liquid to the
on an area of 0.2 m2. [2] depth below the liquid surface. [2]
iii A girl of weight 0.5 kN wearing high- b Name the unit of pressure. [1]
heeled shoes standing on an area of c Calculate the depth of water of density
0.0002 m2. [2] 1030 kg/m3 where the pressure is
b A wood-block floor can withstand a pressure 7.5 × 106 Pa. [3]
of 2000 kPa (2000 kN/m2). [Total: 6]
State which of the objects in a will damage
the floor and explain why. [2]
[Total: 8]
Going further
3 In a hydraulic press a force of 20 N is applied to 6 Figure 1.8.15 shows a simple barometer.
a piston of area 0.20 m2. The area of the other a What is the region A? [1]
piston is 2.0 m2. b What keeps the mercury in the tube? [1]
c What is the value of the atmospheric
a Calculate the pressure transmitted through pressure being shown by the barometer? [1]
the liquid. [2] d State what would happen to this reading
b Calculate the force on the other piston. [2] if the barometer were taken up a high
c Explain why a liquid and not a gas is used mountain? Give a reason. [2]
as the ‘fluid’ in a hydraulic machine. [1] [Total: 5]
d State another property of a liquid on which A 2 cm
hydraulic machines depend. [1]
[Total: 6]
74 cm
mercury
1 cm
1 cm
▲ Figure 1.8.15
84
In this topic you will learn about the three states of matter: solids, liquids and gases. The particles
in each are ordered differently and this leads to each state having different properties. You will
find that solids have a high level of internal order, a liquid has less, and in a gas the particles have
no order and move about randomly. The state of a material can be altered by heating or cooling. In
a solid the bonds between particles break down on heating and it melts into a liquid; for example,
ice melts into water. Boiling a liquid produces a gas with well separated particles; water turns into
steam. The three states of matter can be represented in a particle diagram.
86
When a liquid is cooled sufficiently, solidification are heated. When a gas is cooled sufficiently it will
occurs and it returns to the solid state. The density of return to the liquid state in a process known as
a material in its solid state is usually higher than it is condensation.
in its liquid state. When a liquid is heated, particles Drops of water are formed when steam condenses
can escape from its surface by a process called on a cold window pane, for example.
evaporation. When sufficient heat is supplied to the
liquid boiling occurs and the liquid turns into a gas. Test yourself
Gases 1 Using what you know about the compressibility
Gases have no definite shape or volume as these (squeezability) of the different states of matter,
explain why
depend on the dimensions of the container. The
a air is used to inflate tyres
particles in a gas are much further apart than they b steel is used to make railway lines.
are in a liquid and the density of a gas is much lower 2 Name the processes in which
than that of a liquid. The particles have no ordered a a solid turns into a liquid
structure and are able to move about freely in a b a liquid turns into a gas
random manner. Gases are more easily compressed c a liquid turns into a solid
d a gas turns into a liquid.
than solids or liquids and expand more when they
★ Understand the factors that affect the properties of solids, liquids and gases.
★ Understand the relationship between the kinetic energy of particles and temperature, including the
concept of absolute zero.
★ Know how a change in pressure in a gas affects the motion and number of collisions of its particles.
★ Describe how a change in pressure of a gas affects the forces exerted by particles colliding with
surfaces (force per unit area).
★ Describe Brownian motion and know that it is evidence for the kinetic particle model of matter.
★ Distinguish atoms or molecules from microscopic particles, and understand how these microscopic
particles may be moved by collisions with much lighter molecules.
The properties of solids, liquids and gases can be related to the arrangement, separation and motion
of the particles in each. In the previous section, you learnt about the properties of solids, liquids
and gases. In this topic, you will learn that in a gas, the particles are well separated and in constant
random motion, producing pressure on a container by their collisions with its surfaces. In a solid, the
particles are closely arranged and firmly bound together, with a regular pattern in crystals. In a liquid
the particles are further apart, with only local ordering between particles that have more freedom
of movement than those in a solid. Although particles are too small to be seen with the unaided eye,
their influence can be detected. When tiny particles in a fluid are observed under a microscope, they
can be seen to move slightly in a random manner under the impact of collisions with many much
lighter molecules. This effect is known as Brownian motion and provides evidence for the kinetic
particle model of matter.
87
Properties marbles
We can imagine springs (Figure 2.1.3) representing ▲ Figure 2.1.4 A model of particle behaviour in a liquid
the electric forces between particles that hold
them together and determine the forces and
distances between them. These forces enable the Properties
solid to keep a definite shape and volume, while In a liquid the forces between particles are less
still allowing the individual particles to vibrate than in a solid and so the distance between
backwards and forwards. Owing to the strong particles is greater. Liquids have a definite
intermolecular forces, solids resist compression volume but individual particles can slide over
and expand very little when heated. each other and are never near another particle
long enough to get trapped in a regular pattern.
This allows liquids to flow and take on the shape
of the vessel containing them. The forces between
particles are strong enough that liquids are only
slightly more easily compressed than solids. When
heated, the particles move further apart, enabling
liquids to expand more easily than solids. As the
temperature increases some particles may have
▲ Figure 2.1.3 The electric forces between particles in a sufficient energy to escape from the surface of
solid can be represented by springs. the liquid resulting in evaporation of the liquid.
88
89
Practical work
microscope
window
lid
lamp
b glass plate
smoke c
smoke
burning match
glass cell
glass rod glass cell
▲ Figure 2.1.6
Carefully adjust the microscope until you see 1 What are the specks of light in the glass cell of
bright specks dancing around haphazardly the Brownian motion experiment?
(Figure 2.1.6c). The specks are smoke particles 2 In a glass cell set up to show Brownian motion,
seen by reflected light; their random motion is describe how the specks of light move.
called Brownian motion and is evidence for
the kinetic particle model of matter. This motion 3 What do you think might cause microscopic
is due to collisions between the microscopic particles to move in the way they do in a
particles in a suspension and the particles of the Brownian motion experiment?
gas or liquid.
90
★ Use the correct equation to calculate pressure and volume of a fixed mass of gas, and be able to
represent this relationship graphically.
★ Convert temperatures between the Celsius and Kelvin temperature scales using the correct equation.
Gases show the simplest behaviour of the three states of matter and respond to changes of
temperature or volume by a change of pressure. By keeping either volume or temperature constant
in an experiment, their relationships with pressure can be determined and explained in terms of the
kinetic particle model of matter. The properties of gases can be exploited for use in thermometers
to measure temperature. You will be familiar with the Celsius scale of temperature for everyday
measurements; the freezing temperature of water is set at 0°C and the boiling temperature of water
at 100°C. In both the Kelvin and Celsius temperature scales, there are 100 degrees between the
freezing temperature and boiling temperature of water, but the Kelvin scale starts from −273°C
where the motion of particles ceases.
Pressure of a gas
to vacuum
The air forming the Earth’s atmosphere stretches pump
upwards a long way. Air has weight; the air in a
normal room weighs about the same as you do,
can
about 500 N. Because of its weight the atmosphere
exerts a large pressure at sea level, about
100 000 N/m2 = 105 Pa (or 100 kPa). This pressure
acts equally in all directions.
A gas in a container exerts a pressure on the
surfaces of the container. If air is removed from
a can by a vacuum pump (Figure 2.1.7), the can
collapses because the air pressure outside is greater
▲ Figure 2.1.7 Atmospheric pressure collapses the
than that inside. A space from which all the air
evacuated can.
has been removed is a vacuum. Alternatively,
the pressure in a container can be increased, for When a gas is heated, as air is in a jet engine, its
example by pumping more gas into the can; a pressure as well as its volume may change. To study
Bourdon gauge (Topic 1.8) is used for measuring gas the effect of temperature on these two quantities
pressures. we must keep one fixed while the other is changed.
When investigating relationships between properties
only one variable should be changed at a time.
91
Effect on pressure of a change in temperature the number of particles per cm3 will be doubled.
(constant volume) There will be twice as many collisions per second
When a gas is heated and its temperature rises, the with the surfaces, i.e. the pressure is doubled.
average speed of its particles increases. If the volume piston
of a fixed mass of gas stays constant, its pressure
increases because there are more frequent and more
violent collisions of the particles with the surfaces.
V
Effect on pressure of a change in volume cylinder
V
(constant temperature) 2
If the volume of a fixed mass of gas is halved by
halving the volume of the container (Figure 2.1.8), ▲ Figure 2.1.8 Halving the volume doubles the pressure.
Practical work
rubber tubing Bourdon
Effect on pressure of temperature (volume pressure
constant) gauge
Safety
l The Bourdon gauge should be firmly clamped
to prevent toppling.
l Eye protection must be worn.
l Take care with hot apparatus.
thermometer
The apparatus is shown in Figure 2.1.9. The rubber
tubing from the flask to the pressure gauge should
be as short as possible. The flask must be in can
92
by the Bourdon gauge. Take about six different 8 A graph of pressure against 1/volume for
measurements. Plot a graph of pressure versus the results of the experiment is shown in
volume as shown in Figure 2.1.11a. Figure 2.1.11b. Name the features of the graph
which suggest that pressure is proportional to
0 0 glass tube 1/volume.
10 10
air a b
20 20 Bourdon gauge p p
30 30
40 40
p
50 50 to foot doubled
oil pump
V
reservoir
halved
▲ Figure 2.1.10 0 V 0 1
V
7 a Name the independent variable in the ▲ Figure 2.1.11
experiment.
b Name the dependent variable.
93
Celsius and Kelvin temperature vessel, over the edge and down the outside. Some
metals and compounds become superconductors
scales of electricity and a current, once started in them,
The volume–temperature and pressure–temperature flows forever, without a battery. Figure 2.1.13 shows
graphs for a gas are straight lines (Figure 2.1.12). research equipment that is being used to create
They show that gases expand linearly with materials that are superconductors at very much
temperature as measured on a mercury thermometer, higher temperatures, such as −23°C.
i.e. equal temperature increases cause equal volume
or pressure increases.
volume or pressure
Going further
Practical work
Effect on volume of temperature The pressure of (and on) the air column is
(pressure constant): Charles’ law constant and equals atmospheric pressure
plus the pressure of the acid index.
Safety
ruler
l Eye protection must be worn. (30 cm) thermometer
l Take care as concentrated sulfuric acid
is highly corrosive. Do not touch it if any capillary can
tube
leaks out of the tube.
concentrated
Arrange the apparatus as in Figure 2.1.14. air sulfuric acid
The index of concentrated sulfuric acid column index
traps the air column to be investigated and rubber
also dries it. Adjust the capillary tube so band
water
that the bottom of the air column is opposite
a convenient mark on the ruler.
heat
Note the length of the air column (between the
▲ Figure 2.1.14
lower end of the index and the sealed end of
the capillary tube) at different temperatures 9 a Name the independent variable in the
but, before taking a reading, stop heating and experiment.
stir well to make sure that the air has reached b Name the dependent variable.
the temperature of the water. Put the results in 10 The results of the experiment are plotted
a table. in a graph of volume versus temperature
and appear similar to those shown in
Plot a graph of volume (in cm, since the length
Figure 2.1.12. What do the results indicate
of the air column is a measure of it) on the
about the relationship between volume and
y-axis and temperature (in ºC) on the x-axis.
temperature?
95
Worked example
A bicycle pump contains 50 cm3 of air at 17°C and at Note that: (i) all temperatures must be in K; (ii) any units
1.0 atmosphere pressure (atm). Find the pressure when can be used for p and V provided the same units are used
the air is compressed to 10 cm3 and its temperature rises on both sides of the equation; (iii) in some calculations the
to 27°C. volume of the gas has to be found at standard temperature
and pressure, or ‘s.t.p.’. This is temperature 0°C and
We have
pressure 1 atmosphere (1 atm = 105 Pa).
p1 = 1.0 atm p2 = ?
Now put this into practice
V1 = 50 cm3 V2 = 10 cm3
1 A fixed mass of gas has a volume of 9 cm3 at a pressure
of 1 × 105 Pa at 27°C. Find its pressure when the
T1 = 273 + 17 = 290 K T2 = 273 + 27 = 300 K
volume is compressed to 5 cm3 and its temperature
rises to 37°C.
From equation (4) we get
2 A certain quantity of gas has a volume of 40 cm3
V1 T2 50 300 at a pressure of 2.0 × 105 Pa at 27°C. Find its
p2 = p1 × × = 1× × = 5.2 atm
V2 T1 10 290 temperature when the volume is 30 cm3 and the
pressure is 3.2 × 105 Pa.
96
Test yourself
6 In terms of particle motion describe the effect 8 a Why is −273ºC chosen as the starting
on the pressure of a fixed mass of gas when the temperature for the Kelvin scale of temperature?
temperature rises but the volume is kept constant. b How do the size of units on the Celsius and Kelvin
7 Describe the effect on the pressure of a fixed mass scales of temperature compare?
of gas if the volume is reduced but the temperature
of the gas is kept constant.
Revision checklist
After studying Topic 2.1 you should know and After studying Topic 2.1 you should be able to:
understand: ✔ recall the terms describing changes in state of
✔ the different physical properties of solids, liquids solids, liquids and gases
and gases ✔ explain temperature, absolute zero and change in
✔ particle diagrams for the different states of matter pressure in terms of molecular motion
✔ the different particle structure of solids, liquids ✔ describe and explain an experiment to show
and gases Brownian motion
✔ describe the effect on the pressure of a fixed
✔ how the particle model explains the physical mass of gas caused by a change in temperature
properties of solids, liquids and gases. (at constant volume) and a change of volume (at
constant temperature)
✔ convert temperatures between the Celsius and
Kelvin scales of temperature
97
Exam-style questions
1 Solids, liquids and gases are composed of iii The pressure increases if the volume
particles. Which one of the following statements of the container increases at constant
is not true? temperature.[1]
A The particles in a solid vibrate about a fixed b i Explain the significance of a
position. temperature of −273°C in terms of
B The particles in a liquid are arranged in a particle motion.[2]
regular pattern. ii State the value of a temperature of
C The particles in a gas exert negligibly small −273°C on the Kelvin temperature
forces on each other, except during collisions. scale.[1]
D The densities of most liquids are about iii Calculate the value of a temperature
1000 times greater than those of gases of −200°C on the Kelvin scale of
because liquid particles are much closer temperature.[1]
together than gas particles. [Total: 7]
[Total: 1]
2 Sketch particle diagrams for 6 The piston in Figure 2.1.15 is pulled out of the
a a solid [2] cylinder from position X to position Y, without
b a liquid [2] changing the temperature of the air enclosed.
c a gas. [2] If the original pressure in the cylinder was
[Total: 6] 1.0 × 105 Pa, calculate
3 a Name the state of matter in which the a the air pressure when the piston is at
particles are furthest apart. [1] position Y [3]
b Use the particle model of matter to b the air pressure when the piston is moved
explain how a gas exerts pressure on the a further 10 cm to the left of position Y. [3]
surfaces of its container. [2] [Total: 6]
c State and explain how the pressure
changes when the temperature of the piston
30 cm 10 cm
gas increases. [4]
[Total: 7]
4 Smoke particles and air exist in a sealed
glass box. The box is illuminated, and the
motion of the smoke particles is observed
through a microscope.
a Describe the motion of the smoke particles.[1] Y X cylinder
b Explain the reason the smoke particles ▲ Figure 2.1.15
move in this way. [4]
7 A certain quantity of gas has a volume of
30 cm3 at a pressure of 1 × 105 Pa.
[Total: 5]
Assuming the temperature remains constant,
5 a The following statements refer to the pressure calculate the volume of the gas when the
exerted by a gas in a container. pressure is
Write down whether each statement is true a 2 × 105 Pa [3]
or false. b 5 × 105 Pa. [3]
i Pressure is due to the particles of the [Total: 6]
gas bombarding the surfaces of the
container. [1]
ii The pressure decreases if the gas is
cooled at constant volume. [1]
98
Alternative to Practical
8 The variation in pressure of a fixed mass of gas is a Plot a graph of pressure against volume. [3]
measured for different volumes. b Work out values for 1/volume and enter
The results obtained are listed in the following them into the table. [1]
table: c Plot a graph of pressure against 1/volume. [3]
d Are the results in agreement with the
Pressure/105 Pa Volume/cm3 1/volume/cm3 equation pV = constant?[2]
24 1.0 [Total: 9]
12 2.0
8 3.0
6 4.0
4 6.0
99
★ Use the motion and arrangement of particles in solids, liquids and gases to explain the relative order of
magnitudes of their expansion as temperature increases.
As thermal energy is transferred to a material, the particles tend to move further apart. As you saw
in Topic 2.1, the effect on heating a gas is large because the particles are free to move and expansion
can easily occur. Expansion is much smaller in solids but thermal effects in a solid can still be
important in conditions where there are wide temperature variations. Special features to absorb
expansion need to be included in railway tracks and engineered structures such as bridges so that
they do not distort on very hot days. In this topic you will encounter some everyday applications and
consequences of expansion in solids and liquids.
When solids, liquids and gases are heated, the magnitude of the expansion for a given temperature
rise is less for a liquid than a gas and even less for a solid where the particles are close together
and the force of attraction between them is high.
100
copper
Uses of expansion iron
Axles and gear wheels are major components of ▲ Figure 2.2.2 A bimetallic strip: a before heating;
clocks on the small scale and wheeled vehicles from b after heating
cars to trains on the large scale.
In Figure 2.2.1 the axles have been shrunk by Fire alarm
cooling in liquid nitrogen at −196°C until the gear Heat from the fire makes the bimetallic strip bend
wheels can be slipped on to them. On regaining normal and complete the electrical circuit, so ringing the
temperature, the axles expand to give a very tight fit. alarm bell (Figure 2.2.3a).
A bimetallic strip is also used in this way to work
the flashing direction indicator lamps in a car, being
warmed by an electric heating coil wound round it.
a
electric
bell
contact
bimetallic
strip
heat
Going further
Linear expansivity
An engineer has to allow for the linear expansion of
a bridge when designing it. The expansion can be
calculated if all the following are known:
l the length of the bridge,
l the range of temperature it will experience, and
l the linear expansivity of the material to be used.
▲ Figure 2.2.4a Tapered overlap of rails The linear expansivity of a material is found by
experiment. For steel it is 0.000 012 per °C. This means
nut nut that 1 m will become 1.000 012 m for a temperature
rise of 1°C. A steel bridge 100 m long will expand by
0.000 012 × 100 m for each 1°C rise in temperature.
rubber seal If the maximum temperature change expected is
60°C (e.g. from −15°C to +45°C), the expansion will be
pipe pipe 0.000 012 per °C × 100 m × 60°C = 0.072 m, or 7.2 cm.
In general,
expansion = linear expansivity × o riginal length ×
temperature rise
▲ Figure 2.2.4b Expansion joint
102
Unusual expansion of water contracts and being denser sinks to the bottom.
Warmer, less dense water rises to the surface to be
As water is cooled to 4°C it contracts, as we would cooled. When all the water is at 4°C the circulation
expect. However, between 4°C and 0°C it expands, stops. If the temperature of the surface water falls
surprisingly. Water has a maximum density at 4°C below 4°C, it becomes less dense and remains at
(Figure 2.2.6). the top, eventually forming a layer of ice at 0°C.
volume Temperatures in the pond are then as in Figure 2.2.8.
ice
ice at 0°C
ice and water
water
Liquid-in-glass thermometer
The temperature of a body tells us how hot the body
is. It is measured using a thermometer usually in
degrees Celsius (0°C).
In the liquid-in-glass thermometer the liquid in
a glass bulb expands up a capillary tube when the
bulb is heated. The liquid must be easily seen and
must expand (or contract) rapidly and by a large
amount over a wide range of temperature. It must
not stick to the inside of the tube or the reading
will be too high when the temperature is falling.
Mercury and coloured alcohol are commonly used
liquids in this type of thermometer. Mercury freezes
at −39°C and boils at 357°C but is a toxic material.
▲ Figure 2.2.7 Result of the expansion of water on freezing A non-toxic metal alloy substitute for mercury,
such as Galinstan, is often used nowadays; it melts
The unusual (anomalous) expansion of water between at −19°C and boils at 1300°C. Alcohol freezes at
4°C and 0°C explains why fish survive in a frozen −115°C and boils at 78°C and is therefore more
pond. The water at the top of the pond cools first, suitable for low temperatures.
103
Going further
Scale of temperature
A scale and unit of temperature are obtained by
choosing two temperatures, called the fixed points, and
dividing the range between them into a number of equal 100°C steam point
divisions or degrees.
On the Celsius scale (named after the Swedish scientist
Anders Celsius who suggested it), the lower fixed point
is the temperature of pure melting ice and is taken
as 0°C. The upper fixed point is the temperature of
the steam above water boiling at normal atmospheric
pressure, 105 Pa (or N/m2), and is taken as 100°C.
100
When the fixed points have been marked on the degrees
thermometer, the distance between them is divided into
100 equal degrees (Figure 2.2.9). The thermometer now
has a linear scale, in other words it has been calibrated
or graduated.
Test yourself
4 a What is meant by the anomalous expansion of
3 Explain the relative order of magnitude of the
water?
expansion of solids, liquids and gases.
b Name two consequences of the unusual
expansion of water.
5 Discuss the action of a liquid-in-glass thermometer.
★ Explain a change in an object’s temperature in terms of the change in kinetic energy of all its particles.
★ Define specific heat capacity, use the correct equation in calculations and describe experiments to
measure it.
104
Some materials require more heat than others to raise their temperature. As discussed in the
previous topic, when the temperature of an object rises, its particles move more rapidly.
The increase in the kinetic energy associated with this motion raises the internal energy of the object.
The extent of the increase in kinetic energy of the particles in a material when it is heated depends
on the nature of the material and its state, and is measured in terms of specific heat capacity.
The specific heat capacity of aluminium is higher than that of copper, so copper is a more energy
efficient material to use for saucepans. In this topic you will find out how to measure and calculate
the specific heat capacity of some solids and liquids.
The internal energy of an object is the energy same temperature. For example, if the red-hot spark
associated with the motion of its particles. landed in the boiling water, thermal energy would be
When an object is heated and its temperature transferred from it to the water even though much
rises, there is an increase in the internal energy more thermal energy could be obtained from the water.
of the object.
Specific heat capacity
Internal energy If 1 kg of water and 1 kg of paraffin are heated in
The kinetic particle theory (Topic 2.1.2) regards turn for the same time by the same heater, the
temperature as a measure of the average temperature rise of the paraffin is about twice
kinetic energy (Ek) of the particles of the body. that of the water. Since the heater gives equal
The greater this is, the faster the particles move amounts of thermal energy to each liquid, it
and the higher the temperature of the body. seems that different substances require different
Increasing the temperature of an object increases amounts of energy to cause the same temperature
its internal energy because the kinetic energy of rise in the same mass, say 1°C in 1 kg.
all the particles increases. The amount of heat required to raise the
temperature of a particular substance by one
degree is measured by its specific heat capacity
Thermal energy and temperature (symbol c).
It is important not to confuse the temperature of a The specific heat capacity of a substance is
body with the thermal energy that can be obtained defined as the energy required per unit mass per
from it. For example, a red-hot spark from a fire is unit temperature increase.
at a higher temperature than the boiling water in a In physics, the word ‘specific’ means that unit
saucepan. In the boiling water the average kinetic mass is being considered.
energy of the particles is lower than in the spark; but In general, for a mass m, receiving energy ΔE
since there are many more water particles, their total which results in a temperature rise Δθ, this can
energy is greater, and therefore more thermal energy be written in equation form as
can be supplied by the water than by the spark.
ΔE
Thermal energy is transferred from a body at a c=
mΔθ
higher temperature to one at a lower temperature.
where c is the specific heat capacity of a material
This is because the average kinetic energy (and speed) of mass m whose temperature rises by Δθ when
of the particles in the hot body falls as a result of its internal energy increases by ΔE.
the collisions with particles of the cold body whose Internal energy is measured in joules (J) and
average kinetic energy, and therefore temperature, the unit of specific heat capacity is the joule per
increases. When the average kinetic energy of the kilogram per °C, i.e. J/(kg °C).
particles is the same in both bodies, they are at the
105
106
107
Test yourself
6 Which one of the following statements is not true?
7 How much thermal energy is needed to raise the
A Temperature tells us how hot an object is.
temperature by 10°C of 5 kg of a substance of
B When the temperature of an object rises so does
specific heat capacity 300 J/(kg °C)?
its internal energy.
8 How long will it take a 3 kW immersion heater to
C Heat flows naturally from an object at a lower
raise the temperature of 5 kg of water from 30°C
temperature to one at a higher temperature.
to 50°C?
D The particles of an object move faster when its
temperature rises.
To melt a bar of chocolate you will need to heat it. Melting and boiling require the input of energy to
change the state of matter from solid to liquid or from liquid to gas. In the reverse changes, heat is
released. During a change of state there is no change in temperature until the process is complete.
The kinetic particle model can help us to understand the processes which occur during a change of
state. In this section you will also learn how the model explains evaporation and cooling in terms of
the escape of energetic particles from the surface of a liquid.
You will learn the differences between the processes of evaporation and boiling and the factors
which affect the rate of cooling of an object.
When a solid is heated, it may melt and change A pure substance melts at a definite temperature,
its state from solid to liquid. If ice is heated it called the melting temperature; it solidifies at
becomes water. The opposite process, freezing, the same temperature – sometimes then called the
occurs when a liquid solidifies. freezing temperature. At standard atmospheric
pressure, the melting temperature of water is 0°C.
108
Practical work
Cooling curve of stearic acid 5 Plot a graph of temperature against time
(a cooling curve) and identify the freezing
Safety temperature of stearic acid.
● Eye protection must be worn. 6 The cooling curve (a plot of temperature
against time) for a pure substance is shown in
Half fill a test tube with stearic acid and place it
Figure 2.2.13. Why is the cooling curve flat in
in a beaker of water (Figure 2.2.12a). Heat the
the region AB?
water until all the stearic acid has melted and its
temperature reaches about 80°C.
Remove the test tube and arrange it as in
Figure 2.2.12b, with a thermometer in the liquid
stearic acid. Record the temperature every
minute until it has fallen to 60°C.
A B
temperature
a b
thermometer
melting temperature
water
stearic acid
time
▲ Figure 2.2.13 Cooling curve
Solidifying, melting and boiling not fall. Conversely when a solid is melting, the
energy supplied does not cause a temperature rise;
The previous experiment shows that the temperature
energy is transferred but the substance does not
of liquid stearic acid falls until it starts to solidify
get hotter. For example, the temperature of a well-
(at 69°C) and remains constant until it has all
stirred ice–water mixture remains at 0°C until all the
solidified. The cooling curve in Figure 2.2.13 is for a
ice is melted. Similarly when energy is supplied to a
pure substance; the flat part AB occurs at the melting
boiling liquid, the temperature of the liquid does not
temperature when the substance is solidifying.
change. The temperature of pure water boiling at
During solidification a substance transfers thermal
standard atmospheric pressure is 100°C.
energy to its surroundings but its temperature does
109
Going further
Latent heat of fusion Specific latent heat of fusion
Energy that is transferred to a solid during melting or The specific latent heat of fusion (lf ) of a substance is
given out by a liquid during solidification is called latent the quantity of heat needed to change unit mass from
heat of fusion. Latent means hidden and fusion means solid to liquid without temperature change.
melting. Latent heat does not cause a temperature
Specific latent heat is measured in J/kg or J/g.
change; it seems to disappear.
In general, the quantity of heat ΔE needed to change
a mass m from solid to liquid is given by
ΔE = m × lf
Practical work
Specific latent heat of fusion for ice To correct for heat transferred from the
surroundings, collect the melted ice in a
Safety beaker for time t (e.g. 4 minutes); weigh the
● Eye protection must be worn. beaker plus the melted ice, m1. Empty the
beaker, switch on the heater, and collect the
Through measurement of the mass of water
melted ice for the same time t; re-weigh the
m produced when energy ΔE is transferred
beaker plus the melted ice, m2. The mass of ice
to melting ice, the specific latent heat of
melted by the heater is then
fusion for ice can be calculated.
m = m2 − m1
Insert a 12 V electric immersion heater of
known power P into a funnel, and pack crushed The energy supplied by the heater is given by
ice around it as shown in Figure 2.2.14. ΔE = P × t, where P is in J/s and t is in seconds;
ΔE will be in joules. Alternatively, a joulemeter
can be used to record ΔE directly.
immersion heater
9 Use your data to calculate the specific latent
heat of fusion, lf, for ice from the equation
ΔE = m × lf.
10 What correction is made in the above
experiment to measure the specific latent
crushed ice
heat of fusion of ice to compensate for heat
funnel gained from the surroundings?
11 How could you reduce heat loss to the
surroundings in this experiment?
beaker
water
▲ Figure 2.2.14
110
111
to the liquid state, where the particles are closer through it (Figure 2.2.16). Energy is transferred
together, potential energy is transferred from the first from the liquid itself and then from the water
particles to thermal energy in the surroundings. below the can. The water soon freezes causing the
block and can to stick together.
Boiling and evaporation air
At standard atmospheric pressure, the boiling
temperature of water is 100°C.
Boiling
For a pure liquid, boiling occurs at a definite glass tube
temperature called its boiling temperature and
is accompanied by bubbles that form within the can
liquid, containing the gaseous or vapour form of
the particular substance. dichloromethane
Energy is needed in both evaporation and
boiling and is stored in the vapour, from which water
it is released when the vapour is cooled or block of wood
compressed and changes to liquid again.
▲ Figure 2.2.16 Demonstrating cooling by evaporation
Evaporation
Explanation
A few energetic particles close to the surface of a
Evaporation occurs when faster-moving particles
liquid may escape and become gas particles. This
escape from the surface of the liquid. The average
process of evaporation occurs at all temperatures.
speed and therefore the average kinetic energy
of the particles left behind decreases, i.e. the
Conditions affecting evaporation temperature of the liquid falls.
Evaporation happens more rapidly when
● the temperature is higher, since then more Cooling by contact
particles in the liquid are moving fast enough When evaporation occurs from a liquid and
to escape from the surface the average kinetic energy of the remaining
● the surface area of the liquid is large, so giving particles decreases, the liquid cools. In Topic
more particles a chance to escape because 2.3.1 we will see that thermal energy flows from
more are near the surface a hotter to a colder object by conduction. If
● a wind or draught is blowing over the surface an object is in contact with the liquid during
carrying vapour particles away from the evaporation, thermal energy will flow from the
surface, thus stopping them from returning to object to the liquid. The object will cool until
the liquid and making it easier for more liquid its temperature equals that of the liquid.
particles to break free. (Evaporation into a
vacuum occurs much more rapidly than into a Uses
region where there are gas particles.)
Water evaporates from the skin when we sweat. This is
the body’s way of losing unwanted heat and keeping
Cooling by evaporation a constant temperature. After vigorous exercise there
In evaporation, energy is transferred to the liquid is a risk of the body being overcooled, especially in a
from its surroundings, as may be shown by the draught; it is then less able to resist infection.
following demonstration, done in a fume cupboard. Ether acts as a local anaesthetic by chilling
(as well as cleaning) your arm when you are
Demonstration
having an injection. Refrigerators, freezers and
Dichloromethane is a volatile liquid, i.e. it has a air-conditioning systems use cooling by evaporation
low boiling temperature and evaporates readily at on a large scale.
room temperature, especially when air is blown Volatile liquids are used in perfumes.
112
Test yourself
11 a When a solid is melting
13 Some water is stored in a bag of porous material,
i does its temperature increase, decrease or
such as canvas, which is hung where it is exposed
remain constant
to a draught of air. Explain why the temperature
ii is energy absorbed or released or neither?
of the water is lower than that of the air.
b When a liquid is boiling does its temperature
increase, decrease or remain constant?
12 a Describe the process of evaporation in particle
terms.
b How does the temperature of a liquid change
during evaporation?
Revision checklist
After studying Topic 2.2 you should know and ✔ explain the relative order of magnitude of the
understand: expansion of solids, liquids and gases
✔ that a rise in the temperature of an object ✔ distinguish between evaporation and boiling
increases its internal energy ✔ define specific heat capacity, c, and solve
ΔE
problems using the equation c =
✔ the relation between an object’s temperature mΔθ
and the kinetic energy of the particles ✔ describe experiments to measure the
specific heat capacity of metals and liquids by
✔ that melting and boiling occur without a change electrical heating
in temperature and recall those temperatures for ✔ describe condensation, solidification and
water. evaporation processes in terms of the kinetic
After studying Topic 2.2 you should be able to: particle model
✔ describe the thermal expansion of solids and
✔ explain cooling by evaporation
liquids
✔ recall the factors which affect evaporation.
✔ describe precautions taken against expansion and
uses of expansion
Exam-style questions
1 2 A bimetallic thermostat for use in an iron is
shown in Figure 2.2.17.
a A gas expands more easily than a liquid.
control knob
Explain in terms of the motion and
arrangement of particles. [3]
insulator
metal B
▲ Figure 2.2.17
113
Alternative to Practical
8 In an experiment to investigate the cooling of a Plot a graph of temperature versus time. [4]
a liquid to a solid, a test tube containing a pure b Estimate the melting temperature of the
solid is warmed in a beaker of hot water until it solid and explain your choice. [2]
has completely melted to a liquid and has reached c Explain what happens to the arrangement of
a temperature of 90°C. The tube is then removed the particles in the liquid during solidification.
from the hot water and the temperature recorded [2]
every 2 minutes while the liquid cools to a solid. [Total: 8]
The results are given in the following table.
Time/minutes 0 2 4 6 8 10 12 14 16 18
Temperature/°C 90 86 82 81 80 80 79 76 73 72
114
★ Use atomic or molecular lattice vibrations and the movement of free (delocalised) electrons in
metallic conductors to describe thermal conduction in solids.
★ Describe, in terms of particles, why thermal conduction is poor in gases and most liquids.
★ Understand that thermal conductors conduct thermal energy better than thermal insulators and some
solids are better thermal conductors than others.
Heat from a stove is quickly transferred to all parts of a metal saucepan; metals are good
conductors of heat. A poor thermal conductor, such as plastic, is often used for the handle of
a saucepan to keep it cool. In this topic you will encounter experiments that demonstrate the
properties of both good and bad thermal conductors.
A knowledge of how heat travels is needed to keep first, showing it is the best conductor, followed
a building or a house at a comfortable temperature by aluminium, brass and then iron.
in winter and in summer, if it is to be done match
economically and efficiently.
copper rod
Conduction iron rod
115
116
2.3.2 Convection
FOCUS POINTS
★ Know that thermal energy transfer in liquids and gases usually occurs by convection.
★ Use density changes to explain convection in liquids and gases.
★ Describe some experiments to show convection.
You may have a convector heater in your home which helps to keep you warm in winter.
In convection, heat is transferred by the motion of matter and it is an important method for
transferring thermal energy in liquids and gases. When the temperature of a fluid increases,
thermal expansion reduces its density and the warmer, less dense parts of the fluid tend to rise,
while cooler, denser parts will sink. The combination sets up fluid flows known as convection
currents that transfer thermal energy from places of high temperature to those of lower
temperature by motion of the fluid itself. In the case of a convector heater, convection currents are
set up in the air in the room.
117
sea
warmer
smoke
▲ Figure 2.3.6 Coastal breezes are due to convection:
a day; b night.
lighted
touch paper
Gliding
glass chimneys
Gliders, including hang-gliders (Figure 2.3.7), are
box carried along on hot air currents, called thermals.
lighted glass
candle window
118
2.3.3 Radiation
FOCUS POINTS
★ Understand that thermal radiation is infrared radiation that does not require a transmission medium and
that this radiation is emitted by all objects.
★ Describe the effects of surface colour and texture on the emission, absorption and reflection of thermal
radiation.
★ Understand the factors which affect the amount of radiation emitted by an object.
★ Understand that a balance between rate of energy received and energy transferred must be achieved
for an object to maintain a constant temperature.
★ Know that factors controlling the balance between incoming radiation and radiation emitted from the
Earth’s surface affect the temperature of the Earth.
★ Describe experiments to distinguish between good and bad absorbers and emitters of infrared radiation.
★ Know that surface temperature and surface area of an object affect the rate of emission of radiation.
On a sunny day it is pleasant to feel the warmth of the radiation reaching you from the Sun.
Radiation is the third way of transferring thermal energy from one place to another without the
need of a transmission medium. On reaching Earth, the Sun’s rays are partly reflected, absorbed or
transmitted by objects. Shiny white surfaces are good reflectors of radiation but dull black surfaces
are good absorbers. The efficiency of emission and absorption of radiation depends on the nature
of the surface of the material.
The rate of radiation emission depends on the temperature of the object. The temperature of the
Earth is controlled by the balance between radiation absorbed and emitted.
119
120
from the Earth’s surface. This has serious implications Rate of cooling of an object
for the global climate. For the average temperature
of the Earth to remain constant, a balance must be If the surface temperature of an object is higher
achieved between the incoming radiation and the than its surroundings, it emits radiation at a
radiation emitted from the Earth’s surface. faster rate than it absorbs radiation from its
If there is a build-up of carbon dioxide and surroundings. As a result, it cools until the two
methane gases in the atmosphere, the balance rates become equal and a constant temperature is
between incoming radiation from the Sun and reached. The higher the surface temperature of the
the average power emitted from the Earth will be object above its surroundings, and the larger its
upset. surface area, the greater the quantity of radiation
it emits and the greater its rate of cooling.
Practical work
Rate of cooling of heat. Use your results to plot a graph of
For safe experiments/demonstrations temperature against time.
related to this topic, please refer to the 1 In the above experiment a student
Cambridge IGCSE Physics Practical Skills recorded the following temperatures on the
Workbook that is also part of this series. thermometer as it cooled in air.
Test yourself
5 The door canopy in Figure 2.3.11 shows clearly the 6 What type of radiation is thermal radiation?
difference between white and black surfaces when
radiation falls on them. Explain why. 7 a The Earth has been warmed by the
radiation from the Sun for millions of
years yet we think its average temperature
has remained fairly steady. Why is this?
b Why is frost less likely on a cloudy night
than a clear one?
▲ Figure 2.3.11
121
★ Explain complex applications and consequences of conduction, convection and radiation involving more
than one type of thermal energy transfer.
You have now encountered the three ways in which thermal energy can be transferred from one
place to another: conduction, convection and radiation. Such transfers occur in many different
situations in everyday living. Transfer of thermal energy by conduction from an external source
enables us to heat cooking pots. Convection is often used in water and convector heaters in our
homes. Radiation from the Sun can be felt directly and an infrared thermometer allows us to
read temperature from a distance. In this topic you will learn more about the uses of both good
conductors and poor conductors (insulators).
Applications in which more than one type of thermal energy transfer is involved are explained.
Uses of conductors
Good conductors
These are used whenever heat is required to travel
quickly through something. Saucepans, boilers and
radiators are made of metals such as aluminium,
iron and copper which are all good conductors that
transfer thermal energy quickly.
Bad conductors (insulators)
The handles of some saucepans are made of wood
or plastic. Cork is used for table mats. These are ▲ Figure 2.3.12a Lagging in a cavity wall provides extra
insulating materials that transfer thermal energy insulation.
only very slowly.
Air is one of the worst conductors and so one of
the best insulators. This is why houses with cavity
walls (two layers of bricks separated by an air space)
and double-glazed windows keep warmer in winter
and cooler in summer.
Because air is such a bad conductor, materials
that trap air, such as wool, felt, fur, feathers,
polystyrene foam and fibreglass, are also very
bad conductors. Some of these materials are used
as ‘lagging’ to insulate water pipes, hot water
cylinders, ovens, refrigerators and the walls and
roofs of houses (Figures 2.3.12a and 2.3.12b).
Others are used to make warm winter clothes like
fleece jackets (Figure 2.3.12c on the next page). ▲ Figure 2.3.12b Laying lagging in a house loft
122
123
Uses of radiation: infrared can be determined from the radiant power detected
and the value is shown on a digital display. It is a
thermometer non-contact method and allows temperature to be
An infrared thermometer detects the thermal measured at a distance. Infrared thermometers are
radiation emitted by an object and converts it into frequently used to monitor the health of passengers
an electrical signal. The temperature of the object arriving at an airport.
which absorb it. Air in contact with the hot wood silvered surfaces
or coal is warmed and rises upwards because it is
less dense than the cold air above. Cooler air is case
drawn down to take its place and a convection vacuum
current is set up which also serves to transfer heat felt pad
into the room. ▲ Figure 2.3.13 The structure of a vacuum flask
Test yourself
8 Explain why on a cold day the metal handlebars of a
9 Name the energy transfers which occur
bicycle feel colder than the rubber grips.
a when a radiator is used to cool the engine
of a car
b when a room is heated by a coal fire.
124
Revision checklist
After studying Topic 2.3 you should know and ✔ describe experiments to show convection in fluids
understand: (liquids and gases) and relate convection in fluids
✔ that thermal energy transferred by radiation does to density changes
not require a medium and that thermal radiation is ✔ describe the effect of surface colour and texture
infrared radiation emitted by all objects on the emission, absorption and reflection of
radiation and recall that good absorbers are also
✔ that for an object at a constant temperature, the good emitters
rate at which it receives radiation equals the
rate that it transfers radiation ✔ describe experiments to study factors affecting
✔ the rate of radiation emission increases as the the absorption and emission of radiation
temperature of the object increases ✔ explain how a greenhouse acts as a ‘heat-trap’
and the consequence for the balance between
✔ how thermal insulation is used to keep liquids cool incoming and emitted radiation at the Earth’s
and to reduce heat loss from buildings. surface
After studying Topic 2.3 you should be able to:
✔ explain some simple uses and consequences of
✔ describe experiments to show the different
conduction, convection and radiation
conducting powers of various substances and
name good and bad conductors ✔ explain applications involving more than one
type of thermal energy transfer.
✔ explain conduction using the kinetic particle
model
125
Exam-style questions
1 Describe an experiment to demonstrate the 7 Explain why
properties of good and bad thermal conductors. a newspaper wrapping keeps hot things hot,
[Total: 4] e.g. fish and chips, and cold things cold,
e.g. ice cream [1]
2 Explain in terms of particles how thermal b fur coats would keep their wearers warmer
energy is transferred by conduction in solids. if they were worn inside out [2]
[Total: 4] c a string vest helps to keep a person warm
even though it is a collection of holes
3 a Explain how thermal energy is transferred bounded by string. [2]
by convection. [3] [Total: 5]
b Describe an experiment to illustrate
convection in a liquid. [3] 8 Figure 2.3.14 illustrates three ways of reducing
[Total: 6] heat losses from a house.
a Explain how each of the three methods
4 The following statements relate to the absorption reduces heat losses. [4]
and emission of radiation. b Why are fibreglass and plastic foam good
State which of the statements are true and which substances to use? [2]
are false. c Air is one of the worst conductors of heat.
A Energy from the Sun reaches the Earth by What is the advantage of replacing it by
radiation only. [1] plastic foam as shown in Figure 2.3.14? [1]
B A dull black surface is a good absorber of d A vacuum is an even better heat insulator
radiation. [1] than air. Suggest one (scientific) reason why
C A shiny white surface is a good emitter of the double glazing should not have a vacuum
radiation. [1] between the sheets of glass. [1]
D The best heat insulation is provided by a [Total: 8]
vacuum. [1]
[Total: 4] a
5 Describe the effect of surface colour and texture house roof rafter
on the
a emission of radiation [2] fibreglass laid
b reflection of radiation [2] between rafters
Alternative to Practical
9 The manufacturers of roof insulation suggest that
two layers of fibreglass are more effective than
one. Describe how you might set up an experiment
in the laboratory to test whether this is true.
[Total: 6]
126
Ripples spread out from a stone dropped into a pond and you can see that energy is transferred
across the water, but a leaf resting on the surface of the pond only bobs up and down when the ripple
passes. You will find out in this topic that waves are disturbances that transfer energy from one
point to another without transport of matter. The vibrations in a wave can lie along the path, as in
sound waves, or be perpendicular, as in water waves. You will learn how to represent waves in terms
of general properties that apply to light, sound, seismic and water waves. You will also learn how
ripple tank experiments are used to model the reflection of waves when they strike a plane surface
or enter a medium in which their speed changes and how waves may spread out when they pass
through gaps.
Types of wave motion moving the other rapidly up and down (Figure 3.1.1).
The disturbance generated by the hand is passed
Several kinds of wave motion occur in physics. on from one part of the rope to the next which
Mechanical waves are produced by a disturbance, performs the same motion but slightly later. The
such as a vibrating object, in a material medium humps and hollows of the wave travel along the rope
and are transmitted by the particles of the medium as each part of the rope vibrates transversely about
vibrating about a fixed position. Such waves can be its undisturbed position.
seen or felt and include waves on a rope or spring, Water waves can be modelled as transverse
water waves and sound waves in air or in other waves, as can seismic S-waves (see Topic 3.4).
materials. In Topic 3.3 we will find that electromagnetic
A progressive wave or travelling wave is a radiations are also transverse waves.
disturbance which carries energy from one place to
direction of wave
another without transferring matter. There are two hump
types, transverse and longitudinal waves.
128
position
The faster the end of a rope is vibrated, the shorter
a crest distance the wavelength of the wave produced. That is, the
A B C D
trough higher the frequency of a wave, the smaller its
a
wavelength. There is a useful connection between f,
λ and v, which is true for all types of wave.
λ Suppose waves of wavelength λ = 20 cm travel
▲ Figure 3.1.3 Displacement–distance graph for a wave at a
on a long rope and three crests pass a certain
particular instant point every second. The frequency f = 3 Hz.
If Figure 3.1.4 represents this wave motion then,
if crest A is at P at a particular time, 1 second
Wavelength later it will be at Q, a distance from P of three
The wavelength of a wave, represented by the wavelengths, i.e. 3 × 20 = 60 cm.
Greek letter λ (‘lambda’), is the distance between
successive crests (peaks) (see Figure 3.1.3).
129
Practical work
Test yourself
5 cm
1 The lines in Figure 3.1.6 are crests of straight ripples.
a What is the wavelength of the ripples?
b If 5 seconds ago ripple A occupied the position
now occupied by ripple F, what is the frequency of
the ripples?
c What is the speed of the ripples? F E D C B A Figure 3.1.6
▲
130
Wavefronts and rays wavelength than those in the deeper parts, i.e. the
wavefronts are closer together (Figure 3.1.8). Both
In two dimensions, a wavefront is a line on which sets of waves have the frequency of the vibrating
the disturbance has the same phase at all points; bar and, since v = fλ, if λ has decreased so has v,
the crests of waves in a ripple tank can be thought since f is fixed. Hence waves travel more slowly in
of as wavefronts. A vibrating source produces a shallow water.
succession of wavefronts, all of the same shape. In
a ripple tank, straight wavefronts are produced by a
vibrating bar (a line source) and circular wavefronts
are produced by a vibrating ball (a point source).
A line drawn at right angles to a wavefront, which
shows its direction of travel, is called a ray. Straight
wavefronts and the corresponding rays are shown
in Figure 3.1.7; circular wavefronts can be seen in
Figure 3.1.16 (p. 134).
▲ Figure 3.1.8 Waves in shallower water have a shorter
The properties of waves (reflection at a wavelength.
plane surface, refraction and diffraction) can be
illustrated by the behaviour of water waves in a When the plate is at an angle to the waves (Figure
ripple tank. 3.1.9a), their direction of travel in the shallow
region is bent towards the normal (Figure 3.1.9b).
Reflection at a plane surface The change in the direction of travel of the
waves, which occurs when their speed and hence
In Figure 3.1.7 straight water waves are falling on wavelength changes, is termed refraction.
a metal strip placed in a ripple tank at an angle of
60°, i.e. the angle i between the direction of travel
of the waves and the normal to the strip is 60°, as
is the angle between the wavefront and the strip.
(The perpendicular to the strip at the point where
the incident ray strikes is called the normal.) The
wavefronts are represented by straight lines and can
be thought of as the crests of the waves. They are
at right angles to the direction of travel, i.e. to the
rays. The angle of reflection r is 60°. Incidence at ▲ Figure 3.1.9a Waves are refracted at the boundary
other angles shows that the angle of incidence and between deep and shallow regions.
angle of reflection are always equal.
incident wavefront normal reflected wavefront slow
direction r
of travel shallow water deep water
i r metal strip
i
fast
▲ Figure 3.1.7 Reflection of waves
▲ Figure 3.1.9b The direction of travel is bent towards the
Refraction normal in the shallow region.
If a glass plate is placed in a ripple tank so that the The speed of waves also changes, and refraction
water over the glass plate is about 1 mm deep but occurs, when waves move from one medium to
is 5 mm deep elsewhere, continuous straight waves another. For example, light waves are refracted when
in the shallow region are found to have a shorter they move from air to glass.
131
Diffraction
Diffraction through a narrow gap
In Figures 3.1.10a and 3.1.10b, straight water
waves in a ripple tank are meeting gaps formed by
obstacles. In Figure 3.1.10a the gap is narrow and
the wavefronts curve around the edges of the gap
producing a circular wavefront.
Diffraction at an edge
For a single edge, diffraction will occur at
the edge. The spreading and curvature of
the wavefront around the edge will be more
▲ Figure 3.1.10a Spreading of waves after passing through noticeable for longer wavelengths. Diffraction
a narrow gap of radio waves around an obstacle is shown in
Figure 3.3.4a.
Test yourself
2 One side of a ripple tank ABCD is raised slightly
(Figure 3.1.12), and a ripple is started at P by a
finger. After 1 second the shape of the ripple is as
shown.
a Why is it not circular?
b Which side of the tank has been raised?
A B
tank
▲ Figure 3.1.10b Spreading of waves after passing through
a wide gap ripple
P
D C
▲ Figure 3.1.12
132
3 The angle of incidence of a ray at a plane reflecting 5 When a wave passes through a narrow gap, which of
surface is 35°. What will be the angle of reflection? the following terms best describes what occurs?
4 During the refraction of a wave, which one of the A Reflection
following properties does not change? B Refraction
A The wave speed C Diffraction
B The frequency D Inversion
C The wavelength
D Direction of travel
Going further
Wave theory be found using Huygens’ construction. A circle of radius
BB′ is drawn about A; the reflected wavefront is then
If the position of a wavefront is known at one instant,
A′B′, the tangent to the wavelet from B′. Measurements
its position at a later time can be found using Huygens’
of the angle of incidence i and the angle of reflection r
construction. Each point on the wavefront is considered
show that they are equal.
to be a source of secondary spherical wavelets (Figure
3.1.13) which spread out at the wave speed; the new A C
wavefront is the surface that touches all the wavelets constructed wavefront
(in the forward direction). In Figure 3.1.13 the straight
wavefront AB is travelling from left to right with speed v. secondary source
At a time t later, the spherical wavelets from AB will be
a distance vt from the secondary sources and the new
surface which touches all the wavelets is the straight
wavefront CD.
Wave theory can be used to explain reflection, first position of
refraction and diffraction effects. wavefront
vt
Reflection and wave theory
B D
Figure 3.1.14 shows a straight wavefront AB incident at
an angle i on a reflecting surface; the wavefront has just secondary wavelet
reached the surface at A. The position of the wavefront
a little later, when B reaches the reflecting surface, can ▲ Figure 3.1.13 Huygens’ construction for a straight
wavefront
i r
i r
A B'
▲ Figure 3.1.14 Reflection of a straight wavefront
133
134
Revision checklist
After studying Topic 3.1 you should know and After studying Topic 3.1 you should be able to:
understand the following: ✔ describe the production and give examples of
✔ the direction of vibration for transverse and transverse and longitudinal waves and use the
longitudinal wave motion and that waves transfer wave equation v = fλ to solve problems
energy without transferring matter ✔ describe experiments and draw diagrams to show
✔ the meaning of wavelength, frequency, wave speed, reflection, refraction and diffraction of water
amplitude, crest (peak), trough and wavefront. waves
Exam-style questions
1 Figure 3.1.19 gives a full-scale representation 8
A 2
0 2 4 6 8 10 12
▲ Figure 3.1.20
▲ Figure 3.1.19 b When a water wave goes from deep to shallow
a What is represented at A at this instant? [1] water, the changes (if any) in its wave speed,
b Estimate wavelength and frequency are described by
i the wavelength [2] which of the following options: [1]
ii the wave speed [3] Wave speed Wavelength Frequency
iii the frequency of the vibrator. [2] A greater greater the same
c Describe a suitable attachment which could
have been vibrated up and down to produce B less less the same
this wave pattern. [2] C the same less greater
[Total: 10] D less the same less
2 a In the transverse wave shown in Figure 3.1.20 [Total: 2]
distances are in centimetres. Which pair of
entries A to D is correct? [1] 3 Copy Figure 3.1.21 and show on it what
happens to the waves as they pass through the
A B C D
gap if the water is much shallower on the right
Amplitude 2 4 4 8 side of the gap than on the left.
Wavelength 4 4 8 8
▲ Figure 3.1.21
[Total: 6]
135
In the last topic you learnt about some of the general properties of waves by studying the behaviour
of water waves. Water waves are transverse waves but so too are light waves and you can expect
them both to have similar properties. In this topic you will explore how light is reflected by a plane
surface. Reflection is made use of in mirrors and instruments such as a periscope. You may have
noticed that images in a plane mirror are laterally inverted. This happens because reflection
produces an apparent image of an object behind the surface of the mirror; this virtual image is the
same size as the object but has left and right switched.
non-luminous
objects reflecting
light
screen
(greaseproof
black paper over
paper square hole
in box)
round
hole in box
box
small
pinhole
b large
pinhole
▲ Figure 3.2.3 Light travels in straight lines.
ray
small
pinhole
Practical work A
pinhole
B'
object image
The pinhole camera A'
B
Safety ▲ Figure 3.2.6 Forming an image in a pinhole camera
● Take care when using the needle to make
1 Can you see three ways in which the image
the pinhole.
differs from the object?
A simple pinhole camera is shown in Figure 2 What is the effect of moving the camera
3.2.5a. Make a small pinhole in the centre of closer to the object?
the black paper. Half darken the room. Hold 3 Make the pinhole larger. What happens to
the box at arm’s length so that the pinhole end the
is nearer to and about 1 metre from a luminous a brightness
object, such as a carbon filament lamp or b sharpness
a candle. Look at the image on the screen c size of the image?
137
Going further
Reflection of light
If we know how light behaves when it is reflected,
Shadows we can use a mirror to change the direction in which
Shadows are formed for two reasons. First, because the light is travelling. This happens when a mirror is
some objects, which are said to be opaque, do not placed at the entrance of a concealed drive to give
allow light to pass through them. Secondly, light warning of approaching traffic, for example.
travels in straight lines. An ordinary mirror is made by depositing a thin
The sharpness of the shadow depends on the size of layer of silver on one side of a piece of glass and
the light source. A very small source of light, called a protecting it with paint. The silver – at the back of
point source, gives a sharp shadow which is equally the glass – acts as the reflecting surface. A plane
dark all over. This may be shown as in Figure 3.2.7a mirror is produced when the reflecting surface is flat.
where the small hole in the card acts as a point
source.
Law of reflection
a small hole
Terms used in connection with reflection are shown
card
screen in Figure 3.2.8. The perpendicular to the mirror at
the point where the incident ray strikes is called
sharp the normal. Note that the angle of incidence i is
100 watt shadow the angle between the incident ray and the normal;
lamp
metal ball
similarly, the angle of reflection r is the angle
between the reflected ray and the normal.
to mains supply
b Key definitions
Normal line which is perpendicular to a surface
penumbra
Angle of incidence angle between incident ray and the
umbra normal to a surface
Angle of reflection angle between reflected ray and the
normal to a surface
▲ Figure 3.2.7 Forming a shadow Law of reflection the angle of incidence is equal to the
angle of reflection
If the card is removed the lamp acts as a large or
extended source (Figure 3.2.7b). The shadow is
then larger and has a central dark region, the plane
umbra, surrounded by a ring of partial shadow, the mirror
penumbra. You can see by the rays that some light
reaches the penumbra, but none reaches the umbra. i r
Speed of light
Proof that light travels very much faster than sound
is provided by a thunderstorm. The flash of lightning incident normal reflected
is seen before the thunder is heard. The length of ray ray
the time lapse is greater the further the observer is ▲ Figure 3.2.8 Reflection of light by a plane mirror
from the storm.
The speed of light has a definite value; light The law of reflection states:
does not travel instantaneously from one point to The angle of incidence is equal to the angle of
another but takes a certain, very small time. Its reflection.
speed is about 1 million times greater than that
of sound. The incident ray, the reflected ray and the normal
all lie in the same plane. (This means that they
could all be drawn on a flat sheet of paper.)
138
shield
lamp
and stand
60°75° A
45°
single 30°
slit 15°
N
O
sheet
of paper
B
plane
mirror
▲ Figure 3.2.9 ▲ Figure 3.2.11 Periscopes being used by people in a crowd.
Mark the position of the reflected ray, remove
In more elaborate periscopes like those used in
the mirror and measure the angle between the
submarines, prisms replace mirrors (see p. 148).
reflected ray and ON. Repeat for rays at other
Make your own periscope from a long, narrow
angles.
cardboard box measuring about 40 cm × 5 cm × 5 cm
4 In the experiment what can you conclude (such as one in which aluminium cooking foil or
about the incident and reflected rays? clingfilm is sold), two plane mirrors (7.5 cm × 5 cm)
5 The silver surface on a mirror is usually on and sticky tape. When you have got it to work, make
the back surface of the glass. How might this modifications that turn it into a ‘see-back-o-scope’,
affect the accuracy of your measurements? which lets you see what is behind you.
139
white paper
Plasticine arrow
block to support glass vertically
▲ Figure 3.2.13
140
N
Kaleidoscope
real rays
▲ Figure 3.2.14 A plane mirror forms a virtual image.
Going further
Lateral inversion
If you close your left eye, your image in a plane mirror
seems to close the right eye. In a mirror image, left
and right are interchanged and the image appears to
be laterally inverted. The effect occurs whenever an
image is formed by one reflection and is very evident
if print is viewed in a mirror (Figure 3.2.15). What
happens if two reflections occur, as in a periscope?
141
sheet of paper
Test yourself
1 How would the size and brightness of the image P
formed by a pinhole camera change if the camera
were made longer?
Q
2 What changes would occur in the image if the single
pinhole in a camera were replaced by
a four pinholes close together R
b a hole 1 cm wide?
3 In Figure 3.2.18 the completely dark region on the S
lamp object
screen is
A PQ B PR C QR D QS
4 When watching a distant firework display do you
screen
see the cascade of lights before or after hearing the
associated bang? Explain your answer. ▲ Figure 3.2.18
142
5 A ray of light strikes a plane mirror at an angle of 7 Figure 3.2.20 shows the image in a plane mirror of a
incidence of 60°, is reflected from the mirror and clock. The correct time is
then strikes a second plane mirror placed so that A 2.25 B 2.35 C 6.45 D 9.25
the angle between the mirrors is 45°. The angle
of reflection at the second mirror, in degrees, is
A 15 B 25 C 45 D 65
C
▲ Figure 3.2.20
object
▲ Figure 3.2.19
If you place a coin in an empty dish and move back until you just cannot see it, the result is
surprising if someone gently pours water into the dish. Try it! In this topic, you will see that, as with
water waves, when a parallel beam of light travels from one medium to another it changes direction
if the speed of light differs in the second medium. For passage from air to a transparent medium,
the angles to the normal to the surface for the incident and refracted beams are related through the
refractive index. At the critical angle of incidence from a transparent medium to air, the refracted
beam lies along the surface. At greater angles of incidence, the beam is totally internally reflected.
Total internal reflection is used in optical fibres to transmit images and signals in applications from
medicine to telecommunications.
143
Although light travels in straight lines in a (ii) A ray of light is bent away from the normal when
transparent material, such as air, if it passes into it enters an optically less dense medium, for
a different material, such as water, it changes example from glass to air.
direction at the boundary between the two, i.e. it (iii) A ray emerging from a parallel-sided block is
is bent. The bending of light when it passes from parallel to the ray entering, but is displaced
one material (called a medium) to another is called sideways, like the ray in Figure 3.2.21a.
refraction. It causes effects such as the coin trick. (iv) A ray travelling along the normal direction at a
Terms used in connection with refraction are boundary is not refracted (Figure 3.2.21b).
shown in Figure 3.2.21. The perpendicular to the
Note that ‘optically denser’ means having a greater
boundary between two mediums is called the
refraction effect; the actual density may or may not
normal. The angle of incidence i is the angle
be greater.
between the incident ray and the normal; similarly,
the angle of refraction r is the angle between the a b
refracted ray and the normal. normal normal
i
air
Key definitions
Angle of refraction angle between refracted ray and the
normal to a surface r
glass glass
Facts about refraction
(i) A ray of light is bent towards the normal when it
air
enters an optically denser medium at an angle, normal
Practical work
Refraction in glass
For safe experiments/demonstrations related shield
to this topic, please refer to the Cambridge
IGCSE Physics Practical Skills Workbook that
is also part of this series.
Safety
● Take care as the filament lamp and shield will sheet
of paper
get hot when in use. lamp
and stand
Shine a ray of light at an angle onto a glass block single A D
(which has its lower face painted white or is slit
frosted), as in Figure 3.2.22. Draw the outline
normal
ABCD of the block on the sheet of paper under it.
Mark the positions of the various rays in air and
in glass.
B C
Remove the block and draw the normals on the
glass block
paper at the points where the ray enters side AB
(see Figure 3.2.22) and where it leaves side CD. ▲ Figure 3.2.22
144
10 What two things happen to the light falling 13 What can you say about the direction of the
on AB? ray falling on AB and the direction of the ray
11 When the ray enters the glass at AB, is it bent leaving CD?
towards or away from the part of the normal in 14 What happens if the ray hits AB at right
the block? angles?
12 How is it bent at CD?
Key definition
Refractive index n the ratio of the speeds of a wave in
two different regions
145
A B
A Critical angle
A When light passes at small angles of incidence from
an optically dense to a less dense medium, such as
from glass to air, there is a strong refracted ray and
▲ Figure 3.2.25a a weak ray reflected back into the denser medium
(Figure 3.2.26a). As well as refraction, some internal
reflection occurs. Increasing the angle of incidence
300 000 km/s
increases the angle of refraction.
air a
air
glass
glass
200 000 km/s
3
n 2
▲ Figure 3.2.25b
b
We saw earlier (Topic 3.1) that water waves are
air
refracted when their speed changes. The change
in the direction of travel of a light ray when glass
its speed changes on entering another medium c c
suggests that light may also be a type of wave
motion.
c critical angle
Worked example
c
air
The refractive index for a certain glass is 1.6.
a Calculate the angle of refraction for an angle of
glass
incidence of 24°.
sin i
n=
sin r
so sin r = sin i/n
= sin 24°/1.6 ▲ Figure 3.2.26
ray of L
Worked example
light
If the critical angle for diamond is 24°, calculate its
sheet of
paper refractive index.
critical angle, c = 24°
angle of sin 24° = 0.4
incidence sin 90° 1
N O n= =
sin c sin 24°
1
= = 2.5
0.4
147
glass main
image Light pipes and optical fibres
O I1 I I2 Light can be trapped by total internal reflection
object inside a bent glass rod and piped along a curved
path (Figure 3.2.30). A single, very thin glass
fibre, an optical fibre, behaves in the same way.
silvering
▲ Figure 3.2.28a Multiple reflections in a mirror ▲ Figure 3.2.30 Light travels through a curved glass rod
or optical fibre by total internal reflection.
45°
45°
45°
Q
R
▲ Figure 3.2.31b Trachea (windpipe) viewed by an
endoscope
▲ Figure 3.2.29 Reflection of light by a prism
148
Increasingly, optical fibres are being used to because the cables are unaffected by electronic
carry telephone, high-speed broadband internet interference. They can be used over longer
and cable TV signals as pulses of visible or distances (since they have lower power loss), are
infrared light. The advantages over copper cables made of cheaper material and, as they are lighter
for telecommunication purposes are that the use and thinner, are easier to handle and install.
of light allows information to be transmitted However, they are not as robust as copper cables
at a higher rate and the data is more secure and can break if bent too much.
Test yourself
8 Figure 3.2.32 shows a ray of light entering a 11 Which diagram in Figure 3.2.33 shows the ray of
rectangular block of glass. light refracted correctly?
a Copy the diagram and draw the normal at the
A B
point of entry.
b Sketch the approximate path of the ray through
the block and out of the other side. water air
air glass
C D
glass water
air glass
▲ Figure 3.2.32
60°
glass
air
glass
45°
60°
▲ Figure 3.2.34
149
★ Describe the characteristics of an image in terms of size, orientation and whether it is real or virtual.
★ Know that when diverging rays are extrapolated backwards a virtual image is formed, which does not form
a visible projection on a screen.
★ Describe how long- and short-sightedness can be corrected through the use of converging and diverging
lenses.
In the last topic you learnt about refraction at plane surfaces. Lenses make use of the refraction
of light at carefully shaped curved surfaces to form images. For a thin converging lens with convex
surfaces, a parallel beam of light is brought to a focus; the principal focus is real and a range of
images can be produced. A diverging lens with concave surfaces has an apparent principal focus and
always produces a diminished virtual image.
A converging lens is used for a magnifying glass. Both converging and diverging lenses are used in
spectacles to correct long- and short-sightedness.
150
▲ Figure 3.2.36a A converging lens forms a magnified ▲ Figure 3.2.36b A diverging lens always forms a
image of a close object diminished image
Practical work
close point
Focal length, f, of a converging lens
For safe experiments/demonstrations related diverging beam
to this topic, please refer to the Cambridge
IGCSE Physics Practical Skills Workbook that distant point
is also part of this series.
almost parallel beam
We use the fact that rays from a point on a very
distant object, i.e. at infinity, are nearly parallel very
(Figure 3.2.37a). distant
point parallel beam
▲ Figure 3.2.37a
151
ruler screen 2F F F 2F
or wall
▲ Figure 3.2.37b
152
F I 2F
Going further
O 2F F C
image Magnification
B The linear magnification M is given by
image size
Image is between F and 2F, real, inverted, diminished M=
object size
▲ Figure 3.2.39a Object beyond 2F
It can be shown that in all cases
A distance of image from lens
M=
distance of object from lens
O F 2F
I
Power of a lens
2F F C
The shorter the focal length of a lens, the stronger
image it is, i.e. the more it converges or diverges a beam
B of light. We define the power of a lens, P, to be
Image is at 2F, real, inverted, same size 1/focal length of the lens, where the focal length is
measured in metres:
▲ Figure 3.2.39b Object at 2F
1
P=
f
A
F 2F I
2F O F C
image
153
β
from point I
on distant
object
b
b
object α
▲ Figure 3.2.40 Magnification by a converging lens: angle
β is larger than angle α I
The fatter (more curved) a converging lens is, the
shorter its focal length and the more it magnifies.
Too much curvature, however, distorts the image.
▲ Figure 3.2.42 Short sight and its correction by a
Spectacles diverging lens
From the ray diagrams shown in Figure 3.2.39
(p. 153) we would expect that the converging lens Long sight
in the eye will form a real inverted image on the A long-sighted person sees distant objects clearly
retina as shown in Figure 3.2.41. Since an object but close objects appear blurred. The image of a
normally appears upright, the brain must invert near object is focused behind the retina because
the image. the eyeball is too short or because the eye lens
154
▲ Figure 3.2.44
You can see the different colours which make up visible light in a rainbow. The sunlight is refracted
by raindrops and a spectrum of colours from violet to red is produced. In this topic you will learn
that the different colours which make up white light can also be separated by using a glass prism.
The frequency of light determines its colour. The speed of light in a transparent medium depends on
frequency, and so for a common incidence angle, the angle of refraction will vary with the colour of
the light. The different colours are spread out into a spectrum and the effect is termed dispersion.
155
red
orange
yellow C D
sunlight prism green
spectrum blue
indigo
violet
▲ Figure 3.2.48
▲ Figure 3.2.46a Forming a spectrum with a prism
156
Revision checklist
After studying Topic 3.2 you should know and After studying Topic 3.2 you should be able to:
understand: ✓ describe an experiment to show that the angle of
✓ the meaning of the terms normal, angle of incidence equals the angle of reflection and use
incidence and angle of reflection the law of reflection to solve problems
✓ describe the formation of an optical image in a
✓ how to construct, calculate and measure plane mirror and recall the properties of the image
reflections from plane mirrors ✓ describe the passage of light through a
transparent medium and an experiment to study
✓ the meaning of the terms refraction, critical angle, refraction
internal reflection and total internal reflection
✓ the terms used to describe images formed in ✓ calculate refractive index, critical angles and
lenses describe some uses of optical fibres
✓ how simple converging and diverging lenses ✓ define the terms optical centre, principal axis,
are used to correct long and short sight principal focus and focal length
✓ draw diagrams showing the effects of converging
✓ how a prism is used to produce a spectrum from and diverging lenses on a beam of parallel rays and
white light the formation of real images by a converging lens
✓ the terms spectrum, dispersion
✓ draw diagrams showing formation of a virtual
✓ the term monochromatic light. image by a converging lens
157
▲ Figure 3.2.50 C
158
▲ Figure 3.2.53
focus
B
18 cm 6 cm
▲ Figure 3.2.54
[Total: 10]
159
★ Know the speed of electromagnetic waves in a vacuum and that it is approximately the same in air.
Visible light forms only a small part of a very wide spectrum of electromagnetic waves, all of
which travel with the speed of light in a vacuum. You will find that the properties of the different
classes of waves vary with frequency from the lowest frequency radio waves through microwaves
to infrared, visible and ultraviolet light, with X-rays and gamma rays at the highest frequencies.
The various electromagnetic waves have a wide range of uses from communications and cooking to
food sterilisation. The energy associated with an electromagnetic wave increases with frequency, so
the highest frequencies are the most dangerous. Damage from over-exposure includes burns from
infrared, sunburn and eye damage from ultraviolet and cell damage from X-rays and gamma rays.
typical
wave length: 0.01 nm 1 nm 0.1 0.4 0.7 0.01 mm 1 cm 1m 1 km
µm µm µm
wavelength decreases wavelength increases
1 nm = 10 –9 m
1 µm = 10 –6 m
Light is one member of the family of electromagnetic electromagnetic spectrum with their corresponding
radiation which forms a continuous spectrum wavelengths. Note that the wavelength increases
beyond both ends of the visible (light) spectrum. from gamma rays to radio waves while the frequency
Figure 3.3.1 shows the main regions of the increases in the reverse direction (radio to gamma).
160
161
Test yourself
1 Give the approximate wavelength in micrometres
(µm) of
a red light
b violet light.
2 Which of the following types of radiation has
a the longest wavelength
b the highest frequency?
A ultraviolet
B radio waves
C light
D X-rays
Infrared radiation
Our bodies detect infrared radiation (IR) by its
heating effect on the skin. It is sometimes called ▲ Figure 3.3.3 Infrared aerial photograph for monitoring
‘radiant heat’ or ‘heat radiation’. land use
Anything which is hot but not glowing, i.e.
below 500°C, emits IR alone. At about 500°C a body
becomes red hot and emits red light as well as IR
Ultraviolet radiation
– the heating element of an electric fire, a toaster Ultraviolet (UV) rays have shorter wavelengths than
or an electric grill are examples. At about 1500°C, light. They cause sun tan and produce vitamins in
things such as lamp filaments are white hot and the skin but too high an exposure can be harmful.
radiate IR and white light, i.e. all the colours of the Ultraviolet radiation causes fluorescent paints
visible spectrum. and clothes washed in some detergents to fluoresce.
Infrared is also used in thermal imaging cameras, They glow by re-radiating as light the energy they
which show hot spots and allow images to be taken absorb as UV. This effect may be used in security
in the dark. Infrared sensors are used on satellites marking to verify ‘invisible’ signatures on bank
and aircraft for weather forecasting, monitoring of documents and to detect fake bank notes. Water
land use (Figure 3.3.3), assessing heat loss from treatment plants often use UV radiation to sterilise
buildings, intruder alarms and locating victims of water.
earthquakes. A UV lamp used for scientific or medical purposes
Infrared lamps are used to dry the paint on contains mercury vapour and this emits UV when an
cars during manufacture and in the treatment electric current passes through it. Fluorescent tubes
of muscular complaints. The remote control for also contain mercury vapour and their inner surfaces
an electronic device contains a small infrared are coated with special powders called phosphors
transmitter to send signals to the device, such as which radiate light.
a television or DVD player. These are short range
communication applications. Infrared is also used to
carry data in long range optical fibre communication
Radio waves
Radio waves have the longest wavelengths in the
systems (Topic 3.2.2).
electromagnetic spectrum. They are radiated from
Infrared radiation can cause burns to the skin
aerials and used to carry sound, pictures and other
and eye damage if the intensity is high.
information over long distances.
162
They are also reflected by layers of electrically satellites (Topic 1.5.1). The microwave signals are
charged particles in the upper atmosphere (the transmitted through the ionosphere by dish aerials,
ionosphere), which makes long-distance radio amplified by the satellite and sent back to a dish
reception possible (Figure 3.3.4b). aerial in another part of the world. Some satellite
a Diffraction of radio waves
phones also use low-orbit artificial satellites.
Microwaves are also used for radar detection of
ships and aircraft, and in police speed traps.
Microwaves can be used for cooking in a
microwave oven since they cause water molecules in
the moisture of the food to vibrate vigorously at the
frequency of the microwaves. As a result, heating
occurs inside the food which cooks itself.
Microwaves
Microwaves have wavelengths of a few cm. They
are used for international telecommunications
and direct broadcast satellite television relay via
geostationary satellites and for mobile phone
networks via microwave aerial towers and low-orbit ▲ Figure 3.3.5 X-rays cannot penetrate bone and metal.
163
Ultraviolet
voltage
‘low’
0
Communication systems time
164
165
Exam-style questions
1 The chart below shows the complete electromagnetic spectrum.
radio waves A infrared visible light B X-rays gamma rays
air glass
▲ Figure 3.3.7
A speed
B wavelength
C direction
D frequency [Total: 1]
166
★ Describe how loudness and pitch of sound waves are determined by amplitude and frequency.
★ Define the terms echo and ultrasound.
Sound waves are produced by vibrating sources. Whether from the vibrations in your vocal
cords, a violin string or a loudspeaker, all the speech, music and noise we hear around us are
transmitted by sound waves. Like waves on a spring, sound waves are longitudinal waves and
they require a medium in which to travel. In this topic you will learn that sound waves progress by
local compression and expansion of the transmitting medium. The speed of sound varies strongly
between materials from around 340 m/s in air to 1500 m/s in water. Sound waves have many of the
same properties as transverse waves and can be reflected (as in an echo), refracted and diffracted.
Reflected sound waves, used in sonar depth sounding at sea, can locate the position of a shoal of fish.
Ultrasound, with frequencies above the range of human hearing (around 20 kHz), is used for material
testing and medical imaging. Do you have some jewellery you would like cleaned? An ultrasonic
cleaner could help remove the dirt.
167
Compression and
audible to humans, 20 Hz to 20 000 Hz
rarefaction
A sound wave, produced for example by a Reflection and echoes
loudspeaker, consists of a train of compressions C Sound waves are reflected well from hard, flat
(where the air molecules are closer together) and surfaces such as walls or cliffs and obey the same
rarefactions R (where the air molecules are further laws of reflection as light. The reflected sound
apart) in the air (Figure 3.4.3). forms an echo; an echo is the reflection of a sound
wave.
168
Practical work
Speed of sound in air between the centres of the microphones with a
For safe experiments/demonstrations related metre ruler. With the small hammer and metal
to this topic, please refer to the Cambridge plate to one side of the ‘start’ microphone,
IGCSE Physics Practical Skills Workbook that produce a sharp sound. When the sound reaches
is also part of this series. the ‘start’ microphone, the timer should start;
when it reaches the ‘stop’ microphone, the timer
Set two microphones about a metre apart, and should stop. The time displayed is then the time t
attach one to the ‘start’ terminal and the other to taken for the sound to travel the distance d.
the ‘stop’ terminal of a digital timer, as shown in Record the time and then reset the timer; repeat
Figure 3.4.4. The timer should have millisecond the experiment a few times and work out an
accuracy. Measure and record the distance d average value for t.
169
prong
stem
▲ Figure 3.4.5 Musical instruments produce regular sound
vibrations.
▲ Figure 3.4.6 A tuning fork
Pitch
The pitch of a note depends on the frequency of the Loudness
sound wave reaching the ear, i.e. on the frequency A note becomes louder when more sound energy
of the source of sound. A high-pitched note has enters our ears per second than before. This will
a high frequency and a short wavelength. The happen when the source is vibrating with a larger
frequency of middle C is 256 vibrations per second amplitude. If a violin string is bowed more strongly,
or 256 Hz and that of upper C is 512 Hz. Notes are an its amplitude of vibration increases, as does that
octave apart if the frequency of one is twice that of of the resulting sound wave, and the note heard
the other. Pitch is like colour in light; both depend is louder because more energy has been used to
on the frequency. produce it.
170
Going further
Quality fundamental frequency, their quality differs. The ‘pure’
note of a tuning fork has a sine waveform and is the
The same note on different instruments sounds
simplest kind of sound wave.
different; we say the notes differ in quality or timbre.
The difference arises because no instrument (except Note that although the waveform on the CRO screen is
a tuning fork and a signal generator) emits a ‘pure’ transverse, it represents a longitudinal sound wave.
note, i.e. of one frequency. Notes consist of a main
or fundamental frequency mixed with others, called
overtones, which are usually weaker and have
frequencies that are exact multiples of the fundamental.
The number and strength of the overtones decides the tuning fork (sine wave) piano
quality of a note. A violin has more and stronger higher
overtones than a piano. Overtones of 256 Hz (middle C)
are 512 Hz, 768 Hz and so on.
The waveform of a note played near a microphone
connected to a cathode ray oscilloscope (CRO) can be violin
displayed on the CRO screen. Those for the same note
on three instruments are shown in Figure 3.4.7. Their ▲ Figure 3.4.7 Notes of the same frequency (pitch) but
different shapes show that while they have the same different quality
171
ultrasonic
waves
Worked example
A research ship is using sonar to map the seabed.
How deep is the water if an ultrasound pulse reflected from
the seabed takes 1.5 s to return to the ship? Take the speed
of sound in water to be 1400 m/s.
s
Rearrange the equation for speed v = to give s = v × t. ▲ Figure 3.4.9 Checking the development of a fetus using
t ultrasound imaging
If the depth of the seabed is d, the ultrasound must travel a
distance of 2d during time t between the transmission and
reception of the signal, then Other uses
v t 1400 m s × 1.5 s Ultrasound can also be used in ultrasound drills
2d = vt and d = = = 1050 m
2 2 to cut holes of any shape or size in hard materials
Now put this into practice such as glass and steel. Jewellery, or more
1 A fishing vessel is using sonar to monitor the position mundane objects such as street lamp covers, can
of shoals of fish. Calculate the depth of a shoal if an be cleaned by immersion in a tank of solvent which
ultrasound pulse reflected from the shoal takes 0.5 s to
has an ultrasound vibrator in the base.
return to the ship. Take the speed of sound in water to
be 1400 m/s.
172
Going further
Seismic waves to travel the shorter distance to Thailand. This was
because the route was through shallower water and the
Earthquakes produce both longitudinal waves (P-waves)
waves travelled more slowly. If an early-warning system
and transverse waves (S-waves) that are known as
had been in place, many lives could have been saved.
seismic waves. These travel through the Earth at
speeds of up to 13 000 m/s, with frequencies less than
100 Hz.
When seismic waves pass under buildings, severe
structural damage may occur. If the earthquake occurs
under the sea, the seismic energy can be transmitted to
the water and produce tsunami waves that may travel
for very large distances across the ocean. As a tsunami
wave approaches shallow coastal waters, it slows down
(see Topic 3.1) and its amplitude increases, which can
lead to massive coastal destruction. This happened
in Sri Lanka (see Figure 3.4.10) and Thailand after the
great 2004 Sumatra–Andaman earthquake. The time of
arrival of a tsunami wave can be predicted if its speed
of travel and the distance from the epicentre of the
earthquake are known; it took about 2 hours for tsunami ▲ Figure 3.4.10 This satellite image shows the tsunami
waves to cross the ocean to Sri Lanka from Indonesia. that hit the south-western coast of Sri Lanka on
A similar time was needed for the tsunami waves 26 December 2004 as it pulled back out to sea, having
caused utter devastation in coastal areas.
Test yourself
7 a State the approximate range of frequencies of the 9 a What properties of sound suggest it is a wave
human ear. motion?
b State an approximate value for the speed of b How does a progressive transverse wave differ
sound in air. from a longitudinal one? Which type of wave is a
8 If 5 seconds elapse between a lightning flash and the sound wave?
clap of thunder, how far away is the storm? (Speed of
sound = 330 m/s)
Revision checklist
After studying Topic 3.4 you should know and ✔ describe experiments to show that sound is not
understand: transmitted through a vacuum and measure the
✔ that sound is produced by vibrating sources and speed of sound in air
echoes are produced by reflection of sound waves ✔ recall the value of the speed of sound in air
✔ the term ultrasound and know its frequency
✔ recall that in general sound travels faster in
✔ some uses of ultrasound. solids that in liquids and faster in liquids than
in gases
After studying Topic 3.4 you should be able to:
✔ state the limits of audibility for the normal human
✔ describe the longitudinal nature of sound waves
ear
✔ describe compression and rarefaction ✔ relate the loudness and pitch of sound waves to
amplitude and frequency.
173
Exam-style questions
1 a A girl stands 160 m away from a high wall 3 a Explain with reference to a sound wave
and claps her hands at a steady rate so that what is meant by the terms
each clap coincides with the echo of the one i compression [3]
before. If her clapping rate is 60 per minute, ii rarefaction. [3]
state the value this gives for the speed of b State how far a compression and the
sound. [3] nearest rarefaction are apart in terms of
b If she moves 40 m closer to the wall she finds the wavelength of a sound wave. [1]
the clapping rate has to be 80 per minute. c A sound wave has a frequency of 220 Hz
Calculate the value these measurements give and travels in air with a speed of
for the speed of sound. [3] 330 m/s. Calculate the distance between
c She moves again and finds the clapping rate consecutive rarefactions. [3]
becomes 30 per minute. Calculate how far she [Total: 10]
is from the wall if the wave speed of sound is
the value you found in a. [4] 4 a Name the state of matter in which
[Total: 10] sound waves travel
i fastest [1]
2 a Draw the waveform of ii slowest. [1]
i a loud, low-pitched note [2] b Describe how sound waves are used in
ii a soft, high-pitched note. [2] sonar. [4]
b If the speed of sound is 340 m/s what is c Name two uses of ultrasound other than
the wavelength of a note of frequency sonar. [2]
i 340 Hz [3] [Total: 8]
ii 170 Hz? [2]
[Total: 9]
174
★ State the differences between temporary and permanent magnets and between magnetic and non-
magnetic materials.
★ Describe, draw and state the direction of magnetic fields.
★ Know that the spacing of the magnetic field lines represents the relative strength of a magnetic field.
★ Describe how magnetic field lines can be plotted using a compass or iron filings.
★ Know the different uses of permanent magnets and electromagnets.
A familiar example of a magnet is a compass needle with one north-seeking pole. You will find that
all magnets have two poles: like poles repel, unlike poles attract. A magnet can induce magnetism
in certain materials such as iron and steel and is surrounded by a magnetic field which exerts a
force on another magnet. The pattern of magnetic field lines can be made visible with the aid of iron
filings. Electromagnets are formed from coils of wire through which an electrical current is passed
that allows the strength of the magnet to be varied and turned on and off easily. They are used
in many electrical devices from doorbells to motors. You will learn that permanent magnets and
electromagnets have differing properties and uses.
In a magnetic field, the closer the field lines are at a point, the stronger is the magnetic field.
176
permanent induced
magnet magnet N S
▲ Figure 4.1.1 Induced magnetism S N
iron nails
This can be checked by hanging two iron nails from N S
the N pole of a magnet. Their lower ends repel each S
steel paper
N
other (Figure 4.1.2a) and both are repelled further N
clips
S
from each other when the N pole of another magnet N
S
is brought close (Figure 4.1.2b).
N S
a b
S S S N
N S
▲ Figure 4.1.2 Magnetic repulsion
177
Test yourself
1 Which one of these statements is true? Copy the diagram and mark on the position of all the
A magnet attracts poles if the magnets
A plastics a attract each other
B any metal b repel each other.
C iron and steel
D aluminium. 3 In Figure 4.1.8a on the next page, is the magnetic
2 Two bar magnets are positioned side by side as field stronger or weaker at X than at a point
shown in Figure 4.1.5. The north pole is marked on closer to one of the magnets? Explain your
one of the magnets. answer.
▲ Figure 4.1.5
178
Practical work
Plotting lines of force A typical field pattern is shown in Figure 4.1.7.
For safe experiments/demonstrations related
to this topic, please refer to the Cambridge
IGCSE Physics Practical Skills Workbook that
is also part of this series.
Plotting compass method
A plotting compass is a small pivoted magnet S N
in a glass case with non-magnetic metal walls
(Figure 4.1.6a).
a
▲ Figure 4.1.6
N X N
Lay a bar magnet on a sheet of paper. Place the
plotting compass at a point such as A (Figure
4.1.6b), near one pole of the magnet. In Figure
4.1.6b it is the N pole. Mark the position of the
poles (n, s) of the compass by pencil dots B, A.
Move the compass so that pole s is exactly over b
B, mark the new position of n by dot C.
Continue this process until the other pole of the
bar magnet is reached (in Figure 4.1.6b it is the
S pole). Join the dots to give one line of force and S N
show its direction by putting an arrow on it. Plot
other lines by starting at different points round
the magnet.
179
Going further
180
Practical work
Simple electromagnet
For safe experiments/demonstrations wooden
related to this topic, please refer to the electromagnet stand
Cambridge IGCSE Physics Practical Skills
Workbook that is also part of this series.
An electromagnet is a coil of wire wound
on a soft iron core. A 5 cm iron nail and 3 m
paper clips
of PVC-covered copper wire (SWG 26) are
needed.
a Leave about 25 cm at one end of the wire
(for connecting to the circuit) and then wind
about 50 cm as a single layer on the nail.
A
Keep the turns close together and always
wind in the same direction. Connect the (0–2 A)
(2–3 V)
circuit of Figure 4.1.10, setting the rheostat (0–15 Ω)
(variable resistor, see p. 199) at its maximum
resistance. ▲ Figure 4.1.10
Find the number of paper clips the c Place the electromagnet on the bench and
electromagnet can support when the current under a sheet of paper. Sprinkle iron filings on
is varied between 0.2 A and 2.0 A. Record the the paper, tap it gently and observe the field
results in a table. pattern. Compare the pattern with that given
Deduce how the strength of the electromagnet by a bar magnet.
changes when the current is increased. d Use a plotting compass to find which end of
b Add another two layers of wire to the nail, the electromagnet is a N pole.
winding in the same direction as the first layer.
4 Name two variables which you think could
Repeat the experiment.
affect the strength of an electromagnet.
Deduce how the strength of the electromagnet
5 How could you use a compass to determine
has been changed by increasing the number
which end of the current-carrying coil is a north
of turns of wire.
pole?
Going further
declination
north
182
Revision checklist
After studying Topic 4.1 you should know and After studying Topic 4.1 you should be able to:
understand: ✔ state the properties of magnets, describe induced
✔ like magnetic poles repel, unlike magnetic poles magnetism and distinguish between the magnetic
attract properties of iron and steel
✔ the difference between magnetic and non- ✔ recall that a magnetic field is the region round a
magnetic materials, and permanent and magnet where a magnetic force is exerted and is
electromagnets represented by lines of force whose direction at
✔ how to map the magnetic field around a bar magnet, any point is the direction of the force on a N pole
by the plotting compass and iron filings methods.
✔ recall that the magnetic field is strongest
in regions where the field lines are closest
together and that magnetic forces result from
the interaction of magnetic fields.
Exam-style questions
1 Copy Figure 4.1.15 which shows a plotting 2 a Describe an experiment using a plotting
compass and a magnet. compass to map the magnetic field lines
a Label the N pole of the magnet. [1] around a bar magnet. [4]
b Draw the magnetic field line on which the b Explain why permanent magnets are used in
compass lies. [2] some applications and electromagnets
c State the direction of the magnetic in others. [4]
field line. [1] c Give two uses of a permanent magnet. [2]
[Total: 10]
183
Electrostatic charges arise when electrons are transferred between objects by rubbing. Sparks can
fly after you comb your hair or walk across a synthetic carpet when you touch an earthed object,
through which the charge can be neutralised; the discharge can lead you to feel a small electric
shock. A flash of lightning is nature’s most spectacular static electricity effect. There are two types
of electrostatic charge. Like charges repel while opposite charges attract. Charges build up on an
insulator such as plastic and remain static, but for conductors like metals, charges flow away to try
to neutralise charge. Both electrical conductors and insulators have their uses.
Electric charges are surrounded by an electric field which exerts a force on a nearby charge.
This effect is made use of in applications from ink-jet printers to crop sprayers. As with a
magnetic field, an electric field exerts an action-at-a-distance force.
184
paper stirrup
rubbed
polythene
▲ Figure 4.2.3 Hydrogen atom
strips like The production of charges by rubbing can be explained
charges
repel by supposing that friction causes electrons to be
transferred from one material to the other. For example,
when cellulose acetate is rubbed with a cloth, electrons
go from the acetate to the cloth, leaving the acetate
short of electrons, i.e. positively charged. The cloth
now has more electrons than protons and becomes
▲ Figure 4.2.2 Investigating charges negatively charged. Note that it is only electrons which
move; the protons remain fixed in the nucleus.
This shows there are two kinds of electric charge.
That on cellulose acetate is taken as positive (+)
and that on polythene is negative (–). It also Test yourself
shows that: 1 Two identical conducting balls, suspended on
nylon threads, come to rest with the threads
Like charges (+ and +, or – and –) repel, while unlike making equal angles with the vertical, as shown in
charges (+ and –) attract. Figure 4.2.4.
Which of these statements is true?
The force between electric charges decreases as This shows that
their separation increases. A the balls are equally and oppositely charged
B the balls are oppositely charged but not
Key definitions necessarily equally charged
Positive charges repel other positive charges, but C one ball is charged and the other is uncharged
positive charges attract negative charges D the balls both carry the same type of charge.
Negative charges repel other negative charges, but
negative charges attract positive charges
185
Practical work
186
Key definition
Direction of an electric field at a point the direction of
the force on a positive charge at that point
▲ Figure 4.2.6 Uniform electric field ▲ Figure 4.2.7b Electric field around a point charge
187
Going further
tall spikes
electrostatic
building charging unit
copper
strip
deflecting
plates
negative positive
metal plate
paper
in ground
Test yourself
Test yourself 5 Name
a two applications
4 Describe the electric field around a
b two dangers
negatively charged conducting sphere.
of static electricity.
188
★ Describe the use of analogue and digital ammeters and the difference between alternating current (a.c.)
and direct current (d.c.).
★ Describe the role of free electrons in electrical conduction in metals.
★ Know that the flow of electrons in a circuit is in the opposite direction to that of the conventional current
flow.
In the previous topic you learnt about positive and negative static charges and how they were
produced on conductors and insulators. In this topic you will discover that moving charges in a
conductor produce an electric current which is proportional to the rate of flow of charge. Every
electrical appliance you use, from hair dryer to computer, relies on the flow of an electric current.
In a metal the current is produced by the movement of electrons. By convention, electric current is
linked to the flow of positive charge, which is in the opposite direction to the way electrons move.
You will find out how to connect an ammeter to a circuit to measure the size of an electric current
and learn about the different types of current.
189
190
Ammeters
An ammeter is used to measure currents. It should
always be placed in series in a circuit with the
positive terminal on the ammeter connected to
the positive terminal of the supply, as described
in the practical work below (see Figure 4.2.13
overleaf). A simple moving coil ammeter will
read d.c. currents only on an analogue display.
It may have two ranges and two scales in the
display.
A multimeter can have either a digital or
analogue display (see Figure 4.1.12a and b) and be
used to measure a.c. and d.c. currents (or voltages
and also resistance). The required function is first
selected, say d.c. current.
When making a measurement on either type
of ammeter a suitable range must be chosen. For
example, if a current of a few milliamps is expected,
the 10 mA range might be selected and the value
of the current (in mA) read from the display; if
the reading is off-scale, the sensitivity should
be reduced by changing to the higher, perhaps
100 mA, range.
▲ Figure 4.2.12b Digital multimeter
Test yourself
6 Explain how electrical conduction occurs in a
metal.
7 Explain how you would connect an ammeter into a
circuit.
Practical work
Measuring current a Connect the circuit of Figure 4.2.13a (on a
For safe experiments/demonstrations related circuit board if possible), ensuring that the +
to this topic, please refer to the Cambridge of the cell (the metal stud) goes to the + of the
IGCSE Physics Practical Skills Workbook that ammeter (marked red). Note the current.
is also part of this series. b Connect the circuit of Figure 4.2.13b. The cells
are in series (+ of one to – of the other), as are
191
0
1 1 time/seconds
current
2
steady d.c.
1 cycle
time
▲ Figure 4.2.15 Alternating current (a.c.)
current
Frequency of a.c.
The number of complete alternations or cycles Test yourself
in 1 second is the frequency of the alternating 10 Sketch
current. The unit of frequency is the hertz (Hz). a a d.c. current
b an a.c. current
The frequency of the a.c. in Figure 4.2.15 is 2 Hz, c the circuit symbol used for a.c.
which means there are two cycles per second, or one 11 An a.c. current has a frequency of 1000 Hz.
cycle lasts 1/2 = 0.5 s. The mains supply in many How long does each cycle last?
countries is a.c. of frequency 50 Hz; each cycle lasts
1/50th of a second. This regularity was used in the
tickertape timer (Topic 1.2) and is relied upon in
mains-operated clocks.
★ Use the correct equations for electromagnetic force and potential difference.
As you will have seen in the previous topic, a complete circuit of conductors is needed for a current
to flow. In this topic you will learn that it is the electromotive force of a supply which provides
the energy needed to move charge around a complete circuit. The supply may vary from a simple
torch battery to your mains electricity supply. There are usually several components in a circuit,
for example lamps, motors or other electrical devices, from which energy is transferred to the
surroundings. The energy transferred from a device can be calculated by introducing the concept of
potential difference. Previously you used an ammeter to measure the current in an electrical circuit;
now you will learn how to use a voltmeter to measure potential difference.
194
195
volts
V
▲ Figure 4.2.20
voltmeter (0–5 V)
a What are the two ranges available when using the
voltmeter?
The lower scale reads 0–5 V and the upper scale reads b 4.5 V
0–10 V.
b What do the small divisions between the numbers 3 and 4
represent?
0.1 V X Y
L1 L2 L3
c Which scale would you use to measure a voltage of 4.6 V?
The lower scale 0–5 V will give a more accurate reading.
d When the voltmeter reads 4.0 V where should you position
c 1.5 V
your eye to make the reading?
Above the 4 to reduce parallax error.
V1
Now put this into practice
1 Use the scales of the voltmeter shown in Figure 4.2.20.
a What do the small divisions between the numbers 6 L1
and 8 represent? L2
b Which scale would you use to measure a voltage of
5.4 V?
c When making the reading for 4.0 V an observer’s eye V2
is over the 0 V mark. Explain why the value obtained by
this observer is higher than 4.0 V. ▲ Figure 4.2.21
196
4.2.4 Resistance
FOCUS POINTS
★ Know the correct equation for resistance and use it correctly to determine resistance using a voltmeter
and an ammeter.
★ Understand the dependence of the resistance of a metal wire on its length and cross-sectional area.
★ Know that resistance is directly proportional to length and inversely proportional to cross-sectional
area in a metallic electrical conductor.
In this topic you will learn that the ease of passage of electrons depends on the nature of the
material. This effect is measured by resistance. More work has to be done to drive a current through
a high resistance than a low resistance. For the element in an electric fire, a high-resistance wire
is needed so that a large amount of energy is transferred. The opposite is required for the connecting
wires in a circuit, where low-resistance wires are used to reduce energy losses. Current flow is
easier in a wire with a large cross-sectional area so thick wires are used where large currents are
needed, for example in the starter motor in a car or a kitchen oven. The longer a wire, the harder
it is for current to flow; energy loss is reduced by using short connecting wires.
197
V
Resistors
▲ Figure 4.2.23a Conductors intended to have resistance are called
resistors (Figure 4.2.24a) and are made either from
wires of special alloys or from carbon. Those used
in radio and television sets have values from a few
V
ohms up to millions of ohms (Figure 4.2.24b).
▲ Figure 4.2.23b
198
199
Resistivity
to three 1.5 V (4.5 V) cells in series
Experiments show that the resistance R of a wire
of a given material is
R
(i) directly proportional to its length l, i.e. R ∝ l
crocodile
clip
(ii) inversely proportional to its cross-sectional
A area A, i.e. R ∝ 1/A (doubling A halves R).
Worked example
ammeter A copper wire has a diameter of 0.50 mm, a length of 1 km
(0–1 A) and a resistance of 84 Ω.
rheostat circuit a Calculate the resistance of a wire of the same material
(0–25 Ω) board and diameter with a length of 500 m.
Let R1 = 84 Ω, length l1 = 1.0 km = 1000 m,
length l2 = 500 m and R2 the required resistance.
Then since R ∝ l/A and A is constant
R2 I
= 2
V voltmeter R1 I1
(0–5 V) I2 500 m
and R2 = R1 × = 84 Ω × = 42 Ω
I1 1000 m
▲ Figure 4.2.28 The resistance is halved when the length of the wire is
halved.
12 Work out R for each pair of readings from the b Calculate the resistance of a wire of the same material
equation R = V/I. with a diameter of 1.0 mm and a length of 1 km.
13 Draw the symbols for a a resistor and Let R1 = 84 Ω, diameter d1 = 0.50 mm, diameter
b a variable resistor. d2 = 1.0 mm and R2 the required resistance.
14 List the equipment you would need to If r is the radius of the wire, the cross-sectional area
A = πr 2 = π(d/2)2 = (π/4) d2 , so
measure the resistance of a wire.
15 Calculate the resistance of a wire that has a A1 ( d1 )2 (0.50 mm)2
= = = 0.25
current of 0.15 A passing through it when the A2 ( d2 ) 2
(1.0 mm)2
p.d. across it is 4.5 V. l
Then since R ∝ and l is constant
A
R2 A1
Resistance of a metal wire R1
=
A2
The resistance of a metallic wire A1
and R2 = R1 × = 84 Ω × 0.25 = 21 Ω
(i) increases as its length increases A2
(ii) increases as its cross-sectional area decreases
Now put this into practice
(iii) depends on the material.
A long thin wire has more resistance than a short 1 A certain wire has a length of 10 m and a resistance of
60 Ω.
thick one of the same material. Silver is the best Calculate the resistance of 20 m of the wire.
conductor, but copper, the next best, is cheaper 2 A certain wire has diameter of 0.20 mm and a
and is used for connecting wires and for domestic resistance of 60 Ω. Calculate the resistance of a wire
electric cables. of the same material with a diameter of 0.40 mm.
Key definition
Resistance of a metallic wire directly proportional to its
length and inversely proportional to its cross-sectional
area
200
201
The e.m.f. applied to a circuit drives current around the circuit. In the process, energy is transferred
from the electrical cell or mains supply to the wires and components of the circuit. The total energy
transferred to a device depends on its power consumption and the time span over which it is used.
In this section you will learn how to measure power consumption, the typical power consumption of
some everyday household appliances and how to calculate the cost of electricity usage.
torch
A V
Worked example (0–1 A)
lamp
(0–5 V)
203
Joulemeter
Instead of using an ammeter and a voltmeter to
measure the electrical energy transferred to an
appliance, a joulemeter can be used to measure
it directly in joules. The circuit connections are
shown in Figure 4.2.33.
electrical appliance
joulemeter
supply
input output
204
Revision checklist
After studying Topic 4.2 you should know and ✔ give examples of conductors and insulators and
understand: explain the differences between them using a
✔ that positive and negative charges are produced simple electron model
by rubbing and like charges repel while unlike ✔ describe the use of ammeters to measure current
charges attract
✔ recall the relation I = Q/t and use it to solve
✔ what is meant by an electric field and that the problems
direction of an electric field at a point is the direction ✔ distinguish between electron flow and
of the force on a positive charge at that point conventional current
✔ that an electric current in a metal is a flow of free ✔ state that e.m.f. and p.d. are measured in volts
electrons from the negative to the positive terminal
of the battery around a circuit ✔ recall and use the equation V = W/Q
✔ the difference between d.c. and a.c.
✔ the meaning of the terms electromotive force and ✔ describe an experiment to measure resistance
potential difference and relate the resistance of a wire to its length and
✔ how to use voltmeters, both analogue and digital diameter
✔ how to solve simple problems using R = V/I
✔ plot and explain I–V graphs for different
✔ that electric circuits transfer energy, from a
battery or mains supply, to the components of the conductors
circuit and then into the surroundings.
✔ recall the relations E = IVt and P = IV and use them
After studying Topic 4.2 you should be able to: to solve simple problems on energy transfers
✔ explain the charging of objects in terms of the ✔ define the kilowatt-hour and calculate of the cost
motion of negatively charged electrons and of using electrical energy.
describe simple experiments to show how
electrostatic charges are produced and detected
205
206
6 +
4 +
p.d./V
d e f +
2
+
0 1 2 3
current/A
207
Alternative to Practical
15 a Write down an expression relating the 16 a Calculate the energy transferred to
resistance of a metal wire to the p.d. across a 6.4 kW cooker in 30 minutes. [3]
it and the current flowing through it. [1] b Calculate the cost of heating a tank of water
b Describe how you could measure the with a 3000 W immersion heater for 80 minutes
resistance of a wire; include the equipment if electricity costs 10 cents per kWh.
you would need. [4] [3]
c In an experiment to determine the resistance [Total: 6]
of a wire the following values were obtained 17 a Below is a list of wattages of various
for the current through the wire and the p.d. appliances. State which is most likely to be
across it. the correct one for each of the appliances
Current/A p.d./V named.
60 W 250 W 850 W 2 kW 3.5 kW
0.04 2.0
i kettle [1]
0.08 4.0 ii table lamp [1]
0.12 6.0 iii iron [1]
0.16 8.0 b Calculate the current in a 920 W appliance
0.20 10.0 if the supply voltage is 230 V. [4]
[Total: 7]
0.24 12.0
208
You will find that electrical circuits can contain many different types of components. The circuit
configuration is expressed by circuit diagrams. Conventional symbols represent the different types
of components. Such diagrams are used in the design of circuits and the analysis of their behaviour.
resistor fuse
variable resistor
▲ Figure 4.3.1 Circuit symbols
★ Understand that the sum of the currents into a junction equals the sum of the currents out of the
junction.
★ Calculate the effective resistance of two resistors in parallel.
★ Know that in a lighting circuit there are advantages to connecting lamps in parallel.
209
In the preceding topic you encountered the concepts of current, p.d. and resistance and how they
are related to each other in simple circuits. Electrical circuits can branch and reconnect. The net
effect depends on the way the components are connected. The sum of the currents into a junction
equals the sum of the currents out of the junction. This means that there are different effects
when resistors follow each other (in series) from those when they lie on parallel wires. There are
significant advantages in connecting lamps in parallel in a lighting circuit.
B
Current at a junction
▲ Figure 4.3.2 Current in a series circuit
Electric current in a circuit cannot be stored.
This means that when circuits join or divide, the
Current in a parallel circuit total current going into a junction must be equal
to the total current leaving the junction. A simple
In a parallel circuit, such as the one shown in example of this is provided by the splitting and
Figure 4.3.3, the lamps are side by side and there re-joining of the current when it goes into and
are alternative paths for the current. The current comes out of a parallel circuit.
splits: some goes through one lamp and the rest
through the other. The current from the source is Potential difference in a series
larger than the current in each branch. For example,
if the ammeter reading was 0.4 A in the position circuit
shown, then if the lamps are identical, the reading The total p.d. across the components in a series
at P would be 0.2 A, and so would the reading at Q, circuit is equal to the sum of the individual p.d.s
giving a total of 0.4 A. Whether the current splits across each component. In Figure 4.3.4
equally or not depends on the lamps; for example,
V = V1 + V2 + V3
if the lamps are not identical, the current might
divide so that 0.3 A goes one way and 0.1 A by the where V1 is the p.d. across L1, V2 is the p.d.
other branch. across L2 and V3 is the p.d. across L3.
210
4.5 V
X Y
L1 L2 L3
V1 A B
b
L1
L2 X Y
1.5 V 1.5 V
V2 c
1.5 V
▲ Figure 4.3.5 p.d.s in a parallel circuit
211
2 Three 2 V cells are connected in series and used as Now put this into practice
the supply for a circuit.
What is the p.d. at the terminals of the supply? 1 Three resistors of value 4 Ω, 6 Ω and 8 Ω are connected in
series. Calculate their combined resistance.
3 How many joules of electrical energy does 1 C 2 A 4.5 V battery is connected across two resistors of value
gain on passing through 3 Ω + 6 Ω. Calculate
a a 2 V cell a the current flowing through the resistors
b three 2 V cells connected in series? b the p.d. across each.
212
R1 Key definition
I1
Combined resistance of two resistors in parallel less than
that of either resistor by itself
I I2
R2
I
You can check these statements are true in the
Worked example below.
Lamps are connected in parallel (Figure 4.3.5)
rather than in series in a lighting circuit.
R3
I3 The advantages are as follows:
(i) The p.d. across each lamp is fixed (at the
supply p.d.), so the lamp shines with the same
brightness irrespective of how many other lamps
are switched on.
V
(ii) Each lamp can be turned on and off
▲ Figure 4.3.10 Resistors in parallel independently; if one lamp fails, the others can
still be operated.
But I1 = V/R1, I2 = V/R2 and I3 = V/R3. Practical work associated with measuring resistance
Also, if R is the combined resistance, I = V/R, can be found in Topic 4.2.4.
V = V +V +V
R R1 R2 R3
Worked example
Dividing both sides by V,
A p.d. of 24 V from a battery is applied to the network of
1 = 1 + 1 + 1 resistors in Figure 4.3.11a.
R R1 R2 R3 a What is the combined resistance of the 6 Ω and 12 Ω
resistors in parallel?
For the simpler case of two resistors in parallel Let R1 = resistance of 6 Ω and 12 Ω in parallel.
Then
1 = 1 + 1 = R2 + R1
1 1 1 2 1 3
R R1 R2 R1 R2 R1 R2 = + = + =
R1 6 12 12 12 12
R + R1
∴1 = 2
12
∴ R1 = = 4Ω
R R1 R2 3
24 V
Inverting both sides,
RR product of resistances
R= 1 2 =
R1 + R2 sum of resistances
6Ω
8Ω
213
Going further
Resistor colour code 1st 2nd number of
Figure Colour
Test yourself
4 a Write down the equation for calculating the
5 a Write down the equation for calculating the
combined resistance R of resistors R1, R2 and R3
combined resistance R of resistors R1 and R2
connected in series.
connected in parallel.
b Is the current in R1 larger, the same or smaller
b Is the current in R1 larger, the same or
than in R3?
smaller than in R2 if R1 is smaller than R2?
214
★ Describe how a variable potential divider works and use the correct equation for two resistors used as a
potential divider.
The action of potential dividers and a range of other components, including thermistors, LDRs,
relays, light-emitting diodes and semiconductor diodes, will be considered in this section.
These components are widely used in electrical circuits in applications ranging from intruder
and temperature alarms to indicator lamps and switching circuits.
Increase in resistance of a This means that the p.d. across the fixed resistor
conductor increases relative to that across the thermistor.
The p.d. across the fixed resistor could then be
In a metal the current in a circuit is carried by
used to monitor temperature.
free electrons. When the temperature of the metal
A variable resistor can also be used as a
increases, the atoms vibrate faster and it becomes
potential divider (see Figure 4.2.26b, p. 199).
more difficult for the electrons to move through
Moving the contact on the resistor changes the
the material. This means that the resistance of the
output p.d.
metal increases.
From Ohm’s law V = IR, so that if R increases
then if a constant current I is to be maintained, the
Potential divider
p.d. V across the conductor also increases. In the circuit shown in Figure 4.3.13 overleaf, two
The effect of increasing resistance can be seen resistors R1 and R2 are in series with a supply of
in the I–V curve for a filament lamp (Figure 4.2.29c, voltage V. The current in the circuit is
p. 201). When the current increases, the metal supply voltage V
filament heats up and its resistance increases as is I= =
total resistance ( R1 + R2 )
indicated by the curvature of the graph.
So the voltage across R1 is
V × R1 R1
Variable potential divider V1 = I × R1 = =V ×
The resistance of materials other than metals (R1 + R2) (R1 + R2)
does not necessarily rise when their temperature and the voltage across R2 is
increases. For example, in a semiconductor
thermistor, the resistance decreases when its V × R2 R2
V2 = I × R2 = =V ×
temperature increases. (R1 + R2 ) (R1 + R2 )
If a thermistor is part of a potential divider
circuit (see Figure 4.2.30, p. 201) then its resistance Also the ratio of the voltages across the two
decreases when the external temperature rises. resistors is
The combined resistance of the two resistors V1 R
then decreases, so if the supply voltage remains = 1
V2 R2
constant, the current in the circuit will increase.
215
216
coil reaches a high enough p.d. (its operating p.d.) Figure 4.3.15c shows how a thermistor can be used
it acts as a switch and the normally open contacts to switch a relay. The thermistor forms part of a
close, allowing current to flow to the bell, which potential divider across the d.c. source. When the
rings. If the light is removed, the p.d. across temperature rises, the resistance of the thermistor
resistor R and the relay drops below the operating falls, and so does the p.d. across it. The voltage
p.d. of the relay so that the relay contacts open across resistor R and the relay increases. When the
again; power to the bell is cut and it stops ringing. voltage across the relay reaches its operating p.d.
the normally open contacts close, so that the circuit
Thermistor to the bell is completed and it rings. If a variable
A negative temperature coefficient (NTC) thermistor resistor is used in the circuit, the temperature at
contains semiconducting metallic oxides whose which the alarm sounds can be varied.
resistance decreases markedly when the temperature
rises. The temperature may rise either because the Relays
thermistor is directly heated or because a current A switching circuit cannot supply much power to an
is in it. appliance so a relay is often included; this allows
Figure 4.3.15a shows one type of thermistor. the small current provided by the switching circuit
Figure 4.3.15b shows the symbol for a thermistor in to control the larger current needed to operate a
a circuit to demonstrate how the thermistor works. buzzer as in a temperature-operated switch or other
When the thermistor is heated with a match, the device. Relays controlled by a switching circuit
lamp lights. can also be used to switch on the mains supply for
A thermistor in series with a meter marked in electrical appliances in the home. In Figure 4.3.16
°C can measure temperatures (Topic 4.2.4). Used in if the output of the switching circuit is ‘high’ (5 V),
series with a resistor it can also provide an input a small current flows to the relay which closes the
signal to switching circuits. mains switch; the relay also isolates the low voltage
circuit from the high voltage mains supply.
a b
thermistor 0 or 5 V
output of
switching relay
6V circuit
d.c.
0V ~ mains
supply
6 V 0.06 A
appliance
c
•
R relay
▲ Figure 4.3.16 Use of a relay to switch mains supply
+
6V •
d.c
thermistor bell
217
‘flat’ A
5V circle
LED
optional
cathode C anode A C
anode
▲ Figure 4.3.17 LED and demonstration circuit
LEDs are used as indicator lamps on computers, ▲ Figure 4.3.19 A diode and its symbol
radios and other electronic equipment. Many
clocks, calculators, video recorders and measuring The typical I–V graph is shown in Figure 4.2.29b
instruments have seven-segment red or green (Topic 4.2.4). The diode conducts when the anode
numerical displays (Figure 4.3.18a). Each segment goes to the + terminal of the voltage supply and
is an LED and, depending on which have a voltage the cathode to the − terminal (Figure 4.3.20a).
across them, the display lights up the numbers 0 It is then forward-biased; its resistance is small and
to 9, as in Figure 4.3.18b. conventional current passes in the direction of the
LEDs are small, reliable and have a long life; arrow on its symbol. If the connections are the other
their operating speed is high and their current way around, it does not conduct; its resistance is
requirements are very low. large and it is reverse-biased (Figure 4.3.20b).
Diode lasers operate in a similar way to LEDs but The lamp in the circuit shows when the diode
emit coherent laser light; they are used in optical is conducting, as the lamp lights up. It also acts
fibre communications as transmitters. as a resistor to limit the current when the diode
is forward-biased. Otherwise the diode might
overheat and be damaged.
218
current passes t
no current
Test yourself
6 Resistors R1 = 12 Ω and R2 = 36 Ω are connected 8 Identify the following components from their
in series and used as a potential divider. symbols.
a Draw a potential divider circuit containing
a battery and resistors R1 and R2 in series.
b Calculate the ratio of the p.d.s across the A B
resistors.
c If the supply voltage is 20 V, what is the p.d.
across each resistor?
C D
7 Identify the following components from their
symbols. ▲ Figure 4.3.23
▲ Figure 4.3.22
219
Revision checklist
After studying Topic 4.3 you should know and After studying Topic 4.3 you should be able to:
understand: ✔ use the equations for resistors in series, and recall
✔ how to connect simple series and parallel circuits that the combined resistance of two resistors in
✔ that the current in a series circuit is the same parallel is less than that of either resistor alone
everywhere in the circuit and that for a parallel
circuit, the current from the source is larger than ✔ calculate current, p.d. and resistance in parallel
the current in each branch circuits; describe the action and calculate p.d. in
✔ the effect on p.d. of a change in the resistance of a potential divider circuits
conductor
✔ the advantages of having lamps connected in ✔ recognise and draw symbols for a variety of
parallel in lighting circuits. components in electric circuits and be able to draw
and interpret circuit diagrams incorporating those
components, and explain their behaviours in a
circuit.
Exam-style questions
1 Three voltmeters are connected as in
Figure 4.3.24. 2 The resistors R1, R2, R3 and R4 in Figure 4.3.25
are all equal in value.
What would you expect each of the voltmeters
A, B and C to read, assuming that the
V1
connecting wires in the circuit have negligible
resistance?
V
A [4]
V2
B [2]
C [2]
A B C
▲ Figure 4.3.24
x [2]
y [2]
z [2]
[Total: 6]
220
R1 R2
3 a Calculate the effective resistance between
A and B in Figure 4.3.26. [4]
4Ω V1 V2
6V
A B ▲ Figure 4.3.28
4Ω
[Total: 10]
▲ Figure 4.3.26 6 A battery of 12 V is connected across
a light-dependent resistor (LDR) in series
b Figure 4.3.27 shows three resistors. with a resistor R.
Calculate their combined resistance a Draw the circuit diagram. [2]
in ohms. [6] b The value of the resistor R is 20 Ω
6Ω and the resistance of the LDR is 28 Ω.
Calculate
6Ω i the value of the current in the circuit [2]
2Ω
ii the p.d. across the resistor [2]
iii the p.d. across the LDR. [2]
c The intensity of the light falling on the
▲ Figure 4.3.27 LDR increases. State what happens to
[Total: 10] i the resistance of the LDR [1]
ii the current in the circuit [1]
iii the p.d. across R.[1]
4 a Resistors of value 6 Ω, 7 Ω and 8 Ω are [Total: 11]
connected in series.
i Calculate the combined resistance 7 Figure 4.3.29a shows a lamp, a semiconductor
of the resistors. [2] diode and a cell connected in series. The lamp
ii The resistance of one of the resistors lights when the diode is connected in this
increases. If the current through the direction. Say what happens to each of the lamps
combination must remain unchanged in b, c and d. Give reasons for your answers.
does the supply voltage need to be b [3]
increased or decreased? [1]
c [4]
b Give two advantages of connecting lamps
in parallel.[4] d [3]
c Two resistors of the same size are connected a b
in parallel. Is the resistance of the
combination greater or less than that of D D1 L2
one of the resistors? [1] L
[Total: 8] L1 D2
5 What are the readings V1 and V2 on the
high-resistance voltmeters in the potential c d
divider circuit of Figure 4.3.28 if
a R1 = R2 = 10 kΩ [2] E1 D L1 E1 D1 L1
[Total: 10]
221
In the twenty-first century we would be lost without all the benefits electricity supplies bring us.
Because electric circuits transfer substantial amounts of energy, use of the mains supply requires
caution and electrical safety is important. You will learn that overheated wires and damaged
insulation pose fire risks. Damp or wet conditions increase the risk of electric shock from faulty
wiring in appliances since water reduces the electrical resistance of a person’s skin. If too many
appliances are connected to a circuit, the current flowing in the circuit increases and can cause
cables to overheat. To prevent problems, devices such as fuses and trip switches (circuit breakers)
are installed to break the circuit before the safe current level is exceeded. Safety features
incorporated into appliances include double insulation and earthing of metal casing via the mains
plug.
Dangers of electricity It is the size of the current (not the voltage) and
the length of time for which it acts which determine
There are a number of hazards associated with the strength of an electric shock. The path the
using the mains electricity supply. current takes influences the effect of the shock;
some parts of the body are more vulnerable than
Key definition others. A current of 100 mA through the heart is
Hazards associated with using mains electricity supply likely to be fatal.
include damaged insulation, overheated cables, damp Damp conditions increase the severity of an
conditions, excess current from overloaded plugs, electric shock because water lowers the resistance
extension leads, single and multiple sockets
of the path to earth; wearing shoes with insulating
rubber soles or standing on a dry insulating floor
Electric shock increases the resistance between a person and earth
Electric shock occurs if current flows from an and will reduce the severity of an electric shock.
electric circuit through a person’s body to earth. To avoid the risk of getting an electric shock:
This can happen if there is damaged insulation or (i) switch off the electrical supply to an appliance
faulty wiring. The typical resistance of dry skin before starting repairs
is about 10 000 Ω, so if a person touches a wire (ii) use plugs that have an earth pin and a cord grip;
carrying electricity at 240 V, an estimate of the a rubber or plastic case is preferred
current flowing through them to earth would be (iii) do not allow appliances or cables to come into
I = V/R = 240/10 000 = 0.024 A = 24 mA. contact with water, for example holding a
For wet skin, the resistance is lowered to about hairdryer with wet hands in a bathroom can be
1000 Ω (since water is a good conductor of dangerous; keep electrical appliances well away
electricity) so the current would increase to from baths and swimming pools
around 240 mA; a lethal current.
222
(iv) do not have long cables trailing across a room, The factors leading to fire or electric shock can
under a carpet that is walked over regularly or be summarised as follows:
in other situations where the insulation can
damaged insulation → electric shock and fire risk
become damaged. Take particular care when using
electrical cutting devices (such as hedge cutters) overheated cables → fire risk
not to cut the supply cable. damp conditions → increased severity of electric shocks
In case of an electric shock, take the following overloading – → fire risk and electric shock
action: plugs, extension
1 Switch off the supply if the shocked person is still leads or sockets
touching the equipment.
2 Send for qualified medical assistance.
3 If breathing or heartbeat has stopped, commence Electric lighting
CPR (cardiopulmonary resuscitation) by applying
chest compressions at the rate of about 100 a LED lights
minute until there are signs of chest movement LEDs (Topic 4.3) are increasingly being used in the
or medical assistance arrives. lighting of our homes. These semiconductor devices
are 40–50% efficient in transferring electrical
Fire risks energy to light. The efficiency of the filament lamps
If flammable material is placed too close to a hot used in the past was only about 10%.
appliance such as an electric heater, it may catch
fire. Similarly, if the electrical wiring in the walls of Fluorescent lamps
a house becomes overheated, a fire may start. Wires Fluorescent strip lamps (Figure 4.4.1a) are long
become hot when they carry electrical currents – lasting and efficient. When one is switched on, the
the larger the current carried, the hotter a particular mercury vapour emits invisible ultraviolet radiation
wire will become, since the rate of production of which makes the powder on the inside of the
heat equals I 2R (see p. 202). tube fluoresce (glow), i.e. visible light is emitted.
To reduce the risk of fire through overheated Different powders give different colours.
cables, the maximum current in a circuit should be Compact energy-saving fluorescent lamps (Figure
limited by taking the following precautions: 4.4.1b) are available to fit straight into normal light
(i) Use the correct fuse in an appliance or plug. sockets, either bayonet or screw-in.
(ii) Do not attach too many appliances to a circuit
via extension leads or single and multiple a
electrodes b
sockets.
(iii) Do not overload circuits by using too many adapters.
(iv) Appliances such as heaters use large amounts of
power (and hence current), so do not connect
mercury glass fluorescent
them to a lighting circuit designed for low vapour tube powder
current use. (Thick wires have a lower resistance
than thin wires so are used in circuits expected ▲ Figure 4.4.1 Fluorescent lamps
to carry high currents.)
Damaged insulation or faulty wiring which leads to
a large current flowing to earth through flammable
material can also start a fire.
223
Going further
Electric heating designed to warm air which is drawn through the heater
by natural or forced convection. In storage heaters the
Heating elements elements heat fire-clay bricks during the night using
‘off-peak’ electricity. On the following day these cool
In domestic appliances such as electric fires, cookers, down, giving off the stored heat to warm the room.
kettles and irons the ‘elements’ (Figure 4.4.2) are
made from Nichrome wire. This is an alloy of nickel Three-heat switch
and chromium which does not oxidise (and so become
A three-heat switch is sometimes used to control
brittle) when the current makes it red hot.
heating appliances. It has three settings and uses
The elements in radiant electric fires are at red heat two identical elements. On ‘high’, the elements are in
(about 900°C) and the radiation they emit is directed parallel across the supply voltage (Figure 4.4.3a); on
into the room by polished reflectors. In convector types ‘medium’, there is only current in one (Figure 4.4.3b);
the element is below red heat (about 450°C) and is on ‘low’, they are in series (Figure 4.4.3c).
element a High
element
switch elements
mains
b Medium
cooker hob
cooker hob mains
radiant fire
radiant fire
c Low
mains
iron
iron
element
element
kettle
kettle
▲ Figure 4.4.2 Heating elements
House circuits
Electricity usually comes to our homes by an the top socket on the power points in the home to
underground cable containing two wires, the live (L) earth. The supply in many countries is a.c. (Topic
and the neutral (N). The neutral is earthed at the 4.2) and the live wire is alternately positive and
local sub-station and so there is no p.d. between it negative. Study the typical house circuits shown
and earth. A third wire, the earth (E) also connects in Figure 4.4.4.
224
N L N L
supply
main immersion cooker
cable
switch heater
N E
LN
L
N
LIGHTING CIRCUIT RING MAIN
L E
CIRCUIT L
L
two-way N
L
switches E
L N
E
▲ Figure 4.4.4 Electric circuits in a house
Circuits in parallel rated at 13 A, are tapped off from them. Thinner
wires can be used since the current to each socket
Every circuit is connected in parallel with the supply, flows by two paths, i.e. from both directions in the
i.e. across the live and neutral, and receives the full ring. The ring has a 30 A fuse and if it has, say, ten
mains p.d. (for example 230 V). sockets, then all can be used so long as the total
The advantages of having appliances connected current does not exceed 30 A, otherwise the wires
in parallel, rather than in series, can be seen by overheat. A house may have several ring circuits,
studying the lighting circuit in Figure 4.4.4. each serving a different area.
(i) The p.d. across each lamp is fixed (at the
mains p.d.), so the lamp shines with the same
brightness irrespective of how many other lamps
Fuses
are switched on. A fuse protects a circuit; it is always placed in the
(ii) Each lamp can be turned on and off live wire. It is a short length of wire of material
independently; if one lamp fails, the others can with a low melting temperature, often ‘tinned
still be operated. copper’, which melts and breaks the circuit when the
In a staircase circuit, the light is controlled from current in it exceeds a certain value. Two reasons
two places by the two two-way switches. for excessive currents are ‘short circuits’ due to
worn insulation on connecting wires and overloaded
circuits. Without a fuse the wiring would become
Switches hot in these cases and could cause a fire. A fuse
Switches and fuses are always in the live wire. should ensure that the current-carrying capacity of
If they were in the neutral, light switches and power the wiring is not exceeded. In general, the thicker a
sockets would be ‘live’ when switches were ‘off’ or cable is, the more current it can carry, but each size
fuses ‘blown’. A fatal shock could then be obtained has a limit.
by, for example, touching the element of an electric Two types of fuse are shown in Figure 4.4.5. Always
fire when it was switched off. switch off before replacing a fuse, and always replace
with one of the same value as recommended by the
Ring main circuit manufacturer of the appliance. A 3 A (red) fuse will
The live and neutral wires each run in two complete be needed for appliances with powers up to 720 W, or
rings round the house and the power sockets, each 13 A (brown) for those between 720 W and 3 kW.
225
226
Double insulation
Appliances such as vacuum cleaners, hairdryers and
food mixers are usually double insulated. Connection
to the supply is by a two-core insulated cable, with
no earth wire, and the appliance is enclosed in a
non-conducting plastic case. Any metal attachments
that the user might touch are fitted into this case
so that they do not make a direct connection with
the internal electrical parts, such as a motor. There
is then no risk of a shock should a fault develop.
Revision checklist
After studying Topic 4.4 you should know and After studying Topic 4.4 you should be able to:
understand ✔ recall the hazards of damaged insulation, damp
✔ why switches, fuses and circuit breakers are wired conditions, overheated cables and excess current
into the live wire in house circuits from overloaded circuits
✔ the benefits of earthing metal cases and double ✔ state the function of a fuse and choose the
insulation. appropriate fuse rating for an appliance; explain
the use, choice and operation of a trip switch.
227
Exam-style questions
1 There are hazards in using the mains electricity 3 a A child whose hands are damp touches a wire
supply. carrying electricity at 240 V. The resistance
a Name two factors which can increase the risk of the child’s skin between hand and earth is
of fire in circuits connected to the mains 800 Ω.
supply.[2] i Calculate the current which would flow
b Name two factors which can increase the risk through the child. [2]
of electric shock. [2] ii State whether the current you
c Describe the steps you would take before calculated in i is likely to be lethal. [1]
replacing a blown fuse in an appliance. [3] iii State how the current could be
d Explain why an electrical appliance is double reduced.[2]
insulated or the outer casing is earthed. [3] b Work out the size of fuse (3 A or 13 A) which
[Total: 10] should be used in the following appliances if
2 Fuses are widely used in electrical circuits the supply is 230 V
connected to the mains supply. i a 150 W television [2]
a Explain the function of a fuse in a circuit. [2] ii a 900 W iron [2]
b The circuits of Figures 4.4.7a and b show iii a 2 kW kettle. [2]
‘short circuits’ between the live (L) and [Total: 11]
neutral (N) wires. In both, the fuse has blown
but whereas circuit a is now safe, b is still
dangerous even though the lamp is out which
suggests the circuit is safe. Explain. [4]
a b
fuse
L L
fuse
N N
228
★ Know that the direction of an induced e.m.f. is such as to oppose the change causing it.
★ Determine the relative directions of force, field and induced current.
Electricity and magnetism are closely linked. You will learn that an electrical conductor moving
through a magnetic field can induce a current. Similarly, an electrical conductor in a changing
magnetic field acquires an electromotive force (e.m.f.). You will find out about the factors which
determine the size of the induced e.m.f. Electromagnetic induction plays an important role in many
electrical applications from induction cookers and motors to electricity generators.
experiments
Two ways of investigating electromagnetic induction
follow.
Straight wire and U-shaped magnet
First the wire is held at rest between the poles of
the magnet. It is then moved in each of the six
directions shown in Figure 4.5.1 and the meter
sensitive
observed. Only when it is moving upwards (direction centre-zero meter
1) or downwards (direction 2) is there a deflection
on the meter, indicating an induced current in the ▲ Figure 4.5.1 A current is induced in the wire when it is
moved up or down between the magnet poles.
wire. The deflection is in opposite directions in
these two cases and only lasts while the wire is in
motion. is induced in the coil in one direction as the
magnet is moved in and in the opposite direction
Bar magnet and coil as it is moved out. There is no deflection when
The magnet is pushed into the coil, one pole first the magnet is at rest. The results are the same if
(Figure 4.5.2 overleaf), then held still inside it. the coil is moved instead of the magnet, i.e. only
It is then withdrawn. The meter shows that current relative motion is needed.
229
230
0
induced
Current seCond
finger galvanometer
▲ Figure 4.5.5
▲ Figure 4.5.4 Fleming’s right-hand (dynamo) rule
2 A straight wire moves vertically upwards at right
angles to a magnetic field acting horizontally
Key definition
from right to left. Make a sketch to represent the
Fleming’s right-hand (dynamo) rule used to show the directions of the magnetic field, the force on the
relative directions of force, field and induced current. wire and the induced current in the wire if it is
When the thumb and first two fingers of the right-hand connected to a complete circuit.
are held at right angles to each other with the first
finger pointing in the direction of the magnetic field
and the thumb in the direction of the motion of the
wire, then the second finger points in the direction of
the induced current.
When a coil is rotated between the poles of a magnet, the conductor cuts the magnetic field lines
and an e.m.f. is induced. The size of the e.m.f. generated changes with the orientation of the
coil and alternates in sign during the course of each rotation. This process is used in the large
generators in power stations to produce an alternating (a.c.) electricity supply.
231
b
1 cycle
e.m.f.
0
¹⁄₄ ¹⁄₂ ³⁄₄ 1
no. of
rotations
a d a
d a a d field lines
coil
d a d b
vertical
coil horizontal
232
water
stator a.c. output
★ Describe the variation of the magnetic field strength around a current-carrying straight wire and a
solenoid and recall the effect on the magnetic field of changing the current’s direction and size.
A further link between electricity and magnetism comes from the presence of a magnetic field
around a conductor carrying a current. The pattern and direction of the magnetic field can be found
by sprinkling iron filings around a current-carrying wire and using a plotting compass. In this topic
you will learn that the magnetic field can be concentrated by the geometry of the conductor. A long
cylindrical coil (a solenoid) will act like a bar magnet when current is switched on. As you have seen
in Topic 4.1, electromagnets have many applications. In this topic you can discover how they are also
used in switches, relays, bells and loudspeakers.
Magnetic field lines are used to represent the variation in magnetic field strength around a
current-carrying conductor and its dependence on the size and direction of the current.
234
N
right
hand
Key definition
Variation of magnetic field strength the magnetic
field decreases with distance from a current-carrying
wire and varies around a solenoid
Applications of the magnetic effect power are larger in the second circuit. Figure 4.5.15
overleaf shows a typical relay. When a current is in
of a current the coil from the circuit connected to AB, the soft
iron core is magnetised and attracts the L-shaped
Relay
iron armature. This rocks on its pivot and closes
A relay is a switch based on the principle of an the contacts at C in the circuit connected to DE.
electromagnet. It is useful if we want one circuit The relay is then ‘energised’ or ‘on’.
to control another, especially if the current and
235
S
iron armature
A
S
B magnet
switch
coil soft iron core N
▲ Figure 4.5.15 Relay alarm
bell
The current needed to operate a relay is called
▲ Figure 4.5.17
the pull-on current and the drop-off current is the
smaller current in the coil when the relay just stops Reed switches are also operated by permanent
working. magnets. Figure 4.5.17b shows the use of a normally
If the coil resistance, R, of a relay is 185 Ω and open reed switch as a burglar alarm. When the
its operating p.d. V is 12 V, then the pull-on current door is closed, the magnetic fields of the magnet
I = V/R = 12/185 = 0.065 A = 65 mA. The symbols in the door and door frame cancel each other and
for relays with normally open and normally closed the reed switch is open. When the door is opened
contacts are given in Figure 4.5.16. the magnetic field of the magnet in the door frame
a b closes the reed switch so that current flows in the
alarm circuit if it has been switched on.
Loudspeaker
Varying currents from a radio, CD player, etc. pass
through a short cylindrical coil whose turns are at right
angles to the magnetic field of a magnet with a central
▲ Figure 4.5.16 Symbols for a relay: a open; b closed pole and a surrounding ring pole (Figure 4.5.18a).
Reed switch The magnetic fields around the coil and the magnet
interact and the coil vibrates with the same frequency
One such switch is shown in Figure 4.5.17a. as the a.c. of the electrical signal it receives. A paper
When current flows in the coil, the magnetic field cone attached to the coil moves with it and sets up
produced magnetises the strips (called reeds) of sound waves in the surrounding air (Figure 4.5.18b).
magnetic material. The ends become opposite poles
a End-on view b
and one reed is attracted to the other, so completing ring central
casing
the circuit connected to AB. The reeds separate pole pole
when the current in the coil is switched off. This
type of reed switch is sometimes called a reed relay.
a Reed switch N
N
A
N S N S
reeds coil
on
N N
tube
coil
glass paper
tube cone
236
★ Know how the directions of force, magnetic field and current relate to each other.
★ Work out the direction of the force acting on charged particles moving in a magnetic field.
Electric motors form the heart of a whole host of electrical devices ranging from domestic
appliances such as vacuum cleaners and washing machines to electric trains and lifts. In a car, the
windscreen wipers are usually driven by one and the engine is started by another. All these devices
rely on the fact that a current flowing in a magnetic field experiences a force. The force will cause a
current-carrying conductor or beam of charged particles to move or be deflected.
wire
S
▲ Figure 4.5.21b
flexible
wire
Fleming’s left-hand rule
to low-voltage The direction of the force or thrust on the wire
high-current supply can be found by Fleming’s left-hand rule, which
is also called the motor rule (Figure 4.5.22).
Hold the thumb and first two fingers of the
left hand at right angles to each other with the
▲ Figure 4.5.20 A wire carrying a current in a magnetic
field experiences a force.
First finger pointing in the direction of the Field
and the seCond finger in the direction of the
Explanation Current, then the Thumb points in the direction
Figure 4.5.21a is a side view of the magnetic field of the Thrust (or force).
lines due to the wire and the magnet. Those due If the wire is not at right angles to the field,
to the wire are circles and we will assume their the force is smaller and is zero if the wire is
direction is as shown. The dotted lines represent parallel to the field.
the field lines of the magnet and their direction is Thumb
Thrust
towards the right.
The resultant field obtained by combining both
fields is shown in Figure 4.5.21b. There are more First finger
lines below than above the wire since both fields
act in the same direction below but they are in Current Fiel d
opposition above. If we suppose the lines are like seCond finger
stretched elastic, those below will try to straighten ▲ Figure 4.5.22 Fleming’s left-hand (motor) rule
out and in so doing will exert an upward force on
the wire. Force on beams of charged
particles in a magnetic field
In Figure 4.5.23 the evenly spaced crosses
N S represent a uniform magnetic field (i.e. one of
the same strength throughout the area shown)
acting into and perpendicular to the paper.
A beam of electrons entering the field at right
angles to the field experiences a force due to the
wire
motor effect whose direction is given by Fleming’s
▲ Figure 4.5.21a left-hand rule. This indicates that the force acts
at right angles to the direction of the beam and
238
▲ Figure 4.5.24
13 An electron beam follows a circular path in a
perpendicular magnetic field. Will the radius of
the path increase or decrease if the strength of
▲ Figure 4.5.23 Path of an electron beam at right angles the magnetic field increases? Why?
to a magnetic field
In the previous topic you learnt that a current flowing in a magnetic field experiences a force. The
force may lead to a turning effect on a current-carrying coil in a magnetic field because of a turning
effect arising from the two sides of the coil. The magnitude of the turning effect is increased by
increasing the number of turns on the coil, increasing the current or increasing the strength of the
magnetic field. This turning effect is the basis of all electric motors from electric toothbrushes to
ship propulsion.
239
N S
a d
brush brush
(fixed) (fixed)
commutator
(rotates with coil)
240
Practical work
A model motor the tube from the first end. The bare ends act
The motor shown in Figure 4.5.27 is made from as the commutator.
a kit. e Push the axle through the metal tube of the
wooden base so that the block spins freely.
a Wrap Sellotape round one end of the metal f Arrange two 0.5 metre lengths of wire to act
tube which passes through the wooden block. as brushes and leads to the supply, as shown.
b Cut two rings off a piece of narrow rubber Adjust the brushes so that they are vertical
tubing; slip them on to the taped end of the and each touches one bare end of the coil
metal tube. when the plane of the coil is horizontal. The
c Remove the insulation from one end of a motor will not work if this is not so.
1.5-metre length of SWG 26 PVC-covered g Slide the base into the magnet with opposite
copper wire and fix it under both rubber rings poles facing. Connect to a 3 V battery (or other
so that it is held tight against the Sellotape. low-voltage d.c. supply) and a slight push of
This forms one end of the coil. the coil should set it spinning at high speed.
d Wind 10 turns of the wire in the slot in the
wooden block and finish off the second end of 3 List the variables in the construction of a
the coil by removing the PVC and fixing this simple d.c. motor.
too under the rings but on the opposite side of 4 How would the motion of the coil change if you
reversed the current direction?
Sellotape brushes
bare ends
of coil
metal rubber
tube rings
split pin
base
magnet
rivet
to battery yoke
coil in slot
241
Moving-coil galvanometer The soft iron cylinder at the centre of the coil
is fixed and along with the concave poles of the
A galvanometer detects small currents or small magnet it produces a radial field (Figure 4.5.28b),
p.d.s, often of the order of milliamperes (mA) or i.e. the field lines are directed to and from the
millivolts (mV). centre of the cylinder. The scale on the meter
In the moving-coil pointer-type meter, a coil is is then even or linear, i.e. all divisions are the
pivoted between the poles of a permanent magnet same size.
(Figure 4.5.28a). Current enters and leaves the coil
by hair springs above and below it. When there is a
current, a turning effect acts on the coil (as in an Test yourself
electric motor), causing it to rotate until stopped by 14 How would the turning effect on a current-
the springs. The greater the current, the greater the carrying coil in a magnetic field change if
a the size of the magnetic field is increased
deflection which is shown by a pointer attached to b the direction of the magnetic field is
the coil. reversed?
a
10
5
15 In the simple d.c. electric motor of Figure
4.5.29, the coil rotates anticlockwise as seen by
15
N
cylinder
hair
S
spring
b view from above
radial field
X
▲ Figure 4.5.29
★ Understand the terms primary, secondary, step-up and step-down and correctly use the transformer equation.
★ Describe how high-voltage transformers are used in the transmission of electricity and why high voltages
are preferred.
★ Use the correct equations to calculate efficiency in a transformer and to explain how losses in cables
are reduced by transmitting power at greater voltages.
242
Many household devices such as electronic keyboards, toys, lights and telephones require a
lower voltage than is provided by the mains supply and a transformer is needed to reduce the
mains voltage. When two coils lie in a magnetic field, variations in the current in one coil induce a
current change in the other. In this section you will learn that this effect is used in a transformer to
raise or lower alternating voltages. The voltage transformation depends on the ratio of the number
of turns of wire in each coil. Alternating current generated in a power station is transformed into
a very high voltage for long-distance electrical transmission. This reduces the size of the current
flowing in the transmission cables and minimises the energy lost to heat due to the resistance of
the cables.
coil A coil B
(600 turns) (600 turns)
tapping key
243
Practical work
Transformer equation
An alternating voltage applied to the primary
induces an alternating voltage in the secondary.
Mutual induction with a.c. The value of the secondary voltage can be shown,
An a.c. is changing all the time and if it flows for a transformer in which all the field lines cut the
in a primary coil, an alternating voltage and secondary, to be given by
current are induced in a secondary coil. primary voltage primary turns
=
Connect the circuit of Figure 4.5.32. All wires secondary voltage secondary turns
used should be insulated. The 1 V high current
In symbols
power unit supplies a.c. to the primary and the
lamp detects the secondary current. Vp Np
=
Find the effect on the brightness of the lamp of Vs Ns
a pulling the C-cores apart slightly A step-up transformer has more turns on the
b increasing the secondary turns to 15 secondary than the primary and Vs is greater than
c decreasing the secondary turns to 5. Vp (Figure 4.5.33a). For example, if the secondary
high current
has twice as many turns as the primary, Vs is about
iron C-cores
power unit twice Vp. In a step-down transformer there are fewer
turns on the secondary than the primary and Vs is
less than Vp (Figure 4.5.33b).
lamp (2.5 V 0.3 A)
a b
Vp VS Vp VS
1 V a.c.
primary
(10 turns)
secondary
(10 turns)
Test yourself
17 The main function of a step-down transformer
▲ Figure 4.5.32 is to
A decrease current
5 In the circuit of Figure 4.5.32, if a d.c. supply B decrease voltage
were used instead of an a.c. supply would C change a.c. to d.c.
you expect the lamp to light? Explain your D change d.c. to a.c.
answer. 18 A transformer has 1000 turns on the primary coil.
The voltage applied to the primary coil is 230 V a.c.
6 In the circuit of Figure 4.5.32 would you
How many turns are on the secondary coil if the
expect the brightness of the lamp to output voltage is 46 V a.c.?
increase or decrease if you lowered the A 20 B 200
voltage to the primary coil? C 2000 D 4000
244
Energy losses in a transformer These are reduced by using a laminated core made
of sheets, insulated from one another to have a
If the p.d. is stepped up in a transformer, the high resistance.
current is stepped down in proportion. This must
be so if we assume that all the electrical energy Leakage of field lines
given to the primary appears in the secondary, All the field lines produced by the primary may not
i.e. that energy is conserved and the transformer cut the secondary, especially if the core has an air
is 100% efficient or ‘ideal’ (many approach this gap or is badly designed.
efficiency). Then
power in primary = power in secondary
Worked example
IpVp = IsVs
A transformer steps down the mains supply from 230 V to
where Ip and Is are the primary and secondary 10 V to operate an answering machine.
currents, respectively. Np
a What is the turns ratio, , of the transformer windings?
I Vp Ns
∴ s =
Ip Vs primary voltage, Vp = 230 V
secondary voltage, Vs = 10 V
So, for the ideal transformer, if the p.d. is N p Vp 230 V 23
doubled the current is halved. In practice, it is turns ratio = = = =
N s Vs 10 V 1
more than halved, because of small energy losses
b How many turns are on the primary if the secondary has
in the transformer arising from the following 100 turns?
three causes. secondary turns, Ns = 100
Resistance of windings From a,
The windings of copper wire have some resistance Np 23
=
and heat is produced by the current in them. Ns 1
Large transformers like those in Figure 4.5.34 ∴ Np = 23 × Ns = 23 × 100
have to be oil-cooled to prevent overheating. = 2300 turns
▲ Figure 4.5.34 Step-up transformers at a power station Now put this into practice
Eddy currents
1 A transformer steps down the mains supply from 240 V to
12 V to operate a doorbell.
The iron core is in the changing magnetic field Np
a What is the turns ratio of the transformer windings?
of the primary coil and currents, called eddy Ns
currents, are induced in it which cause heating. b How many turns are on the primary if the secondary
has 80 turns?
245
275 KV or 400 kV
132 kV
25 kV
415 V or 230 V 11 kV 33 kV
246
20
ii 400 000 V 60
aluminium
power transferred P = IV so N
disc
200000 W
80
247
Revision checklist
After studying Topic 4.5 you should know and After studying Topic 4.5 you should be able to:
understand: ✔ describe experiments to show electromagnetic
✔ Faraday’s explanation of electromagnetic induction induction
✔ the right-hand screw and right-hand grip rules
for relating current direction and magnetic field ✔ predict the direction of induced e.m.f.s and
direction currents and describe and explain the operation
✔ the action and applications of a relay and a of a simple a.c. generator
loudspeaker ✔ draw sketches and describe an experiment to
✔ that a rectangular current-carrying coil identify the pattern of magnetic field lines arising
experiences a turning effect in a magnetic field from currents in straight wires and solenoids
and that the effect is increased by increasing the
number of turns on the coil, the current in the coil ✔ identify regions of different magnetic field
or the strength of the magnetic field strength around a solenoid and straight wire
and describe the effect on their magnetic fields
✔ how to use Fleming’s left-hand rule for relating of changing the magnitude and direction of the
directions of force, field and current current
✔ the terms primary, secondary, step-up and step- ✔ describe an experiment that demonstrates a force
down in relation to a transformer acts on a current-carrying conductor in a magnetic
✔ the use of transformers in the high voltage field, and recall the factors which influence the
transmission of electrical power size and direction of the force
✔ the reasons why greater voltage a.c. is preferred ✔ explain the action of a simple d.c. electric
with reference to the equation P = I 2R. motor
✔ describe the construction of a transformer and
use the transformer equation Vs/Vp = Ns/Np
248
Exam-style questions
1 a Describe an experiment to demonstrate 4 a Describe an experiment to plot the
electromagnetic induction. [4] magnetic field lines around a straight
b State the factors affecting the magnitude current-carrying wire. [4]
of an induced e.m.f. [3] b Sketch the magnetic field lines (including
[Total: 7] their direction) around a current-carrying
2 a Describe the deflections observed on the solenoid.[4]
sensitive, centre-zero galvanometer G c What happens if the direction of the
(Figure 4.5.38) when the copper rod XY is current in the wire is reversed? [1]
connected to its terminals and is made [Total: 9]
to vibrate up and down (as shown by the 5 Part of the electrical system of a car is shown
arrows), between the poles of a U-shaped in Figure 4.5.40. Explain why
magnet, at right angles to the magnetic a connections are made to the car body [2]
field.[2] b there are two circuits in parallel with
b Explain the behaviour of the galvanometer the battery[2]
in part a. [4] c wire A is thicker than wire B [1]
d a relay is used. [2]
Y
G contacts
N A
S
B starter coil
X switch
starter
motor
▲ Figure 4.5.38 relay
[Total: 6]
249
[Total: 11]
10 a Describe the construction of a simple
transformer with a soft iron core. [4]
b Explain the function of a step-up 13 a Explain the use of transformers in the
transformer.[2] transmission of electrical power. [3]
c A step-up transformer is used to obtain a b Give two reasons for the use of high
p.d. of 720 V from a mains supply of 240 V. voltages in the transmission of
Calculate the number of turns that will electricity.[2]
be needed on the secondary if there are [Total: 5]
120 turns on the primary. [4]
[Total: 10]
11 a Calculate the number of turns on the
secondary of a step-down transformer
which would enable a 12 V lamp to be used
with a 230 V a.c. mains power, if there are
460 turns on the primary. [4]
250
★ Describe how the nuclear model of the atom is supported by the scattering of alpha (a-) particles by a
sheet of thin metal.
The discoveries of the electron and of radioactivity indicated that atoms contained negatively and
positively charged particles and were not indivisible as was previously thought. The questions then
were ‘How are the particles arranged inside an atom?’ and ‘How many are there in the atom of each
element?’ In this topic you will learn that atoms have a small dense nucleus surrounded by a cloud of
negatively charged electrons orbiting the nucleus. In a neutral atom the charge of the electrons and
nucleus are equal and opposite.
The experiments by Geiger and Marsden on the scattering of a-particles from thin metal films
provided evidence for the nuclear model of the atom.
An early theory, called the ‘plum-pudding’ model, Experiments carried out by physicists in the early
regarded the atom as a positively charged sphere in twentieth century cast doubts about this model.
which the negative electrons were distributed all The structure of an atom is now described in terms
over it (like currants in a pudding) and in sufficient of negatively charged electrons orbiting a positively
numbers to make the atom electrically neutral. charged nucleus.
252
They found that most of the a-particles were an atom. Putting it another way, the nucleus is like
undeflected, some were scattered by appreciable a sugar lump in a very large hall and the electrons a
angles and a few (about 1 in 8000) surprisingly swarm of flies.
‘bounced’ back. To explain these results Rutherford Figure 5.1.2 shows the paths of three a-particles.
proposed in 1911 a ‘nuclear’ model of the atom in Particle 1 is clear of all nuclei and passes
which all the positive charge and most of the mass straight through the gold atoms.
of an atom formed a dense core or nucleus, of Particle 2 is deflected slightly.
very small size compared with the whole atom. The Particle 3 approaches a gold nucleus so closely
electrons surrounded the nucleus some distance away. that it is violently repelled by it and ‘rebounds’,
He derived a formula for the number of appearing to have had a head-on ‘collision’.
a-particles deflected at various angles, assuming atom of
that the electrostatic force of repulsion between the nucleus of
gold foil
gold atom
positive charge on an a-particle and the positive
charge on the nucleus of a gold atom obeyed an 1
inverse-square law (i.e. the force increases four times 2
if the separation is halved). Geiger and Marsden’s 3
experimental results confirmed Rutherford’s formula
and supported the view that an atom is mostly -particle
empty space. In fact, the nucleus and electrons ▲ Figure 5.1.2 Electrostatic scattering of a-particles
occupy about one-million-millionth of the volume of
Going further
Rutherford–Bohr model of the atom electrons may jump to an outer orbit. The atom is then said
to be excited. Very soon afterwards the electrons return
Shortly after Rutherford proposed his nuclear model of
to an inner orbit and, as they do, energy is transferred by
the atom, Niels Bohr, a Danish physicist, developed it
bursts of electromagnetic radiation (called photons), such
to explain how an atom emits light. He suggested that
as infrared light, ultraviolet or X-rays (Figure 5.1.4). The
the electrons circled the nucleus at high speed, being
wavelength of the radiation emitted depends on the two
kept in certain orbits by the electrostatic attraction of
orbits between which the electrons jump. If an atom gains
the nucleus for them. He pictured atoms as miniature
enough energy for an electron to escape altogether, the
solar systems. Figure 5.1.3 shows the model for three
atom becomes an ion and the energy needed to achieve
elements.
this is called the ionisation energy of the atom.
lithium
hydrogen helium inner orbit electron jump electron
jump
outer
orbit
orbits
proton
neutron
electron
energy in radiation out
▲ Figure 5.1.3 Electron orbits
▲ Figure 5.1.4 Bohr’s explanation of energy changes in an
Normally the electrons remain in their orbits but if
atom
the atom is given energy, for example by being heated,
253
Going further
Schrödinger model of the atom This theory does away with the idea of electrons moving
in definite orbits and replaces them by energy levels
Although it remains useful for some purposes, the
that are different for each element. When an electron
Rutherford–Bohr model was replaced by a mathematical
‘jumps’ from one level, say E3 in Figure 5.1.6, to a
model developed by Erwin Schrödinger, which is not easy
lower one E1, a photon of electromagnetic radiation is
to picture. The best we can do, without using advanced
emitted with energy equal to the difference in energy
mathematics, is to say that in the Schrödinger model the
of the two levels. The frequency (and wavelength) of
atom consists of a nucleus surrounded by a hazy cloud of
the radiation emitted by an atom is thus dependent
electrons. Regions of the atom where the mathematics
on the arrangement of energy levels. For an atom
predicts that electrons are more likely to be found are
emitting visible light, the resulting spectrum (produced
represented by denser shading (Figure 5.1.5).
for example by a prism) is a series of coloured lines
that is unique to each element. Sodium vapour in a gas
discharge tube (such as a yellow street light) gives two
adjacent yellow–orange lines (Figure 5.1.7a). Light from
the Sun is due to energy changes in many different
atoms and the resulting spectrum is a continuous one
with all colours (see Figure 5.1.7b).
E2
Test yourself
1 Describe how charge and mass are distributed in an 2 How can a positive ion be formed from a neutral
atom. atom?
★ Describe nuclear fission and nuclear fusion and the corresponding nuclide equations.
★ Understand what is meant by proton number (Z) and nucleon number (A) and calculate the number of
neutrons in a nucleus.
★ Know how the proton and nucleon numbers relate to the charge on or mass of a nucleus.
★ Describe and explain isotopes in terms of number of protons and neutrons and use nuclide notation.
254
The nucleus of an atom is composed of positively charged protons and uncharged neutrons of very
similar mass. The properties of an atom are determined by the number of protons, but the number of
neutrons can vary to give different isotopes of the same element.
Some heavy nuclei are unstable and break up into multiple parts in nuclear fission. Light nuclei
may combine in nuclear fusion. Both processes emit substantial amounts of energy.
We now believe as a result of many experiments, in Hydrogen Helium Lithium Oxygen Copper
some of which a- and other high-speed particles protons 1 2 3 8 29
were used as ‘atomic probes’, that atoms contain
neutrons 0 2 4 8 34
three basic particles – protons, neutrons and
electrons. electrons 1 2 3 8 29
A proton is a hydrogen atom minus an electron,
i.e. a positive hydrogen ion. Its charge is equal in The atomic or proton number Z of an atom is
size but opposite in sign to that of an electron, but the number of protons in the nucleus. The proton
its mass is about 2000 times greater. number is also the number of electrons in the atom.
A neutron is uncharged with almost the same The electrons determine the chemical properties
mass as a proton. The relative charges of protons, of an atom and when the elements are arranged in
neutrons and electrons are +1, 0, –1, respectively. order of atomic number in the Periodic Table, they
Protons and neutrons are in the nucleus and are fall into chemical families.
called nucleons. Together they account for the mass The mass or nucleon number A of an atom is the
of the nucleus (and most of that of the atom); the number of nucleons in the nucleus.
protons account for its positive charge. These facts In general, the number of neutrons in the
are summarised in Table 5.1.1. nucleus = A – Z.
Atomic nuclei are represented by symbols. Hydrogen
is written as 11 H, helium as 42 He and lithium as 73 Li.
Key definition In general atom X is written in nuclide notation as ZA X ,
Relative charges of protons, neutrons and electrons where A is the nucleon number and Z the proton number.
+1, 0, –1, respectively
Key definitions
▼ Table 5.1.1 Proton number Z number of protons in the nucleus
Nucleon number A number of protons and neutrons in the
Particle Relative mass Relative charge Location
nucleus
proton 1836 +1 in nucleus
neutron 1839 +0 in nucleus
electron 1 –1 outside
nucleus
Mass and charge on a nucleus
The relative charge on a nucleus is equal to the
In a neutral atom the number of protons equals the product of the proton number Z and the charge on
number of electrons surrounding the nucleus. Table a proton.
5.1.2 shows the particles in some atoms. Hydrogen is The relative mass of a nucleus is equal to the
simplest with one proton and one electron. Next is total mass of the neutrons and protons in the
the inert gas helium with two protons, two neutrons nucleus. For a nucleus of nucleon number A this
and two electrons. The soft white metal lithium has will be approximately equal to the product of A
three protons and four neutrons. and the mass of a proton.
255
Test yourself
3 An atom consists of protons, neutrons and electrons. iii neutrons in the nucleus
Which one of the following statements is not true? iv electrons in a neutral atom.
A An atom consists of a tiny nucleus surrounded by b Give the symbol for the lithium atom in nuclide
orbiting electrons. notation.
23
B The nucleus always contains protons and 5 An atom of sodium has the symbol 11 Na.
neutrons, called nucleons, in equal numbers. a State the values of Z and A.
C A proton has a positive charge, a neutron is b How many protons are there in the nucleus?
uncharged and their mass is about the same.
D An electron has a negative charge of the same
6 An atom of helium has the symbol 42 He. State the
size as the charge on a proton but it has a much
charge on the nucleus of the atom.
smaller mass. 37
7 An atom of chlorine has the symbol 17 Cl .
4 A lithium atom has a nucleon number of 7 and a
a State the nucleon number of the atom.
proton number of 3.
b Explain how the nucleon number is related to
a State the number of
the mass of a nucleus.
i nucleons in the nucleus
ii protons in the nucleus
Worked example
Three stable isotopes of oxygen are 168 O , 178 O and 188 O . ii number of nucleons A =18
Give the number of i protons, ii nucleons and iii neutrons in iii number of neutrons = A – Z = 10
each isotope.
Now put this into practice
Oxygen-16
i number of protons Z = 8 1 Two isotopes of carbon are 126 C and 146 C .
ii number of nucleons A =16 Give the number of
iii number of neutrons = A – Z = 8 a protons b nucleons c neutrons
in each isotope.
Oxygen-17 2 In the nucleus of two isotopes of the same element,
i number of protons Z = 8 state whether the following numbers are the same or
ii number of nucleons A =17 different.
iii number of neutrons = A – Z = 9 A Number of neutrons
Oxygen-18 B Number of protons
i number of protons Z = 8 C Number of nucleons
256
Fission
The heavy metal uranium is a mixture of isotopes
of which 235
92
U , called uranium-235, is the most ▲ Figure 5.1.8 Chain reaction
important. Some atoms of this isotope decay
Nuclear reactor
quite naturally, emitting high-speed neutrons.
If one of these hits the nucleus of a neighbouring In a nuclear power station, heat from a nuclear
uranium-235 atom (as it is uncharged the neutron reactor produces the steam for the turbines.
is not repelled by the nucleus), the nucleus may Figure 5.1.9 (on the next page) is a simplified
break (fission of the nucleus) into two nearly equal diagram of one type of reactor.
radioactive nuclei, often of barium and krypton, The chain reaction occurs at a steady rate
with the production of two or three more neutrons: which is controlled by inserting or withdrawing
neutron-absorbing control rods of boron among
235
U + 10 n → 144
Ba + 90 Kr + 210 n the uranium rods. The graphite core is called the
92 56 36
moderator and slows down the fission neutrons:
neutron fission fragments neutrons fission of uranium-235 occurs more readily with
slow than with fast neutrons. Carbon dioxide gas
The mass defect is large and appears mostly as is pumped through the core as a coolant. In the
kinetic energy of the fission fragments. These fly heat exchanger the heated gas transfers energy
apart at great speed, colliding with surrounding to pipes containing cold water so that the water
atoms and raising their average kinetic energy, i.e. boils to produce steam. The concrete shield gives
their temperature. workers protection from γ-emissions and escaping
Note that the total values of A and Z must neutrons. The radioactive fission fragments must
balance on both sides of the equation because be removed periodically if the nuclear fuel is to be
nucleons and charge are conserved. used efficiently.
On the left of the equation: In an atomic bomb, an increasingly uncontrolled
total A = 235 + 1 = 236 and total Z = 92 + 0 = 92. chain reaction occurs when two pieces of uranium-235
On the right of the equation: come together and exceed the critical mass.
total A = 144 + 90 + 2 = 236 and
total Z = 56 + 36 + 0 = 92.
The total values of A and Z on each side of the
equation are equal.
257
steam
boron rod
heat exchanger
uranium rod
graphite core
cold water
cold
gas
pump
258
Revision checklist
After studying Topic 5.1 you should know and After studying Topic 5.1 you should be able to:
understand: ✔ describe the location in the atom of protons,
✔ the terms proton number (Z), nucleon number (A), neutrons and electrons
isotope and nuclide, and how to use the nuclide
notation. ✔ describe the Geiger–Marsden experiment which
established the nuclear model of the atom
✔ balance equations involving nuclide notation
and outline the processes of nuclear fission and
fusion.
Exam-style questions
1 a Define i proton number Z and 3 a Describe the importance of Geiger and
ii nucleon number A. [2] Marsden’s experiment on the scattering
b Explain the meaning of the term isotope. [2] of a-particles by a thin metal film to
c An isotope of helium can be written understanding the structure of the atom.[5]
in nuclide notation as 32 He. b State the charge on i a proton, ii a neutron
Describe how an atom of 32 He differs from and iii a helium nucleus. [3]
one of 42 He. [2] [Total: 8]
[Total: 6]
4 a Explain what is meant by
2 An atom of calcium can be written in nuclide i nuclear fission [2]
notation as 4020
Ca. ii nuclear fusion. [2]
a State the values of the nucleon number A b Energy is released in the following
and the proton number Z for an atom of nuclear fusion reaction
calcium. [2] 3
b In a neutral atom of calcium state the 2
He + 32 He → 4X Y+ 11H + 11H
number of i Determine the total values of A and
i protons [1] Z on the left side of the equation. [2]
ii nucleons [1] ii Work out X and identify Y. [2]
iii neutrons [1] [Total: 8]
iv electrons. [1]
c When a calcium atom loses an electron it
becomes an ion. State whether the ion is
negatively or positively charged. [1]
[Total: 7]
259
In the previous topic you learnt that an atom has a small dense nucleus containing neutrons
and protons which is surrounded by a cloud of electrons. In this topic you will encounter the
consequences of instability in the nucleus – radioactivity. We are all continually exposed to radiation
from a range of radioactive sources, including radon gas in the air we breathe, cosmic rays from the
Sun, food and drink and the rocks and buildings around us. These sources all contribute to what is
called background radiation.
The discovery of radioactivity in 1896 by the French (v) Various radioisotopes are used in certain
scientist Henri Becquerel was accidental. He found medical procedures.
that uranium compounds emitted radiation that (vi) Radiation is produced in the emissions from
(i) affected a photographic plate even when it was nuclear power stations and in fall-out from the
wrapped in black paper and (ii) ionised a gas. Soon testing of nuclear bombs; the latter produce
afterwards Marie Curie discovered the radioactive strontium isotopes with long half-lives which
element radium. We now know that radioactivity are absorbed by bone.
arises from unstable nuclei which may occur
radioactivity in the air
naturally or be produced in reactors. Radioactive
materials are widely used in industry, medicine and cosmic rays
research.
rocks
We are all exposed to natural background
radiation, both natural and artificial, as indicated food
in Figure 5.2.1. medical
(i) Cosmic rays (high-energy particles from the
nuclear power stations
Sun) are mostly absorbed by the atmosphere but
some reach the Earth’s surface. nuclear bombs
(ii) Radon gas is in the air.
▲ Figure 5.2.1 Radiation sources
(iii) Numerous homes, particularly in Scotland, are
built from granite rocks that emit radioactive
radon gas; this can collect in basements or well- Ionising effect of radiation
insulated rooms if the ventilation is poor. A charged electroscope discharges when a lighted
(iv) Radioactive potassium-40 is present in food and match or a radium source (held in forceps) is brought
is absorbed by our bodies. near the cap (Figure 5.2.2).
260
450 V
forceps
radium source mica
window
▲ Figure 5.2.2
261
★ Describe the deflection of a-particles, b-particles and γ-radiation in magnetic and electric fields.
★ Explain the ionising effects of a-particles, b-particles and γ-radiation in terms of electric charge and
kinetic energy.
Certain isotopes can decay into a more stable state with emission of radiation in the form of discrete
particles (a- and β-particles) or high-frequency electromagnetic waves (γ-radiation). The emission
of the radiation is random in direction. You will learn about the different properties of these three
types of radiation and how they interact with matter. An a-particle is a doubly positively charged
helium ion and a b-particle is a negatively charged electron.
Owing to their electric charge both a-particles and b-particles are deflected by electric and
magnetic field; γ-radiation is deflected by neither. Their kinetic energy and electric charge affect
the ionising properties of each type of radiation.
Alpha, beta and gamma radiation Penetrating power of the different types of radiation
can be investigated as shown in Figure 5.2.5 by
Experiments to study the penetrating power, observing the effect on the count-rate of placing
ionising ability and behaviour of radiation in one of the following in turn between the GM tube
magnetic and electric fields show that a radioactive and the lead sheet:
substance emits one or more of three types of (i) a sheet of thick paper (the radium source, lead
radiation – called alpha (a-), beta (b-) and gamma and tube must be close together for this part)
(γ-) radiation. The emission of radiation from a (ii) a sheet of aluminium 2 mm thick
nucleus is a spontaneous and random process (iii) a further sheet of lead 2 cm thick.
in direction; we will consider this again later Radium (Ra-226) emits a-particles, b-particles and
(see p. 269). γ-emissions. Other sources can be used, such as
4 mm plug ratemeter americium, strontium and cobalt.
a-particles
These are stopped by a thick sheet of paper and
radium
source have a range in air of only a few centimetres since
GM tube
they cause intense ionisation in a gas due to
frequent collisions with gas molecules. They are
deflected by electric and strong magnetic fields in
a direction and by an amount which suggests they
lead sheet with 1 mm hole to prevent
overloading of GM tube
are helium atoms minus two electrons, i.e. helium
ions with a double positive charge. From a particular
▲ Figure 5.2.5 Investigating the penetrating power of
radiation
substance, they are all emitted with the same speed
(about 1/20th of that of light).
Experiments using radiation sources are teacher Americium (Am-241) is a pure a-particle source,
demonstrations only. used in smoke detectors.
262
263
+ a a-particles
metal plate
+ + + +
γ γ
β−
α++
– – – –
metal plate –
Particle tracks
The paths of particles of radiation were first
shown up by the ionisation they produced in
devices called cloud chambers. When air containing
a vapour, alcohol, is cooled enough, saturation
occurs. If ionising radiation passes through the
air, further cooling causes the saturated vapour to
condense on the ions created. The resulting white
line of tiny liquid drops shows up as a track when
illuminated. ▲ Figure 5.2.8 Tracks in a cloud chamber
In a diffusion cloud chamber, a-particles The bubble chamber, in which the radiation leaves a
showed straight, thick tracks (Figure 5.2.8a). trail of bubbles in liquid hydrogen, has now replaced
Very fast b-particles produced thin, straight the cloud chamber in research work. The higher
tracks while slower ones gave short, twisted, density of atoms in the liquid gives better defined
thicker tracks (Figure 5.2.8b). γ-emissions tracks, as shown in Figure 5.2.9 than obtained in a
eject electrons from air molecules; the ejected cloud chamber. A magnetic field is usually applied
electrons behaved like b–-particles in the cloud across the bubble chamber which causes charged
chamber and produced their own tracks spreading particles to move in circular paths; the sign of the
out from the γ-emissions. charge can be deduced from the way the path curves.
264
Test yourself
4 Which type of radiation from radioactive materials
a has a positive charge
b is the most penetrating
c has the shortest range in air
d has a negative charge?
★ Know why isotopes of an element may be radioactive and describe the effect of a-, b-decay and
γ-emissions on the nucleus.
★ Determine the emission of a-, b-decay and γ-radiation using decay equations.
Radioactive decay occurs when an unstable nucleus emits an a- or b-particle. Radioactive decay is
a random process; when and in which direction a particular atom will decay cannot be determined.
When radioactive decay occurs, a different element is formed.
A nucleus is unstable if it has too many neutrons or is too heavy. Stability is increased in β-decay
because the number of neutrons is decreased when a neutron turns into a proton and an electron.
Heavy nuclei become lighter and more stable by emission of an a-particle. Decay equations using
nuclide notation can be used to represent the changes that a nucleus undergoes in radioactive
decay.
a-decay
An a-particle is a helium nucleus, having two Going further
protons and two neutrons, and when an atom
Other particles
decays by emission of an a-particle, its nucleon
Positrons are subatomic particles with the same
number decreases by 4 and its proton number by 2.
mass as an electron but with opposite (positive)
For example, when radium of nucleon number charge. They are emitted in some decay processes
226 and proton number 88 emits an a-particle, it as b+-particles. Their tracks can be seen in bubble
decays to radon of nucleon number 222 and proton chamber photographs. The symbol for a positron
number 86. We can write the following radioactive is b+. In b+-decay a proton in a nucleus is converted
decay equation using nuclide notation: to a neutron and a positron as, for example, in the
reaction:
226
88
Ra → 222
86
Rn + 42 He 64
Cu → 64 Ni + +01e
29 28
The values of A and Z must balance on both sides A neutrino (ν) is also emitted in b+-decay. Neutrinos
of the equation since nucleons and charge are are emitted from the Sun in large numbers,
but they rarely interact with matter so are very
conserved. In a-decay the number of nucleons
difficult to detect. Antineutrinos and positrons
in the nucleus is reduced and a heavy nucleus are the ‘antiparticles’ of neutrinos and electrons,
becomes lighter, tending to increase its stability. respectively. If a particle and its antiparticle
collide, they annihilate each other and energy
b-decay is transferred to γ-radiation.
In b–-decay a neutron changes to a proton and an An antineutrino (υ ), with no charge and negligible
electron. mass, is also emitted in b– -decay.
neutron → proton + electron
266
267
The half-life of a particular isotope is the time Half-lives vary for different isotopes from
taken for half the nuclei of that isotope in a given millionths of a second to millions of years.
sample to decay. For radium it is 1600 years.
It is difficult to know when a substance has lost
all its radioactivity, but the time for its activity to
fall to half its value can be found more easily. 80
activity (disintegrations/s)
Key definition
Half-life of a particular isotope the time taken for half 40
the nuclei of that isotope in any sample to decay
20
10
Decay curve 0 10 20 30 time/min
The average number of disintegrations (i.e. decaying
atoms) per second of a sample is its activity. If it
is measured at different times (e.g. by finding the
half-lives
count-rate using a GM tube and ratemeter), a decay
curve of activity against time can be plotted. The ▲ Figure 5.2.11 Decay curve
ideal curve for one element (Figure 5.2.11) shows
that the activity decreases by the same fraction in The information in Figure 5.2.11 may also be
successive equal time intervals. It falls from 80 to 40 represented in table form:
disintegrations per second in 10 minutes, from 40 to Time/min 0 10 20 30
20 in the next 10 minutes, from 20 to 10 in the third
Counts/s 80 40 20 10
10 minutes and so on. The half-life is 10 minutes.
Worked example
a In an experiment to find the half-life of radioactive iodine, Now put this into practice
the following results were obtained. 1 In an experiment to find the half-life of a radioisotope the
following results were obtained.
Time/min 0 25 50 75
Counts/s 200 100 50 25 Time/min 0 10 20 30 40 50
i
What is the half-life of the iodine? Counts/s 200 133 88 59 39 26
The count-rate drops by half every 25 minutes. a Estimate the half-life of the radioisotope from the
The half-life of iodine is 25 minutes. data.
ii
What fraction of the original material is left after 75 b Determine the half-life of the radioisotope by plotting
minutes? a graph.
75 minutes corresponds to 3 half-lives. 2 A radioactive source has a half-life of 15 minutes. Find
After 25 minutes, fraction left = 1/2 the fraction left after 1 hour.
After 50 minutes, fraction left = 1/2 × 1/2 = 1/4 3 In an experiment to determine the half-life of a
After 75 minutes, fraction left = 1/2 × 1/4 = 1/8 radioactive material its count-rate falls from 140 counts/
b Carbon-14 has a half-life of 5700 years. A 10 g sample minute to 35 counts/minute in an hour. Calculate the half-
of wood cut recently from a living tree has an activity life of the material.
of 160 counts/minute. A piece of charcoal taken from a 4 Carbon-14 has a half-life of 5700 years. A 5 g sample
prehistoric campsite also weighs 10 g but has an activity of wood cut recently from a living tree has an activity
of 40 counts/minute. Estimate the age of the charcoal. of 80 counts/minute. A 5 g piece of wood taken from an
After 1 × 5700 years the activity will be 160/2 = 80 counts ancient dugout canoe has an activity of 20 counts/minute.
per minute. Estimate the age of the canoe.
After 2 × 5700 years the activity will be 80/2 = 40 counts
per minute.
The age of the charcoal is 2 × 5700 = 11 400 years.
268
thoron
The half-life of the a-emitting gas thoron can be stopper
found as shown in Figure 5.2.12. The thoron bottle screw clip
is squeezed three or four times to transfer some
thoron to the flask (Figure 5.2.12a). The clips are
then closed, the bottle removed and the stopper
replaced by a GM tube so that it seals the top
(Figure 5.2.12b).
When the ratemeter reading has reached its
maximum and started to fall, the count-rate is
noted every 15 s for 2 minutes and then every 60 s filter flask
for the next few minutes. (The GM tube is left in thoron bottle
the flask for at least 1 hour until the radioactivity
b
has decayed.) ratemeter
A measure of the background radiation is
obtained by recording the counts for a period
(say 10 minutes) at a position well away from
the thoron equipment. The count-rates in the
thoron decay experiment are then corrected by
subtracting the average background count-rate
from each reading. A graph of the corrected count-
rate against time is plotted and the half-life (52 s)
estimated from it. clip closed
GM tube
(thin end-window)
▲ Figure 5.2.12
Test yourself
8 In an experiment to determine the half-life of a Correct the count-rates for background
thorium the following results were obtained. radiation.
b Plot a graph of corrected counts/s against
Time/s 0 30 60 90 120 150 180 time and estimate the half-life of thorium.
269
270
Test yourself
10 What type of radiation is used
a to sterilise equipment
b in a smoke alarm?
11 Explain how radioisotopes can be used to monitor
the thickness of metal sheets in industry. ▲ Figure 5.2.14 The year of construction of this Viking ship has
been estimated by radiocarbon techniques to be 800 CE.
Although a-, b- and γ-radiations have many uses, they can also be very dangerous to humans due to
their ionising properties which damage body cells. Careful safety measures have to be taken when
handling radioactive materials and moving, storing and disposing of them. The symbol warning of the
presence of radioactive materials is universally recognised.
271
272
Revision checklist
After studying Topic 5.2 you should know and After studying Topic 5.2 you should be able to:
understand: ✔ recall the nature of a-, b- and γ-radiation and
✔ the meaning of the term ‘background radiation’ describe experiments to compare their range,
and recall its sources penetrating power and ionising effects
✔ that radioactivity is (i) a spontaneous random
process, (ii) due to nuclear instability and (iii) ✔ predict how a-, b- and γ-radiation will be
independent of external conditions deflected in magnetic and electric fields and
✔ that some isotopes of an element are unstable and explain their relative ionising effects
that during a- or b-decay the nucleus changes to a ✔ describe the effect of a-particles, b-particles
different element and γ-ray emissions on the stability and the
✔ discuss the dangers of radioactivity and necessary number of excess neutrons in the nucleus and
safety precautions. interpret decay equations
Exam-style questions
1 a Three types of radiation, X, Y and Z, are shown iii a neutron [1]
in Figure 5.2.16. iv an electron? [1]
A −10 e B 10 n C 42 He D −11 e
X
[Total: 7]
Y 2 a Explain what is meant by the half-life of a
Z radioisotope. [2]
b The graph represented in Figure 5.2.17 shows
the decay curve of a radioisotope.
paper aluminium lead
▲ Figure 5.2.16
120
count-rate/counts per s
60
A B C D
X a b g g 30
Y b g a b
0 1 2 3 4 5
Z g a b a
time/min
[3]
▲ Figure 5.2.17
b Nuclide notation is used to represent particles
in nuclear reactions. Which symbol A to D, is Calculate its half-life in minutes. [4]
used in equations to represent [Total: 6]
i an a-particle [1]
ii a b-particle [1]
273
3 The ratio of the number of atoms of argon-40 5 a Discuss the effects ionising nuclear radiation
to potassium-40 in a sample of radioactive rock has on living things. [2]
is analysed to be 1 : 3. Assuming that there was b a-, b- and g-emissions have different powers
no potassium in the rock originally and that of ionisation and range.
argon-40 decays to potassium-40 with a half-life Choose the type of radiation whose power of
of 1500 million years, estimate the age of the ionisation is
rock. Assume there were N atoms of argon-40 in i greatest [1]
the rock when it was formed. ii least. [1]
a Calculate Choose the type of radiation whose range in
i the number of argon atoms left after air is
1500 million years [1] iii greatest [1]
ii the number of potassium atoms formed iv least. [1]
after 1500 million years [1] c Describe two safety precautions you should
iii the argon : potassium ratio after 1500 take when using radioactive materials. [2]
million years [1] [Total: 8]
iv the number of argon atoms left after
3000 million years [1] 6 Describe how radioactive sources are used in
v the number of potassium atoms formed the following applications. Name and explain
after 3000 million years [1] the choice of the radiation used in each case.
vi the argon : potassium ratio after 3000 a Smoke alarms [4]
million years. [1] b Thickness measurements in industry [3]
b Estimate the age of the rock. [1] c Irradiation of food [3]
[Total: 7] [Total: 10]
4 a i Radon-222 decays by emitting an
a-particle to form an element whose
symbol is
A 216
85
At B 216
86
Rn
C 218
84
Po D 216
84
Po [1]
ii Write the decay equation in nuclide
notation. [3]
b i Thorium-234 decays by emitting a
b-particle to form an element whose
symbol is
A 235
90
Th B 234
91
Pa
C 234
89
Ac D 232
88
Ra [1]
ii Write the decay equation in nuclide
notation. [3]
[Total: 8]
274
★ Use the Moon’s orbiting of the Earth to explain the Moon’s phases.
Day and night and the rising and setting of the Sun can be explained by the rotation of the Earth on its
axis. The repeating pattern of spring, summer, autumn and winter arises from the motion of the Earth
around the Sun. In this section you will learn more about these natural occurrences. The Earth is the
third planet from the Sun and travels in a nearly circular orbit controlled by the large gravitational
attraction exerted by the Sun. The Earth takes one year to travel around the orbit, moving closer and
further away from the Sun with the seasons. The Moon orbits the Earth under the influence of the
Earth’s gravitational attraction and always has the same area of its surface facing towards the Earth.
The Moon is lit by the light from the Sun so that its appearance changes over the course of each month.
You will learn how to calculate the average orbital speed of an object such as the Moon or a planet.
The Earth is a planet of the Sun travelling in a summer it rises north of east and sets north of west.
nearly circular orbit around the Sun, and the Moon In winter it rises and sets south of these points.
orbits the Earth as a satellite. The motion of the
noon
Earth and Moon account for the occurrence of a
number of natural events. mer
sum
inox
Motion of the Earth equ
winter
Day and night
These are caused by the Earth spinning on its axis south
(i.e. about the line through its north and south
poles) and making one complete revolution every
24 hours. This creates day for the half of the
Earth’s surface facing the Sun and night for the east west
other half, facing away from the Sun.
Rising and setting of the Sun
The Earth’s rotation on its axis causes the Sun to
have an apparent daily journey from east to west.
It rises exactly in the east and sets exactly in the
west only at the equinoxes (around 20 March and ▲ Figure 6.1.1 Rising and setting of the Sun (in the northern
23 September). In the northern hemisphere in hemisphere)
276
Each day the Sun is highest above the horizon At C, around 21 June, the northern hemisphere
at noon and directly due south in the northern has its longest day while the southern hemisphere
hemisphere; this height itself is greatest and the has its shortest day. At G, around 21 December, the
daylight hours longest about 21 June. After that the opposite is true.
Sun’s height slowly decreases and near 21 December At A and E of the orbit, night and day are equal
it is lowest and the number of daylight hours is in both hemispheres; these are the equinoxes, which
smallest, as shown in Figure 6.1.1. often fall on 20 March and 23 September.
The seasons
Two factors are responsible for these. The first is
Motion of the Moon
the motion of the Earth around the Sun once in The moon is a satellite of the Earth and travels
approximately 365 days (i.e. in one year). The second round it in an approximately circular orbit
is the tilt (23.5°) of the Earth’s axis to the plane of approximately once a month at an average
its path around the Sun. Figure 6.1.2 shows the tilted distance away of about 400 000 km. It also revolves
Earth in four different positions of its orbit. on its own axis in a month and so always has the
same side facing the Earth, so that we never see
A
the ‘dark side of the Moon’. We see the Moon by
B H
win reflected sunlight since it does not produce its
ing ter
spr own light. It does not have an atmosphere. It does
Earth tilted 20 Mar have a gravitational field due to its mass, but the
on axis
field strength is only one-sixth of that on Earth.
C 21 Jun 21 Dec G
Hence the astronauts who walked on the Moon
Sun
moved in a ‘springy’ fashion but did not fly off
into space.
23 Sept
su
mm
n
Phases of the Moon
er m
aut u The Moon’s appearance from the Earth changes
D F
during its monthly journey; it has different phases.
E In Figure 6.1.3 the outer circle shows that exactly
▲ Figure 6.1.2 Seasons for the northern hemisphere half of it is always illuminated by the Sun. How
it looks from the Earth in its various positions is
Over part BCD of the Earth’s orbit, the northern shown inside this. In the new Moon phase, the Moon
hemisphere is tilted towards the Sun so that is between the Sun and the Earth and the side facing
the hours of daylight are greater than those of the Earth, being unlit, is not visible from the Earth.
darkness, i.e. it is spring and summer. The southern A thin new crescent appears along one edge as it
hemisphere is tilted away from the Sun and has travels in its orbit, gradually increasing in size until
shorter days than nights so it is autumn and winter at the first quarter phase, when half of the Moon’s
there. The northern hemisphere receives more solar surface can be seen. At full Moon, the Moon is on
radiation and so the weather is warmer. the opposite side of the Earth from the Sun and
Over part FGH of the orbit, the situation is appears as a complete circle. After that it wanes
reversed. The southern hemisphere is tilted towards through the last quarter phase until only the old
the Sun, while the northern hemisphere is tilted crescent can be seen. Figure 6.1.4 shows the surface
away from it, and experiences autumn and winter. of the Moon partially illuminated as seen from Earth.
277
full Moon
Moon’s motion
Orbital speed
In Topic 1.2 we defined
average speed = total distance/total time.
Moon as seen So, for the Moon, moving in a circular orbit
from Earth around the Earth with average orbital speed n,
last first circumference of orbit 2πr
quarter quarter ν= =
T T
Earth
where r is the average radius of the orbit, and T
is the orbital period (the time for one orbit), also
known as the orbital duration.
Key definitions
2πr
new Moon Average orbital speed ν = where r is the average
Sun’s rays T
radius of the orbit and T is the orbital duration
278
★ Know which planets are rocky and small and which are large and gaseous and explain the difference with
reference to an accretion model for Solar System formation.
★ Know what affects the gravitational field strength of a planet.
★ Calculate the time it takes for light to travel large distances in the Solar System.
★ Explain why planets orbit the sun and know that gravitational attraction of the Sun is what keeps an object
in orbit around the Sun.
★ Know the effect of the distance from the Sun on gravitational field and orbital speed of the planets.
★ Use conservation of energy to explain the effect of the distance from the Sun on the speed of an object in
an elliptical orbit.
In this topic you will learn that all the bodies in the Solar System move under the influence of the
gravitational attraction of the large mass of the Sun. The orbits of the planets, dwarf planets and
comets are elliptical with the Sun at one focus. Planetary orbits are nearly circular, but comets
travel far away before returning close to the Sun after a considerable period of time. Moons orbit
planets bound by the gravitation of the planet. The planets are thought to have condensed from
a cloud of dust and gas, called a nebula, with the heavier materials drawn close to the Sun by its
gravity; the inner four small planets are rocky and the much larger outer planets are gaseous with
icy moons. Light from the Sun takes about 8 minutes to reach the Earth.
Space programmes have allowed much data to be collected about the planets and other objects
in our Solar System. You will learn how to use of some of this data, about elliptical orbits, and why
comets and other bodies travel faster when they are nearer to the Sun.
Planet Av distance Orbit time Surface Density Diameter Mass Surface No. of
from Sun round sun temperature /kg/m3 /103 km /1024 kg gravity moons
/million km /days or years /°C /N/kg
Mercury 57.9 88 d 350 5427 4.8 0.330 3.7 0
Venus 108.2 225 d 460 5243 12.1 4.87 8.9 0
Earth 149.6 365 d 20 5514 12.8 5.97 9.8 1
Mars 227.9 687 d –23 3933 6.8 0.642 3.7 2
Jupiter 778.6 11.9 y –120 1326 143 1898 23.1 79
Saturn 1433.5 29.5 y –180 687 120 568 9.0 82
Uranus 2872.5 84 y –210 1271 51 86.8 8.7 27
Neptune 4495.1 165 y –220 1638 50 102 11.0 14
It can be seen from Table 6.1.2 that a planet’s year dioxide. In some parts there are large extinct
(i.e. orbit time around the Sun) increases with volcanoes and evidence such as gorges of torrential
distance from the Sun. The orbital speed, however, floods in the distant past (Figure 6.1.8). Mars is
decreases with distance; Neptune travels much more now a comparatively inactive planet although high
slowly than Mercury. Surface temperatures decrease winds do blow at times causing dust storms.
markedly with distance from the Sun with one
exception. Venus has a high surface temperature
(460°C) due to its dense atmosphere of carbon
dioxide acting as a heat trap (i.e. the greenhouse
effect). Its very slow ‘spin time’ of 243 Earth days
means its day is longer than its year of 225 days!
Mercury, also with a slow ‘spin time’ (58.5 days),
has practically no atmosphere and so while its noon
temperature is 350°C, at night it falls to –170°C.
Mars is the Earth’s nearest neighbour. It is
colder than the Earth, temperatures on its equator
are rarely greater than 0°C even in summer. Its
atmosphere is very thin and consists mostly of
carbon dioxide with traces of water vapour and
oxygen. Its axis is tilted at an angle of 24° and
so it has seasons, but these are longer than on ▲ Figure 6.1.8 The surface of Mars as seen by the Mars
Earth. There is no liquid water on the surface, but Global Surveyor, showing a vast canyon 6000 km long and
it has polar ice-caps of water, ice and solid carbon layered rocks indicating a geologically active history.
282
Jupiter is by far the largest planet in the Solar Uranus and Neptune are large, cold and windy
System. It is a gaseous planet and is noted for its planets with small rocky cores surrounded by an icy
Great Red Spot, Figure 6.1.9, which is a massive mass of water, methane and ammonia; they both
swirling storm that has been visible from Earth for have rings and many moons. Their atmospheres
over 200 years. consist of methane, as well as hydrogen and
helium. The four outer ‘gas giants’ are able to
retain these lighter gases in their atmospheres,
unlike the Earth, because of the greater
gravitational attraction their large masses exert.
The dwarf planet Pluto is smaller than our Moon
and has an atmosphere of frozen methane and
nitrogen. It has five moons, the largest of which
is Charon, which are thought to have formed in a
collision between two dwarf planets early in the life
of the Solar System. The reddish-brown cap around
the north pole of Charon was found to contain
organic molecules, which together with water, can
form chemicals needed for the evolution of life.
▲ Figure 6.1.9 Jupiter’s Great Red Spot pictured by the Unmanned space missions such as Voyager
Voyager 2 space probe 1 and 2 obtained much information about the
Saturn has spectacular rings made up of ice outer planets and their many moons on flybys.
particles (Figure 6.1.10) which are clearly visible The Cassini spacecraft spent 13 years orbiting and
through a telescope. Like Jupiter it has an ever- collecting data on Saturn and its moons, before
changing, very turbulent atmosphere of hydrogen, plunging into its atmosphere in 2017. Much of
helium, ammonia and methane gas. the information we have on the dwarf planet
Pluto and its moons was obtained from the New
Horizons spacecraft flyby in 2015; it also collected
data on Jupiter’s atmosphere, ring system and
moons on its outward journey. Mars has been
comprehensively mapped by the Global Surveyor
satellite, while the robotic vehicles Spirit and
Opportunity, which were landed on the planet
and roved the surface for many years, obtained
extensive data on Martian rocks. Currently the
Curiosity rover is making its way across the
Martian landscape sampling geological features.
On 26 November 2018 the InSight spacecraft
landed on Mars with a large package of scientific
instruments. The seismometers have recorded
many Mars quakes, providing information about
the planet’s interior. The rover Perseverance, due
to land on Mars in February 2021, will search for
signs of past microbial life. It carries the Mars
helicopter, Ingenuity, designed to test if powered
flight is possible for future human exploration of
the planet.
283
Gravity and planetary motion force; this results in a lower orbital speed and
longer orbital duration.
In Topic 1.5 we saw that to keep a body moving in In the case of a comet with a large elliptical
a circular path requires a centripetal force acting orbit, its speed increases as it approaches the Sun
towards the centre of the circle. In the case of the and decreases as it moves further away. Energy
planets orbiting the Sun in near circular paths, it is conserved, with some of the kinetic energy it
is the force of gravity between the Sun and the has when close to the Sun being transferred into
planet that provides the necessary centripetal potential energy as it moves away.
force. The strength of the Sun’s gravitational field The Moon is kept in a circular orbit around the
decreases with distance so the further a planet Earth by the force of gravity between it and the
is away from the Sun, the weaker the centripetal Earth.
Test yourself
9 From the data given in Table 6.1.2 calculate 10 From the data given in Table 6.1.2 state
a the circumference of the orbit of the planet a the surface gravity on Jupiter
Mars about the Sun b the weight of an object of mass 50 kg on the
b the speed of Mars in its orbit. surface of Jupiter.
11 Would you expect the orbital speed of Jupiter to be
greater or less than that of Saturn? Explain your
answer.
Revision checklist
After studying Topic 6.1 you should know and After studying Topic 6.1 you should be able to:
understand:
✔ that the Earth is a planet which orbits the Sun once ✔ define and calculate average orbital speed from
in approximately 365 days and spins on its axis 2πr
ν=
once in 24 hours T
✔ that the Moon orbits the Earth once in
approximately one month and how the motion of ✔ recall that planets, dwarf planets and comets orbit
the Moon explains the phases of the Moon the Sun, while moons orbit planets
✔ how the motion of the Earth explains day and night, ✔ recall that the four inner planets are rocky and small
the rising and setting of the Sun and the periodic and the four outer planets are gaseous and large
nature of the seasons ✔ calculate the time taken for light to travel over
✔ that the force that keeps an object in orbit around a large distance, such as between objects in the
the Sun is due to the gravitational attraction of Solar System
the Sun and that the Sun contains over 99% of the
✔ interpret planetary data and use it to solve
mass of the Solar System
problems
✔ the differences between the inner and outer planets
✔ recall that the planets, dwarf planets and
in terms of how the Solar System was formed
comets have elliptical orbits and that the Sun is
✔ that the strength of the Sun’s gravitational field not at the centre of the ellipse
weakens, and orbital speeds of planets decrease, ✔ explain in terms of conservation of energy why
as the distance from the Sun increases. the speed of an object in orbit is greater when it
is closer to the Sun.
284
Exam-style questions
1 The motion of the Earth and Moon explain many 5 a When a comet enters the Solar System from
natural events. beyond Pluto and approaches the Sun its
State which of the following statements is not speed changes.
true. i State how the strength of the Sun’s
A The Earth orbits the Sun once every 365 days. gravitational field changes as the
B The Moon orbits the Earth in approximately distance from the Sun increases. [1]
one month. ii State how the speed of the comet
C Day and night are due to the Earth spinning changes as it approaches the Sun. [1]
on its axis. b Venus is nearer to the Sun than the Earth.
D The Sun rises in the west and sets in the east i Compare the orbital speed of Venus
in the Southern Hemisphere. with that of the Earth. Explain your
[Total: 1] answer.[2]
2 The appearance of the Moon from Earth can be ii Explain why Venus takes less than one
explained by the motion of the Moon and the Earth year to orbit the Sun. [3]
Earth. Explain why [Total: 7]
a we never see the other side of the Moon [2] 6 a Jupiter is further away from the Sun than is
b the Moon has phases [3] the Earth.
c the Moon rises and sets. [1] i Compare the surface temperature
[Total: 6] of Jupiter with that of the Earth.
3 Calculate how long it takes light to travel from Explain your answer. [2]
the Sun to Mars. Take the distance of Mars from ii Compare the mass of Jupiter with
the Sun to be 228 × 106 km and the speed of light that of the Earth. [1]
to be 3 × 108 m/s. iii Compare the orbital speed of Jupiter
[Total: 3] with that of the Earth. [1]
4 The inner and outer planets are very different in b The orbital time of Mars round the Sun
size and composition. In terms of their formation is 1.9 Earth years and the orbital path is
explain why 1.5 times longer than that of the Earth.
a the inner planets are small and rocky [4] i Calculate the ratio of the orbital speed
b the outer planets are large and gaseous. [4] of Mars to the orbital speed of the
[Total: 8] Earth. [3]
ii Compare the speed of Mars with that
of the Earth. [1]
[Total: 8]
285
★ Know that stars are powered by nuclear reactions that release energy and that these reactions involve
the fusion of hydrogen into helium in stable stars.
The Sun is our closest star and is so bright that it banishes the darkness of space with its light.
The radiation it emits comes from glowing hydrogen and provides energy for all life on the Earth.
The hydrogen is heated by the energy released in nuclear reactions in the Sun’s interior. In stable
stars these reactions involve the conversion of hydrogen into helium by nuclear fusion. Stars have
several stages in their life cycle and our Sun is currently in its stable phase which will last for a
few more billion years.
286
6.2.2 Stars
FOCUS POINTS
★ Know that galaxies consist of billions of stars.
★ Know that the Sun is a star in the Milky Way and that other stars in the Milky Way are much further away
from Earth than the Sun.
★ Know that light-years are used to measure astronomical distances, and understand what is meant by a
light-year.
Our Sun lies in the Milky Way galaxy that contains billions of stars far enough away that the light
from even the nearest takes 4 years to arrive. The most distant events, observable today through
ever more powerful telescopes, occurred many millions of years ago.
Observations of events both near and far have enabled astronomers to build up a picture of
how stars form from the clouds of dust and gas in interstellar space, how they grow and evolve
over millions of years and how they eventually die, sometimes in a violent explosion such as a
supernova, in which their constituents are again scattered into space. In this section you will learn
about how stars are formed, how they are powered by nuclear fusion and the life cycle of some low
and high mass stars.
The Sun is our closest star and is so bright that it the light arriving from it at the Earth today left
banishes the darkness of space with its light. 4.3 years ago. The Pole Star is 142 light-years from
When the Sun sets, due to the rotation of the Earth. The whole of the night sky we see is past
Earth, the night sky is revealed. Away from light history and we will have to wait a long time to find
produced by humans, the night sky presents a out what is happening there right now.
magnificent sight with millions of visible stars.
Light-years
The night sky One light-year is the distance travelled in (the
The night sky has been an object of wonder and vacuum of) space by light in one year and equals
study since the earliest times. On a practical level it nearly 10 million million kilometres:
provided our ancestors with a calendar, a clock and 1 light-year = 9.5 × 1012 km = 9.5 × 1015 m
a compass. On a theoretical level it raised questions
about the origin and nature of the Universe and its
future. In the last 100 years or so, technological Galaxies
advances have enabled much progress to be made in A galaxy is a large collection of stars; there are
finding the answers and making sense of what we see. billions of stars in a galaxy.
Although the stars may seem close on a dark As well as containing stars, galaxies consist of
night, in fact the distances involved are enormous clouds of gas, mostly hydrogen and dust. They move
compared with the distances across our Solar System. in space, many rotating as spiral discs like huge
So great are they, that we need a new unit of length, Catherine wheels with a dense central bulge. The
the light-year. This is the distance travelled in (the Milky Way, the spiral galaxy to which our Solar
vacuum of) space by light in one year. System belongs, can be seen on dark nights as
The star nearest to the Solar System is Alpha a narrow band of light spread across the sky,
Centauri, 4.31 light-years away, which means Figure 6.2.1a.
287
Test yourself
3 The Universe is composed of stars and galaxies.
Which of the following statements are not true?
A The Universe is a collection of galaxies.
B There are billions of stars in a galaxy.
C The Sun is a star.
D Our Solar System belongs to the Andromeda
galaxy.
▲ Figure 6.2.1a The Milky Way from Earth
4 How long does it take light to reach the Earth from
a galaxy 10 million light-years distant from the
Earth? Choose your answer from the following
times.
A 10 years
B 30 years
C 300 thousand years
D 10 million years
288
stable
star
red giant
289
oxygen, nitrogen and finally iron to occur. Nuclear The centre of the supernova collapses to a very
fusion then stops and the energy of the star is dense neutron star, which spins rapidly and acts
released in a supernova explosion. as a pulsar, sending out pulses of radio waves.
In the explosion there is a huge increase in the If the red giant is very massive, the remnant
star’s brightness and the temperature becomes high at the centre of the supernova has such a large
enough for fusion of nuclei into many elements density that its gravitational field stops anything
heavier than iron to occur. Material, including escaping from its surface, even light; this is a
these heavy elements, is thrown into space as a black hole. In a black hole matter is packed so
nebula, and becomes available for the formation of densely that the mass of the Earth would only
new stars and their associated planetary systems. occupy the volume of one cubic centimetre! Since
The Crab Nebula is the remains of the supernova neither matter nor radiation can escape from a
seen by Chinese astronomers on Earth in 1054. It black hole, we cannot see it directly. However, if
is visible through a telescope as a hazy glow in the nearby material, such as gas from a neighbouring
constellation Taurus. Figure 6.2.4 is an image of the star, falls towards a black hole, intense X-ray
Crab Nebula taken by the Hubble Space Telescope. radiation may be emitted which alerts us to its
presence. Objects believed to be massive black
holes have been identified at the centre of many
spiral galaxies.
Test yourself
5 When a low mass red giant has consumed most
of the helium in its core it may turn into a
A yellow dwarf
B white dwarf
C supernova
D neutron star.
6 When a high mass red giant has consumed most
of the helium in its core it may become a
A white dwarf
B yellow dwarf
C planetary nebula
D neutron star.
290
Stars cluster together in galaxies. A typical galaxy has a diameter of around 30 000 light-years
with neighbouring galaxies around 3 million light-years away. The Universe is composed of billions
of galaxies that all appear to be receding from the Earth so that the light from glowing hydrogen
takes on a redder colour. Redshift measurements of the light from distant galaxies suggest that the
Universe is expanding and support the Big Bang theory of the origin of the Universe.
Cosmic microwave background radiation (CMBR) pervades all of space. It is thought to have been
produced in the early stages of the formation of the Universe and has been redshifted into the
microwave region as the Universe expanded. Hubble’s law, which relates the speed of recession of
a distant galaxy to its distance away, and the evaluation of the Hubble constant enable the age of
the Universe to be estimated as 14 billion years.
The Universe the light is redder. From the size of the redshift of
starlight, the speed of recession of the galaxy can
The Milky Way is one of the millions of galaxies that be calculated; the most distant ones visible are
make up the Universe. The diameter of the Milky Way receding with speeds up to one-third of the speed
galaxy is around 100 000 light-years and it contains of light.
800 billion or more stars.
The redshift in the light from distant galaxies
provides evidence that the Universe is expanding
The expanding Universe and gives support to the Big Bang theory of the
In developing a theory about the origin of the formation of the Universe.
Universe, two discoveries about galaxies have to be
wavelength observer
taken into account. The first is that light emitted source at rest
from glowing hydrogen in stars in distant galaxies, at rest
is ‘shifted’ to the red end of the spectrum (longer
wavelength) in comparison with the value on Earth. wavelength seems smaller
The second is that the further away a galaxy is from source
us, the greater is this redshift. These observations approaching
can be explained if other galaxies are moving away frequency and pitch rise
from us very rapidly, and the further away they are,
the faster is their speed of recession. Evidently the wavelength seems longer
291
The resulting expansion of the Universe continues it does not emit radiation. It may be that this hidden
today, but predictions vary about what will happen in mass exerts sufficient gravitational force to lead the
the future. The critical factor appears to be the density Universe to collapse. The gravitational force between
of matter in the Universe. This is difficult to calculate masses not only determines the motion and evolution
because scientists currently believe that as much as of planets, stars and galaxies, but will also control the
80% of the material in the Universe is invisible, since ultimate fate of the Universe.
292
The more distant a galaxy is from us, the faster it But 1 year ≈ 3.2 × 107 s, so the age of the Universe
is receding. Hubble’s law provides further evidence 4.5 × 1017 s
≈
in support of the Big Bang theory.
The age of the Universe can be shown to be 3.2 × 107 s/year
1 ≈ 1.4 × 1010 years
equal to and calculated very roughly from ≈ 14 billion years
H0
d 1
the equation = in terms of the distance d
v H0 Test yourself
and speed of recession v of distant galaxies. 7 Explain the evidence in favour of the Big Bang
We assume that the time for which two galaxies theory of the origin of the Universe.
are close together (when they were formed at 8 Redshift measurements from a distant galaxy
the Big Bang) is negligible, compared with their show that it is moving away from the Earth at a
speed of 8500 km/s. Assuming H0 = 2.2 × 10 –18
present age. If so, their age is approximately the per second, how far away is the galaxy from the
age of the Universe, which equals the time since Earth?
expansion began. A 200 million light years
For the two galaxies, assuming the speed of B 400 million light years
recession has not changed, we have C 600 million light years
d D 800 million light years
age = distance apart/speed of recession =
v
From Hubble’s law, it follows that
1 1
age = ≈ = 4.5 × 1017 s
H0 2.2 × 10 –18
Revision checklist
After studying Topic 6.2 you should know and After studying Topic 6.2 you should be able to:
understand:
✔ that the Sun is a star, consists of mostly hydrogen ✔ recall that a protostar becomes a stable
and helium and emits radiant energy from glowing star when the inward gravitational force is
hydrogen balanced by the outward force due to the high
temperature in the centre of the star
✔ that stable stars are powered by the release of ✔ describe how stars are thought to originate and
energy during nuclear fusion of hydrogen into outline the life cycle of low and high mass stars
helium ✔ recall that the speed at which a galaxy is
receding can be found from the change in
✔ that the Sun is one of the billion stars in our
wavelength of starlight due to redshift
galaxy, the Milky Way, and that other stars in the
✔ recall the origin and properties of cosmic
Milky Way are much further away from Earth than
microwave background radiation and know
the Sun
that it has been redshifted into the microwave
✔ the term light-year and relate it to star distances
region of the electromagnetic spectrum as the
✔ that a galaxy is a large collection of stars, that
Universe expanded
the Milky Way is one of many billions of galaxies
✔ recall the evidence in favour of the Big Bang theory
making up the Universe and that the diameter of
✔ recall how the distance d of a galaxy can be
the Milky Way galaxy is around 100 000 light-years
estimated
✔ that light from glowing hydrogen in stars in all
✔ define the Hubble constant H 0 and recall that
distant galaxies is redshifted in comparison with 1 represents the estimated age of the
light from glowing hydrogen on Earth and this is H0
evidence of an expanding Universe and the Big Universe.
Bang theory.
293
Exam-style questions
1 a Explain what is meant by the redshift of 4 a State the forces, and give their direction,
starlight. [3] which are balanced when a star is in a
b Explain what the redshift of starlight tells stable state. [4]
us about the motion of distant galaxies. [2] b Write down the sequence of stages in the
[Total: 5] life cycle of a star like the Sun. [5]
2 State which of the following provides evidence in [Total: 9]
support of the Big Bang theory. 5 a Calculate Hubble’s constant if a galaxy
A Gravitational attraction 500 million light-years from Earth is
B Supernova explosions receding at 11 000 km/s. [5]
C Redshift of starlight from distant galaxies b Explain the significance of 1 . [2]
D Fusion of hydrogen into helium H0 [Total: 7]
[Total: 1]
294
When tackling physics problems using mathematical Multiplying both sides by b as before, we get
equations it is suggested that you do not substitute a = b× x
numerical values until you have obtained the
expression in symbols which gives the answer. That is, Dividing both sides by x:
work in symbols until you have solved the problem
a b× x
and only then insert the numbers in the expression = =b
to get the final result. x x
This has two advantages. First, it reduces the a
∴ b=
chance of errors in the arithmetic (and in copying x
down). Second, you write less since a symbol is Note that the reciprocal of x is 1/x.
usually a single letter whereas a numerical value is Can you show that
often a string of figures.
Adopting this ‘symbolic’ procedure frequently 1 b
= ?
requires you to change round an equation first. x a
The next two sections and the questions that follow
them are intended to give you practice in doing this Now try the following questions using these ideas.
and then substituting numerical values to get the
answer. Questions
1 What is the value of x if
Equations – type 1 a 2x = 6 b 3x = 15 c 3x = 8
In the equation x = a/b, the subject is x. To change x x 2x
d = 10 e = 4 f =4
it we multiply or divide both sides of the equation by 2 3 3
the same quantity. 4 x 4
g =2 h 9 = 3 i =
To change the subject to a, we have x x 6 3
a 2 Change the subject to
x=
b a f in v = fλ b λ in v = fλ
c I in V = IR d R in V = IR
If we multiply both sides by b, the equation will still
m m
be true. e m in d = f V in d =
V V
a s s
g s in v = h t in v=
∴ x× b= ×b t t
b
3 Change the subject to
The bs on the right-hand side cancel a I2 in P = I2 R b I in P = I2 R
1 1
a c a in s = at2 d t2 in s = at2
∴ b× x= ×b=a 2 2
b 1 2 1 2
e t in s = at f v in mv = mgh
and 2 2
ay pl
g y in λ = h p in R =
a=b × x D A
295
Equations – type 2 x
y
1
2
2
4
3
6
4
8
To change the subject in the equation x = a + by
we add or subtract the same quantity from each side. We see that when x is doubled, y doubles; when
We may also have to divide or multiply as in type 1. x is trebled, y trebles; when x is halved, y halves;
Suppose we wish to change the subject to y in and so on. There is a one-to-one correspondence
x = a + by between each value of x and the corresponding
value of y.
Subtracting a from both sides,
We say that y is directly proportional to x, or y
x – a = a + by – a = by varies directly as x. In symbols
Dividing both sides by b, y ∝ x
x − a by Also, the ratio of one to the other, e.g. y to x, is
= =y always the same, i.e. it has a constant value which
b b
in this case is 2. Hence
x−a
∴ y= y
b = a constant = 2
x
Questions The constant, called the constant of proportionality
6 What is the value of x if or constant of variation, is given a symbol, e.g. k,
and the relation (or law) between y and x is then
a x + 1 = 5 b 2x + 3 = 7 c x – 2 = 3 summed up by the equation
x 1 x 1
d 2(x – 3) = 10 e − = 0 f + =0 y
2 3 3 4 = k or y = kx
5 x 3 x
g 2 x + = 6 h 7 − = 11 i +2=5
3 4 x Notes
7 By changing the subject and replacing, find the 1 In practice, because of inevitable experimental
value of a in v = u + at if errors, the readings seldom show the relation so
a v = 20, u = 10 and t = 2
clearly as here.
b v = 50, u = 20 and t = 0.5
c v = 5/0.2, u = 2/0.2 and t = 0.2 2 If instead of using numerical values for x and y
8 Change the subject in v2 = u2 + 2as to a. we use letters, e.g. x1, x2, x3, etc., and y1, y2, y3,
etc., then we can also say
y1 y2 y3
= = = ... = k
x1 x2 x3
or
y1 = kx1, y2 = kx2, y3 = kx3, ...
296
p 3 4 6 12 6 2 0.50
V 4 3 2 1 12 1 1.00
y
There is again a one-to-one correspondence between
each value of p and the corresponding value of V, but 8
when p is doubled, V is halved, when p is trebled, V 6
has one-third its previous value, and so on.
4
We say that V is inversely proportional to p, or V
varies inversely as p, i.e. 2
1 x
V∝ 0 1 2 3 4
p
▲ Figure M1
0 v 20 40 56 72
0 0.1 0.2 0.3 I/A a Plot a graph of m along the vertical axis and v
▲ Figure M4 along the horizontal axis.
b Is m directly proportional to v? Explain your
Note that in Figure M4 each axis is labelled with answer.
c Use the graph to find v when m = 1.
the quantity and the unit. Also note that there is a 11 The distances s (in metres) travelled by a car at
scale along each axis. The statement V/V against I/A various times t (in seconds) are shown below.
means that V/V, the dependent variable, is plotted
s/m 0 2 8 18 32 50
along the y-axis and the independent variable I is
plotted along the x-axis (see Figure M5). t/s 0 1 2 3 4 5
Draw graphs of
a s against t
b s against t2 .
What can you conclude?
y-axis
(dependent)
Pythagoras’ theorem
The square of the hypotenuse of a right-angled
x-axis (independent)
triangle (see Figure M6) is equal to the sum of the
▲ Figure M5 squares of the other two sides: c2 = a2 + b2.
This is a useful equation for determining the
Practical points unknown length of one side of a right-angled
i T he axes should be labelled giving the quantities triangle. Also the angle θ between sides b and c is
being plotted and their units, e.g. I/A meaning given by: sin θ = a/c or cos θ = b/c or tan θ = a/b.
current in amperes.
ii If possible, the origin of both scales should be
on the paper and the scales chosen so that the c
a
points are spread out along the graph. It is good
practice to draw a large graph.
b θ
▲ Figure M6
298
9 a State how energy is transferred from the ii If the volume of a fixed mass of gas at
following devices: constant temperature doubles, what
i an electric lamp [1] happens to the pressure of the gas? [2]
ii a battery [1] c Explain in terms of the molecular kinetic
iii an electric motor [1] theory how the pressure of a gas is affected
iv the generator in a power station. [1] by a rise in temperature if the volume
b The efficiency of a certain coal power remains constant. [3]
station is 30%. [Total: 10]
Explain the meaning of efficiency. [2]
[Total: 6] 14 Explain why
a in cold weather the wooden handle of a
10 Which one of the following statements is not true? saucepan feels warmer than the metal pan [2]
A Pressure is the force acting on unit area. b convection occurs when there is a change
B Pressure is calculated from force/area. of density in parts of a fluid [4]
C The SI unit of pressure is the pascal (Pa) which c conduction and convection cannot occur
equals 1 newton per square metre (1 N/m2). in a vacuum. [2]
D The greater the area over which a force acts [Total: 8]
the greater is the pressure.
[Total: 1] 3 Waves
11 a A stone of mass 2.0 kg is dropped from a 15 a The wave travelling along the spring in the
height of 4.0 m. Neglecting air resistance, diagram is produced by someone moving
calculate the kinetic energy of the stone end X of the spring back and forth in the
just before it reaches the ground. [3] directions shown by the arrows.
b An object of mass 2.0 kg is fired vertically i Is the wave longitudinal or transverse?
upwards with a kinetic energy of 100 J. [1]
Neglecting air resistance, calculate ii What is the region called where the coils
i the speed with which it is fired [4] of the spring are closer together than
ii the height to which it will rise. [4] normal? [1]
[Total: 11] ii What is the region called where the
12 a An object has kinetic energy of 10 J at coils of the spring are further apart
a certain instant. If it is acted on by an than normal? [1]
opposing force of 5.0 N, calculate the furthest
distance it travels before coming to rest.[3]
X
b An object of mass 6.0 kg accelerates at a
constant rate of 3.0 m/s2. Calculate the force
acting on it in the direction of acceleration.[3] b When the straight water waves in the
c An object is brought to rest by a force diagram pass through the narrow gap in the
of 18 N acting on it for 3.0 s. Calculate barrier they are diffracted. What changes
i the impulse of the force [2] (if any) occur in
ii the change of momentum of the object. [1] i the shape of the waves [1]
[Total: 9] ii the speed of the waves [1]
iii the wavelength? [1]
2 Thermal physics [Total: 6]
300
16 In the diagram a ray of light is shown reflected c State the seven colours of the visible
at a plane mirror. spectrum in order of increasing
a State the angle of incidence. [1] wavelength. [3]
b State the angle the reflected ray makes
with the mirror. [1]
screen
c List the characteristics of the image formed
te
in a plane mirror. [5] whi
A
[Total: 7] t
ligh
incident ray prism B
30° [Total: 6]
19 a Explain what is meant by the terms
i principal axis of a lens [2]
ii principal focus of a converging lens. [2]
b A magnifying glass is used to view a small
object.
i How far from the lens should the
object be? [1]
reflected ray
ii Is the image upright or inverted? [1]
iii Is the image real or virtual? [1]
17 In the diagram, which of the rays A to D is most [Total: 7]
likely to represent the ray emerging from the 20 The diagram below shows the complete
parallel-sided sheet of glass? electromagnetic spectrum.
D C B A
radio microwaves A visible ultraviolet B γ -rays
air waves light
301
22 The waveforms of two notes P and Q are shown 25 For the circuit below calculate
below. Which one of the statements A to D is true? a the total resistance [3]
A P has a higher pitch than Q and is not so loud. b the current in each resistor [4]
B P has a higher pitch than Q and is louder. c the p.d. across each resistor. [3]
C P and Q have the same pitch and loudness. 6V
D P has a lower pitch than Q and is not so loud.
2Ω 1Ω
[Total: 10]
Q
26 For the circuit below calculate
P
a the total resistance [4]
[Total: 1] b the current in each resistor [4]
23 a Name two examples of waves that can be c the p.d. across each resistor. [1]
modelled as transverse. [2] 6V
b Name two examples of waves that can be
modelled as longitudinal. [2] 2Ω
c Name three properties of waves. [3]
[Total: 7]
2Ω
4 Electricity and magnetism
24 Which one of the following statements about the [Total: 9]
diagram below is not true?
27 a An electric kettle for use on a 230 V supply is
Y
S N rated at 3000 W.
i Calculate the current required by the
N P S
Q kettle. [3]
X ii For safe working, the cable supplying it
should be able to carry at least
A 2 A B 5 A C 10 A D 15 A [1]
coil S b Calculate the cost of operating three 100 W
lamps for 10 hours. Take the cost of 1 kWh to
N be 10 cents. [3]
[Total: 7]
28 Which one of the following statements is not
true?
A If a current is passed through the wire XY, a A In a house circuit, lamps are wired in parallel.
vertically upwards force acts on it. B Switches, fuses and circuit breakers should be
B If a current is passed through the wire PQ, it placed in the neutral wire.
does not experience a force. C An electric fire has its earth wire connected to
C If a current is passed through the coil, it the metal case to prevent the user receiving a
rotates clockwise. shock.
D If the coil had more turns and carried a larger D When connecting a three-core cable to a 13 A
current, the turning effect would be greater. three-pin plug the brown wire goes to the
[Total: 1] live pin.
[Total: 1]
302
29 State the units for the following quantities 33 a One light-year is the distance travelled by
a electric charge [1] light in one year and is equal to 9.5 × 1012 km.
b electric current [1] Calculate the distance in light years of a star
c p.d. [1] that is 2.85 × 1014 km away from the Earth. [2]
d energy [1] b Choose the approximate distance from the
e power. [1] Sun of the following bodies.
[Total: 5] i Earth [1]
ii Pluto [1]
iii the nearest star outside the Solar
5 Nuclear physics System [1]
30 a A radioactive source which has a half-life of iv the Andromeda galaxy. [1]
1 hour gives a count-rate of 100 counts per A 4 light-years
second at the start of an experiment and B 150 million km
25 counts per second at the end. C 6000 million km
Calculate the time taken for the experiment. [3] D 2 million light-years
b i State the relative penetrating powers of [Total: 6]
α-particles, β-particles and γ-radiation. [2]
ii State the relative ionising powers of 34 a Outline two pieces of evidence which
α-particles, β-particles and γ-radiation. [2] support the Big Bang theory of the origin
[Total: 7] of the Universe. [5]
b Redshift measurements show that a galaxy
is receding from Earth at a speed of
6 Space physics 16 000 km/s. Use Hubble’s Law to find how
31 The Earth is tilted on its axis as it orbits the Sun. many light-years the galaxy is distant from
a In December is the northern hemisphere tilted the Solar System. (Take Hubble’s constant
towards or away from the Sun? [1] to be 2.2 × 10–18 s–1
b State when the Sun is highest on the horizon and 1 light-year = 9.5 × 1012 km.) [5]
in the northern hemisphere. [2] [Total: 10]
c State when the longest hours of daylight
occur in the southern hemisphere. [2]
d State the months in which the hours of day
and night are equal. [2]
[Total: 7]
303
tap (faucet)
8
rule string
7
drop of water
6
5
container
4
3
P Q
2
R
water pendulum bob
0 1
▲ Fig. T3
cm
▲ Fig.T1
a A student starts two stopwatches at the same
time while the pendulum bob is swinging.
a Name the quantity that the student is The student stops one stopwatch when the
measuring with the rule. [1] pendulum bob is at P. He stops the other
b The student uses a digital stopwatch to stopwatch when the pendulum bob next is at Q.
measure the time between the drops of water. Fig. T4 shows the readings on the
She repeats her measurement. stopwatches.
Fig. T2 shows the reading on the stopwatch for
all her measurements. reading at P reading at Q
th th th
1/100 1/100 1/100
min sec sec min sec sec min sec sec
304
i Use readings from Fig. T4 to determine the b Calculate the distance travelled between
time for one complete oscillation of the 60 s and 100 s. [3]
pendulum. c The size of the acceleration is greater than
time = s [2] the deceleration.
ii The method described in a does not Describe how Fig. T5 shows this. [1]
give an accurate value for one complete [Total: 6]
oscillation of the pendulum. Cambridge IGCSE Physics 0625 Paper 32 Q1
Describe how the student could obtain an Oct/Nov 2018
accurate value for one complete oscillation 4 A student moves a model car along a bench.
of the pendulum. [4] Fig. T6 is the speed–time graph for the motion of
b As the pendulum bob moves from R to Q it the model car.
gains 0.4 J of gravitational potential energy.
4.0
Air resistance can be ignored. B
State the value of kinetic energy of the
pendulum bob at 3.0
1. R
speed / m / s
2. Q. [2] 2.0
A
C
[Total: 8]
Cambridge IGCSE Physics 0625 Paper 32 Q3 1.0
May/June 2019
D
3 A person on roller skates makes a journey. 0
0 5.0 10.0 15.0 20.0
Fig. T5 shows the speed–time graph for the time / s
journey.
▲ Fig. T6
25
a Describe the motion of the car in each of
20 X Y the sections A, B, C and D. [4]
b Determine the distance moved by the model
speed / m / s
305
speed / m / s
between time = 10 s and time = 20 s. [2] 6
b Fig. T8 shows the axes of a speed–time 4
graph for a different object. 2
50 0
0 10 20 30 40 50 60 70 80 90 100
40
time / s
speed / m / s
30
▲ Fig. T10 [5]
20
10 b On another part of the journey, the average
0 speed of the bus is 7.5 m/s.
0 20 40 60 80 100 Calculate the distance the bus travels
time / s in 150 s. [3]
▲ Fig. T8 [Total: 8]
i The object has an initial speed of 50 m/s Cambridge IGCSE Physics 0625 Paper 32 Q2
and decelerates uniformly at 0.35 m/s2 Feb/March 2019
for 100 s.
On a copy of Fig. T8, draw the graph to 7 a Define acceleration. [1]
represent the motion of the object. [2] b Fig. T11 shows the distance–time graph for
ii Calculate the distance travelled by the the journey of a cyclist.
object from time = 0 to time = 100 s. [3] 350
[Total: 9] 300
306
8 Fig. T12 shows a set of masses made from the Forces, Momentum, Energy, work
same material.
and power and Pressure
10 A load is attached to a spring, as shown in Fig. T14.
Two arrows indicate the vertical forces acting on
the load. The spring and the load are stationary.
support
spring
4.0 N
▲ Fig. T12
2.8 N
▲ Fig. T13 ▲ Fig. T15
a The average mass of each log is 65.0 kg. Calculate the resultant force on the load and
Calculate the total weight of the raft. [3] state its direction. [2]
b i The mass of one of the logs is 66.0 kg. It is c i State the principle of conservation of
3.0 m long and has a cross sectional area of energy. [1]
0.040 m2. ii Eventually the load stops moving up and
Calculate the density of the wood in the down.
log. [3] Describe and explain why the load stops
ii Explain why the log in b i floats on water. moving. Use your ideas about conservation
[1] of energy. [2]
[Total: 7] [Total: 7]
Cambridge IGCSE Physics 0625 Paper 32 Q2 Cambridge IGCSE Physics 0625 Paper 32 Q3
May/June 2018 Feb/March 2019
307
iii A
heavier child wants to sit on the tyre.
11 a An object is moving in a straight line at
Describe how the tyre position should be
constant speed.
adjusted so that the moment is the same
State three ways in which a force may
as in b ii. [1]
change the motion of the object. [2]
[Total: 8]
b Fig. T16 shows an object suspended from two
ropes. The weight of the object is 360 N. The Cambridge IGCSE Physics 0625 Paper 31 Q3
magnitude of the tension in each rope is T. May/June 2017
13 Fig. T18 shows the speed–time graph for a
T T
student cycling along a straight, flat road.
45º 45º
8
object
360 N 6
speed / m / s
▲ Fig. T16 4
P rope B 50 N 50 N
tyre
backward force forward force
▲ Fig. T17
C 20 N 70 N
a The mass of the tyre is 15 kg.
Calculate its weight. [2] backward force forward force
b The weight of the tyre exerts a moment on the
▲ Fig. T19
branch, about point P where the branch joins
the tree. Identify which pair of forces, A, B or C, acts
i Explain what is meant by the term on the cyclist between 11 s and 16 s. Explain
moment. [1] your choice. [3]
ii A child sits on the tyre. The weight of the c The cyclist pushes on one pedal with a force
child and tyre together is 425 N. Calculate of 120 N. The area of his shoe in contact with
the moment of this force about point P. the pedal is 16 cm2.
Use information given in Fig. T17. Include
the unit. [4]
308
309
The mass of the aircraft is 9500 kg. b Electrical energy from the power station is
a Calculate the kinetic energy of the aircraft at used to power two different lamps. Fig. T23
take-off. [3] shows how the light outputs from two types
b On an aircraft carrier, a catapult provides of lamp vary with the power input.
an accelerating force on the aircraft. The 1000
catapult provides a constant force for a filament
310
15 m
lid
wooden
box
0.80 m
1.2 m NOT TO ▲ Fig. T25
SCALE
a The metal changes from hot liquid to cool
▲ Fig. T24 solid.
Describe what happens to the arrangement,
The dimensions of the lid of the box are 1.2 m by separation and motion of the atoms as the
0.80 m and the pressure of the atmosphere is metal changes from hot liquid to cool solid. [3]
1.0 × 105 Pa. The lid is 15 m below the surface b The workers cool their tools in water. They
of the sea. spill some water onto the floor but later the
a The density of sea-water is 1020 kg/m3. floor is dry.
Calculate Explain what happens to the water. State the
i the pressure on the lid of the box due name of the process. [3]
to the sea-water, [2] [Total: 6]
ii the total pressure on the lid, [1]
iii the downward force that the total Cambridge IGCSE Physics 0625 Paper 31 Q6
pressure produces on the lid. [2] May/June 2017
b The force needed to open the lid is not 21 a Fig. T26 shows the apparatus used to
equal to the value calculated in a iii. observe the motion of smoke particles that
Suggest two reasons for this. [2] are in the air in a box.
[Total: 7]
eye
Cambridge IGCSE Physics 0625 Paper 42 Q4
May/June 2016
microscope
air molecules
light and
smoke particles
▲ Fig. T26
311
Light from a lamp enters the box through a c A cylinder of volume 0.012 m3 contains a
window in one side of the box. The smoke compressed gas at a pressure of 1.8 × 106 Pa.
particles are observed using a microscope A valve is opened and all the compressed
fixed above a window in the top of the box. gas escapes from the cylinder into the
i The motion of a single smoke particle is atmosphere.
observed through the microscope. The temperature of the gas does not change.
Draw a circle as shown, and sketch the Calculate the volume that the escaped gas
path of this smoke particle. occupies at the atmospheric pressure of
1.0 × 105 Pa. [3]
[Total: 7]
Cambridge IGCSE Physics 0625 Paper 42 Q7
Feb/March 2019
23 a State and explain, in terms of molecules, any
[1] change in the pressure of a gas when the
ii Explain why the smoke particle follows volume is reduced at a constant temperature.
the path that is observed. [3] [3]
b A tennis player is practising by hitting a ball b Copy and complete Table T1 to give the
many times against a wall. relative order of magnitude of the expansion
The ball hits the wall 20 times in 60 s. of gases, liquids and solids for the same
The average change in momentum for each increase of temperature.
collision with the wall is 4.2 kg m/s. Write one of these words in each blank space:
Calculate the average force that the ball gas liquid solid
exerts on the wall. [3]
▼ Table T1
[Total: 7]
Cambridge IGCSE Physics 0625 Paper 42 Q5 expands most
Feb/March 2018 expands least [2]
22 a In Fig. T27, the small circles represent
molecules. The arrows refer to the change of [Total: 5]
state from the arrangement of molecules on Cambridge IGCSE Physics 0625 Paper 42 Q4
the left to the arrangement of molecules on May/June 2019
the right.
24 A thermometer is used to measure the temperature
X inside a room in a house.
a State a physical property that varies
with temperature and can be used in
Y a thermometer. [1]
b Fig. T28 shows how the temperature of the
▲ Fig. T27 room changes between 6:00 pm and 11:00 pm.
20
Complete the following by writing solid,
liquid or gas in each of the blank spaces.
temperature / °C
312
thermometer
thermometer
313
The metal block has a mass of 2.7 kg. i On a copy of Fig. T34, draw three wavefronts
The metal of the block has a specific that have passed through the gap. [2]
heat capacity of 900 J/(kg °C). ii State the name of the effect in b i. [1]
In 2 min 30 s, the temperature of the [Total: 5]
block increases from 21°C to 39°C. Cambridge IGCSE Physics 0625 Paper 32 Q7
Calculate the power of the heater. [4] Feb/March 2018
ii State and explain a precaution that can 28 Fig. T35 shows a ray of light that is reflected by a
be taken to improve the accuracy of the mirror.
experiment. [2]
[Total: 8] YZ mirror
▲ Fig. T35
z F
F
▲ Fig. T33 image I
lens
i State which angle w, x, y or z, is the angle ▲ Fig. T36
of refraction. [1]
ii Light is a transverse wave. i State the name of the points labelled F on
State another example of a transverse Fig. T36. [1]
wave. [1] ii Describe the nature of the image I. [2]
b Fig. T34 represents some wavefronts [Total: 6]
approaching a barrier with a narrow gap. Cambridge IGCSE Physics 0625 Paper 32 Q6
barrier with
May/June 2019
narrow gap 29 Fig. T37 represents an object positioned on the
principal axis of a thin lens.
direction of travel
for wavefronts principal
object axis
F F
▲ Fig. T34
▲ Fig. T37
314
315
radiation it requires.
use 1000
type of radiation
100
radio waves
10
detecting an intruder at night microwaves
0
humans elephants mice dolphins
infra-red ▲ Fig. T42
[3]
316
iv S tate the term given to the high ii A small bar of unmagnetised iron is placed
frequencies that dolphins can hear but next to a bar magnet, as shown in Fig. T45.
humans cannot hear. [1] iron
magnet
[Total: 8] bar
Cambridge IGCSE Physics 0625 Paper 32 Q8 S N
May/June 2018 ▲ Fig. T45
35 a A healthy human ear can hear a range of
The iron bar moves towards the magnet.
frequencies.
Explain why the iron bar moves. [2]
Three frequency ranges are shown.
b Fig. T46 shows a coil of wire wrapped around
Choose the range for a healthy human ear.
an iron core. A student uses these to make an
0 Hz–20 Hz 10 Hz–10 000 Hz 20 Hz–20 000 Hz [1]
electromagnet.
b Explain the meaning of the term ultrasound. [2]
c A student listens to two different sounds, coil
P and Q. iron core
The two different sounds are represented on a
computer screen on the same scale.
Fig. T43 shows the screens.
▲ Fig. T46
insulating support
▲ Fig. T47
317
38 a A student rubs a polythene rod with a dry cloth. b The circuit is changed.
The polythene rod becomes negatively charged. The two resistors are connected in parallel.
Describe and explain how the rod becomes Explain what happens, if anything, to the
negatively charged. [3] current reading on the ammeter. [2]
b The negatively charged polythene rod hangs [Total: 7]
from a nylon thread so that it is free to turn. Cambridge IGCSE Physics 0625 Paper 32 Q9
The student charges a second polythene rod May/June 2018
and brings it close to the first rod, as shown
in Fig. T48. 40 a The lamp of a car headlight is rated at
nylon thread 12 V, 50 W.
Calculate the current in the lamp when
negatively charged operating normally. [2]
polythene rod
b A car is driven at night.
negatively charged In a journey, the total charge that passes
polythene rod through the 12 V battery is 270 kC.
i Calculate the electrical energy transferred.
[3]
ii The fuel used by the car provides
▲ Fig. T48 3.6 × 104 J/cm3.
Calculate the volume of fuel used to
Describe and explain what happens when the provide the energy calculated in b i. [2]
negatively charged rods are close to each [Total: 7]
other. [2] Cambridge IGCSE Physics 0625 Paper 42 Q8
[Total: 5] Feb/March 2018
Cambridge IGCSE Physics 0625 Paper 32 Q11
41 Fig. T50 shows current–potential difference
Feb/March 2018
graphs for a resistor and for a lamp.
39 a Fig. T49 shows a simple circuit. 6.0
4.0 lamp
current / V
A 0.50 A
V
2.0
resistor
12.0 Ω 6.0 Ω
▲ Fig. T49 0
0 2.0 4.0 6.0 8.0
i T he current in the wires of the circuit is a potential difference / V
flow of particles. ▲ Fig. T50
Indicate the name of these particles.
Tick one box. a i The potential difference (p.d.) applied
electrons to the resistor is increased. Choose the
atoms box that indicates the effect on the
protons [1] resistance of the resistor.
ii Calculate the combined resistance of the resistance increases
two resistors. [1] resistance is constant
iii Calculate the potential difference (p.d.) resistance decreases [1]
reading that would be shown on the
voltmeter. [3]
318
ii The potential difference (p.d.) applied 43 Fig. T52 shows a circuit containing a filament
to the lamp is increased. Choose the lamp of resistance 0.30 Ω and two resistors,
box that indicates the effect on the each of resistance 0.20 Ω.
resistance of the lamp.
resistance increases 0.20 Ω
0.20 Ω
resistance is constant
resistance decreases [1]
0.30 Ω
b The p.d. across the lamp is 6.0 V. Calculate
▲ Fig. T52
the resistance of the lamp. [2]
c The lamp and the resistor are connected in a Calculate the combined resistance of the
parallel to a 6.0 V supply. lamp and the two resistors. [3]
Calculate the current from the supply. [2] b The potential difference (p.d.) of the supply
d The lamp and the resistor are connected in is increased so that the current in the lamp
series to another power supply. The current increases.
in the circuit is 4.0 A. State and explain any change in the
Calculate the total p.d. across the lamp and resistance of the lamp. [2]
the resistor. [2] [Total: 5]
[Total: 8] Cambridge IGCSE Physics 0625 Paper 42 Q10
Cambridge IGCSE Physics 0625 Paper 42 Q9 May/June 2019
Feb/March 2018
44 a The resistance of a long piece of wire is
42 Fig. T51 shows a circuit used by a student to test 6.0 Ω. The potential difference across the wire
a metal wire made of nichrome. is 2.0 V.
ammeter X Calculate the current in the wire. [3]
A
b A force acts on a wire carrying a current in a
0.8 A ammeter Y magnetic field.
V A Fig. T53 shows the direction of the current in
component Z
the wire and the direction of the force acting
on the wire.
nichrome wire
wire
▲ Fig. T51
current
a State the name of component Z. [1]
b The current reading on ammeter X is 0.8 A. N S
State the reading on ammeter Y. [1]
c The current in the nichrome wire is 0.8 A. The direction of force
319
to
+ battery
magnet S S –
axle
▲ Fig. T54
320
B
50 a A detector of ionising radiation measures the
background count rate in a classroom where
▲ Fig. T59
there are no radioactive samples present.
The readings, in counts/minute, taken over
i The primary coil P has 4000 turns and an a period of time are shown in this chart.
input of 120 V. The secondary coil S has
counts/minute 16 12 14 16 15 17
an output of 9.0 V.
Calculate the number of turns in the i State two possible sources of this
secondary coil. [2] background radiation. [2]
ii State a suitable material for the core of ii Explain why the readings are not the
the transformer. [1] same. [1]
[Total: 6] b With no radioactive sample present, a
Cambridge IGCSE Physics 0625 Paper 42 Q10 scientist records a background radiation
Feb/March 2019 count of 40 counts/minute.
He brings a radioactive sample close to
the detector. The count rate increases to
200 counts/minute.
After 24 days the count rate is 50 counts/
minute.
Calculate the half-life of the radioactive
sample. [4]
c On a copy of this chart, draw a line between
each type of ionising radiation and its
property and another line between the
property and its use. One has been done
for you.
321
322
Complete the nuclide equation for the decay c A radioactive substance decays by emitting an
of radon-220. a-particle.
220
An a-particle can be represented as 42 a .
Rn → ….a + …..Po [3] Draw a labelled diagram showing the
86
323
324
square A
base
▲ Fig. P3
325
3 In this experiment, you will investigate the State whether your readings support this
stretching of a spring. suggestion. Justify your answer by reference
Carry out the following instructions, referring to to the graph line. [1]
Fig. P4. f Use your results to predict the load L that
would give a length l twice the value of l0.
Show clearly how you obtained your answer. [2]
metre
rule
[Total: 11]
Cambridge IGCSE Physics 0625 Paper 51 Q1
boss clamp
May/June 2017
4 A student is investigating whether the distance
spring that a toy truck will travel along a horizontal
stand
floor, before stopping, depends on its mass.
The following apparatus is available to the
student:
a ramp
blocks to support the ramp as shown in Fig. P5
toy truck
a selection of masses
other standard apparatus from the physics
laboratory.
bench Plan an experiment to investigate whether the
▲ Fig. P4 distance that the toy truck will travel along a
horizontal floor, before stopping, depends on
a • Do not remove the spring from the clamp.
its mass.
Use the metre rule to measure the length l0
You are not required to carry out this
of the coiled part of the spring.
investigation.
• Record l0, in a copy of Table P1 at load
In your plan, you should:
L = 0.0 N.
• explain briefly how you would carry out the
On a copy of Fig. P4, show clearly the
investigation
length l0. [1]
• state any apparatus that you would use that is
b • Place a load L = 1.0 N on the spring.
not included in the list above
Record, in Table P1, the length l of the
• state the key variables that you would control
coiled part of the spring.
• draw a table, or tables, with column headings
• Repeat this procedure using loads L = 2.0 N,
to show how you would display your readings
3.0 N, 4.0 N and 5.0 N.
(you are not required to enter any readings in
▼ Table P1 the table).
You may add to a copy of the diagram in Fig. P5
L/N 0.0 1.0 2.0 3.0 4.0 5.0
to help your description.
l/mm
ramp
[2] blocks floor
c Describe one precaution that you took in
order to obtain reliable readings. [1] ▲ Fig. P5
d On graph paper, plot a graph of l/mm [Total: 7]
(y-axis) against L/N (x-axis).[4] Cambridge IGCSE Physics 0625 Paper 52 Q4
e A student suggests that the length l of the May/June 2018
spring is directly proportional to the load L.
326
5 In this experiment, you will investigate how the c Write a conclusion stating how the volume of
volume of water affects the rate at which water water in the beaker affects the rate of cooling
in a beaker cools. of the water. Justify your answer by reference
Carry out the following instructions, referring to to your results. [2]
Fig. P6. d i Using your results for 100 cm of water,
3
The thermometer must remain in the clamp calculate the average rate of cooling x1 for
throughout the experiment. the first 90 s of the experiment. Use your
thermometer clamp readings from the table and the equation
θ 0 − θ 90
x1 = ,
t
beaker where t = 90 s and θ0 and θ90 are the
temperatures at 0 s and 90 s.
bench Include the unit for the rate of cooling. [1]
ii Using your results for 100 cm3 of water,
▲ Fig. P6
calculate the average rate of cooling x2 in
a Pour 200 cm3 of hot water into the beaker. the last 90 s of the experiment. Use your
Place the thermometer in the water. readings from the table and the equation
Copy Table P2 and in the first row, record the θ 90 − θ180
maximum temperature θ of the water and x2 = ,
immediately start the stopclock. t
Record, in the table, the temperature θ of the where t = 90 s and θ90 and θ180 are the
water at times t = 30 s, 60 s, 90 s, 120 s, 150 s temperatures at 90 s and 180 s.
and 180 s. Include the unit for the rate of cooling. [1]
Remove the thermometer from the beaker and e A student suggests that it is important
empty the beaker. [1] that the experiments with the two volumes
b i Repeat a, using 100 cm of hot water in
3
of water should have the same starting
the beaker. [1] temperatures.
ii Complete the headings and the time column State whether your values for x1 and x2 support
in the table. [2] this suggestion. Justify your statement with
▼ Table P2 reference to your results. [1]
f Another student wants to investigate whether
beaker beaker more thermal energy is lost from the water
with 200 cm of hot
3
with 100 cm3 of hot water surface than from the sides of the beakers.
water Describe an experiment that could be done to
t/ θ/ θ/ investigate this.
0
You are not required to carry out the experiment.
You may draw a diagram to help your
description. [2]
[Total: 11]
Cambridge IGCSE Physics 0625 Paper 52 Q3
Feb/March 2018
6 In this experiment, you will investigate the
reflection of light by a plane mirror.
Carry out the following instructions, using the
separate ray-trace sheet provided.
327
328
329
330
▲ Fig. P13
00 : 20 : 22
▲ Fig. P14
ii The student places the cup upside down d Suggest, with a reason, a part of the procedure
and draws around the rim of the cup. a, b or c that could give an unreliable result for
She determines the diameter DT of the rim the density of water. [1]
of the cup. e The student pours the water from the cup into
DT = 7.2 cm a measuring cylinder.
Draw a diagram to show water in a measuring
Calculate the average diameter D of the cylinder. Show clearly the meniscus and the
D + DT
cup using the equation D = B . [1] line of sight the student should use to obtain
2 an accurate value for the volume of the
b i On Fig. P15, measure the vertical height h water. [2]
of the cup. [Total: 10]
Cambridge IGCSE Physics 0625 Paper 62 Q1
May/June 2018
3 A student has a selection of rubber bands
of different widths. He is investigating the
extension produced by adding loads. Fig. P17
shows the set-up used.
boss clamp
h
stand
rubber band
hook bench
▲ Fig. P17
332
4 Students are investigating how the use of a lid c Write a conclusion stating whether the
or insulation affects the rate of cooling of hot insulation or the lid is more effective in
water in a beaker. They use the apparatus shown reducing the cooling rate of the water in the
in Fig. P18. beakers in this experiment.
thermometer Justify your answer by reference to the
insulation beakers lid results. [2]
d One student thinks that the experiment does
not show how effective insulation is on its
own or how effective a lid is on its own.
A B Suggest an additional experiment which
could be used to show how effective a lid or
4
insulation is.
30
▲ Fig. P18
used. [2]
e i Calculate xA, the average cooling rate for
a Record the room temperature θ R shown on the beaker A over the whole experiment. Use
thermometer in Fig. P18. [1] the readings for beaker A from Table P5
b • 100 cm3 of hot water is poured into beaker A and the equation
and the initial temperature θ is recorded in θ 0 − θ180
Table P5. xA =
• The temperature θ of the water at times T
t = 30 s, 60 s, 90 s, 120 s, 150 s and 180 s are where T = 180 s and θ0 and θ180 are the
shown in Table P5. temperatures at time t = 0 and time t = 180 s.
• This process is repeated for beaker B. Include the unit for the cooling rate. [2]
Copy Table P5 and complete the headings and ii Students in another school are carrying out
the time column. [2] this experiment using identical equipment.
▼ Table P5 State why they should make the initial
temperature of the water the same as in this
beaker A beaker B experiment if they are to obtain average
with insulation with a lid cooling rates that are the same as in Table P5.
t/ θ/ θ/ Assume that the room temperature is the
same in each case.
0 83.0 86.0
Use the results from beaker A to explain
79.0 84.0 why this factor should be controlled. [2]
75.5 82.5 [Total: 11]
73.0 81.0 Cambridge IGCSE Physics 0625 Paper 62 Q2
71.0 80.0 Feb/March 2019
69.5 79.0
68.5 78.5
333
5 The class is investigating the refraction of light c • Measure and record the angle a between
passing through a transparent block. A student is the line joining the positions of P3 and P4
using optics pins to trace the paths of rays of light. and the line KM.
Fig. P19 shows the student’s ray-trace sheet. • Measure and record the length x between
points M and K. [2]
d The student repeats the procedure with the
angle of incidence i = 50°.
His readings for a and x are shown.
a = 52°
x = 19 mm
A B A student suggests that the angle a should
always be equal to the angle of incidence i.
State whether the results support this
suggestion. Justify your answer by reference
to the values of a for i = 30° and i = 50°. [2]
e Suggest one precaution that you would
D P3 C take with this experiment to obtain reliable
results. [1]
[Total: 8]
Cambridge IGCSE Physics 0625 Paper 61 Q2
May/June 2017
P4 6 A student is investigating a circuit containing
different lamps.
ray-trace eye She is using the circuit shown in Fig. P20.
sheet
power supply
▲ Fig. P19
c i T he student uses the voltmeter to measure ii The student sets up the circuit as described
the p.d. VX across lamp X and then in e i.
reconnects the voltmeter to measure the She measures and records the current in
p.d. VY across lamp Y. lamp X and the p.d. across the lamps.
She then calculates a new resistance R2 for
2 3 2 3 lamp X in this parallel circuit.
1 4 1 4
R2 = 8.3 Ω
0 5 0 5
The student notices that lamp X is very
V V
bright in this parallel circuit, but it was
dim in the series circuit in a.
Suggest how temperature affects the
▲ Fig. P22a ▲ Fig. P22b resistance of a lamp.
Record the value of the p.d. VX across Justify your suggestion by reference to the
lamp X, shown in Fig. P22a. value of R1 from d and the value of R2.[2]
Record the value of the p.d. VY across [Total: 11]
lamp Y, shown in Fig. P22b. [1] Cambridge IGCSE Physics 0625 Paper 62 Q3
She then measures the p.d. VS across both
ii Feb/March 2018
lamps in series. 7 A student is investigating the power of two lamps.
The circuit is shown in Fig. P24.
2 3
1 4
0 5
A
V X Y
▲ Fig. P23 V
335
B
She repeats the procedure with the voltmeter C resistance
connected across lamp Y only. wires
VY = 1.2 V ▲ Fig. P27
IY = 0.18 A
i Calculate the power PX produced by the a On a copy of Fig. P27, draw a voltmeter
lamp filament X using the equation connected so that it will measure the
PX = VX IX, and calculate the power PY potential difference across wire A. [1]
b In the first line of a copy of Table P6, record
produced by the lamp filament Y using
the potential difference V and current I for
the equation PY = VYIY.[1]
wire A, as shown in Figs. P28 and P29. [2]
ii State and explain briefly whether the two
values for power PX and PY are the same 2 3
1 4
within the limits of experimental 5
0
accuracy. [2] V
c The student repeats the experiment using
two other lamps. She notices that one lamp
is dimly lit, but the other lamp does not light
▲ Fig. P28
at all.
The p.d. VT across the lamps is the same 0.4 0.6
as in b, but the current IT in the circuit is 0.2 0.8
0 1.0
approximately half of the original value. A
The student concludes that the filament of one
of the lamps is broken.
State whether you agree with the student and
▲ Fig. P29
give a reason for your answer. [2]
d Draw a circuit diagram to show the circuit in ▼ Table P6
Fig. P24 rearranged so that:
• the lamps are connected in parallel wire l/m V/V I/A R/Ω
• a variable resistor is connected to control A 0.900
the total current in the circuit B 0.500 2.4 0.75
• the ammeter will measure the total current C 0.400 2.2 0.85
in the circuit
• the voltmeter will measure the p.d. across c The student connects the crocodile clips to
the lamps. [3] wire B and then wire C in turn. His readings of
[Total: 11] potential difference and current are shown in
Cambridge IGCSE Physics 0625 Paper 62 Q2 Table P6.
Oct/Nov 2018 Calculate, and record in a copy of Table P6, the
8 A student is investigating the resistance of three resistance R of each wire.
wires A, B and C. He is using the circuit shown in V
Use the equation R = L . [2]
Fig. P27.
The circuit is set up to test wire A. The length, d i Calculate the resistance per unit length r of
l, of each wire is measured and recorded. R
each wire using the equation r = .
l
336
337
338
impulse N s
moment of a force N m
work done W J, kJ, MJ
energy E J, kJ, MJ, kWh
power P W, kW, MW
pressure p N/m2, N/cm2 pressure p Pa
temperature θ, T °C, K
specific heat capacity c J/(g °C), J/(kg °C)
frequency f Hz, kHz
wavelength λ m, cm wavelength λ nm
focal length f m, cm
angle of incidence i degree (°)
angle of reflection r degree (°)
angle of refraction r degree (°)
critical angle c degree (°)
339
Core Supplement
Usual Usual
Quantity symbol Usual unit Quantity symbol Usual unit
refractive index n
340
341
conduction flow of thermal energy through matter from diffuse reflection a parallel beam of light is reflected in
places of higher temperature to places of lower temperature many different directions at a rough surface
without movement of the matter as a whole
diffusion cloud chamber a device which makes the paths
conductor material which allows thermal energy or of α-, β- and γ-radiation visible
electrons to flow easily
* digital using discrete values only
constant having the same value
direct current d.c.; electrons flow in one direction only
constant of proportionality the ratio of two variables
direction of a magnetic field at a point the direction of
which are directly proportional to each other
the force on the N pole of a magnet at that point
continuous ripples a wave
direction of an electric field at a point the direction of
convection flow of thermal energy through a fluid from the force on a positive charge at that point
places of higher temperature to places of lower temperature
dispersion separation of white light into its component
by movement of the fluid itself
colours
convection currents streams of warm moving fluids
displacement distance moved in a stated direction
convector warms air using convection currents
displacement–distance graph graph of the displacement
conventional current direction in which a positive charge from their undisturbed position of the particles
would flow in a circuit transmitting a wave, plotted against their distance from
converging light bends inwards the source, at a particular instant of time
* coulomb C; unit of charge distance–time graph graph of distance on the vertical axis
plotted against time on the horizontal axis
count-rate counts/second
diverging light spreads out
crest of a wave maximum amplitude of a wave
dynamic friction frictional force acting on a body moving
* critical a chain reaction becomes critical when on at a constant speed
average each fission results in another fission event,
so that the reaction is sustained * dynamo d.c. generator
critical angle angle of incidence which produces an angle echo reflection of a sound wave
of refraction of 90° * eddy currents currents induced in a metal which is in a
crumple zones front and rear sections of a vehicle, changing magnetic field; they cause energy loss in the core
designed to collapse on impact so that kinetic energy is of a transformer
absorbed gradually * efficiency (useful energy output/energy input) × 100%;
cubic centimetre unit used to measure volume (cm3) (useful power output/power input) × 100%
cubic metre SI unit of volume (m3) effort force required to lift a weight
current flow of electric charges; symbol I, measured in * elastic limit for extensions beyond the elastic limit,
ampere (A) a material will not return to its original length when
unloaded; it is permanently stretched and the law of
* deceleration a negative acceleration; velocity decreases proportionality no longer applies
as time increases
* electric current the charge passing a point per unit
degrees Celsius °C; unit of temperature time (current I = Q/t where Q is the charge flowing past a
density mass per unit volume particular point in time t)
dependent variable quantity whose value depends on that electrical energy energy transferred by an electric current
of another electric cell changes chemical energy into electrical
2
deuterium H isotope of hydrogen with one proton and energy
1 H;
one neutron in the nucleus * electric field a region of space where an electric charge
diffraction spreading of a wave at the edges of an obstacle experiences a force due to other charges
342
electric force force between electric charges * fission the break-up of a large nucleus into smaller parts
electrode emitter or collector of electric charges * Fleming’s left-hand (motor) rule when the thumb and
first two fingers of the left hand are held at right angles to
electromagnet temporary magnet produced by passing an
each other with the first finger pointing in the direction of
electric current through a coil of wire wound on a soft iron
the magnetic field and the second finger in the direction of
core
the current then the thumb points in the direction of the
electromagnetic induction the production of a p.d. across thrust on a wire
a conductor when it moves through a magnetic field or is at
* Fleming’s right-hand (dynamo) rule used to show the
rest in a changing magnetic field
relative directions of force, field and induced current: when
electromagnetic radiation radiation resulting from the thumb and first two fingers of the right hand are held
electrons in an atom undergoing an energy change; all at right angles to each other with the first finger pointing
types travel in a vacuum at 3 × 108 m/s (the speed of in the direction of the magnetic field and the thumb in the
light), obey the wave equation and exhibit interference, direction of the motion of the wire, then the second finger
diffraction and polarisation points in the direction of the induced current
electromotive force (e.m.f.); the electrical work done by a fluid a liquid or gas
source in moving unit charge around a complete circuit
0
fluorescent emitting light when struck by ultraviolet
electron −1
e ; negatively charged elementary particle radiation or electrons
electrostatic induction production of charge on a focal length distance between the optical centre and the
conductor when a charge is brought close to it principal focus of a lens
emitter gives out heat or radiation focus bring beams to a point
energy may be stored as kinetic, gravitational potential, force a push or pull on a body
chemical, elastic (strain), nuclear, electrostatic and internal
(thermal) fossil fuels coal, oil and natural gas formed from the remains
of plants and animals which lived millions of years ago
energy density energy/volume
* forward bias p.d. connected across a diode such that it
energy sources materials and resources from which energy has a low resistance and conducts
can be produced
freezing temperature temperature at which a liquid
energy transfer change of store or location of energy changes to a solid
equilibrium when there is no resultant force and no frequency number of complete oscillations per second
resultant moment on an object
friction force which opposes one surface moving, or trying
evaporation loss of vapour from a liquid surface at a to move, over another surface
temperature below the boiling temperature of the liquid
fulcrum pivot
* exciter supplies d.c. to the electromagnets in the rotor of
an alternator fuse a short length of wire which melts when the current in
the circuit exceeds a certain value; it protects the circuit
expansion increase in size from carrying a large current
extension change in length of a body being stretched * fusion the union of light nuclei into a heavier one
factors affecting the magnitude of an induced e.m.f. galaxy made up of many billions of stars
e.m.f increases with increases of: (i) the speed of motion of
the magnet or coil, (ii) the number of turns on the coil, (iii) galvanometer an instrument used to detect small currents
the strength of the magnet and p.d.s
field line line which shows the direction of an electric, gamma radiation γ-radiation; high-frequency, very
magnetic or gravitational field at each point penetrating electromagnetic waves
filament thin coil of wire which can transfer electrical gas turbine gas is used to turn the blades of a rotor
energy to heat and light (as in a lamp) Geiger–Müller tube GM tube; detects radiation
343
* impulse force × time for which force acts length greatest dimension of an object; SI unit is the
metre (m)
independent variable quantity whose value does not
depend on that of another light-dependent resistor LDR; semiconductor device
in which the electrical resistance decreases when the
induction motor a.c. motor intensity of light falling on it increases
infrared radiation electromagnetic waves emitted by hot, * light emitting diode LED; semiconductor device which
but not glowing, bodies emits light when it is forward biased but not when it is
insulator material which does not allow thermal energy or reverse biased
electrons to flow easily
344
light-year used to measure astronomical distances; the microwaves radio waves with a wavelength of a few cm
distance travelled in (the vacuum of) space by light in one year
Milky Way the spiral galaxy to which our Solar System
* limit of proportionality the point at which the load- belongs. The Sun is a star in this galaxy and other stars
extension graph becomes non-linear that make up this galaxy are much further away from the
Earth than the Sun is from the Earth
limits of audibility the approximate range of frequencies
audible to humans, 20 Hz to 20 000 Hz millimetre 10–3 m
* linear conductor conductor which obeys Ohm’s law * moderator graphite core of a nuclear reactor which slows
down fission neutrons
linearly values lie along a line
molecule combination of atoms
line of force see field line
moment of a force moment = force × perpendicular
live wire connected to a high p.d. distance from pivot
load weight * momentum mass × velocity
longitudinal wave direction of vibration of particles of the * monochromatic single colour (frequency) of light
transmitting medium is parallel to the direction of travel of
the wave * motor rule see Fleming’s left-hand rule
loudspeaker converts an electric current into a sound wave multimeter an instrument which can be used to measure
a.c or d.c. currents and voltages and also resistances
luminous object which makes its own light
multiplying factor number of times a force is increased,
magnetic field a region of space where a magnet experiences for example in a hydraulic system
a force due to other magnets or an electric current
musical notes produced by regular vibrations
magnetic force force between magnets
mutual induction occurs when a changing current in one
magnetic materials materials that can be magnetised by a coil produces a changing current in a nearby coil as a result
magnet; in their unmagnetised state they are attracted by of electromagnetic induction
a magnet
nanometre 10 −9 m
mass a measure of the quantity of matter in an object at
National Grid network of electricity transmission lines
rest relative to an observer
negative charges repel other negative charges, but
* mass defect mass lost in a reaction; it can be large in
negative charges attract positive charges
nuclear reactions such as fission or fusion and become a
source of energy (E = mc2) neutral equilibrium occurs when a body stays in its new
position when slightly displaced and then released
mass number A; number of protons and neutrons (nucleons)
in the nucleus of an atom neutral point point at which magnetic fields cancel
mechanical waves to and fro vibration of the particles of a neutral wire connected to earth
transmitting medium neutron uncharged particle found in the nucleus of an atom
* medical ultrasound imaging technique used to image (except that of hydrogen)
internal organs of the body using the reflection of newton SI unit of force; N
ultrasonic pulses
Newton’s first law of motion a body stays at rest, or if
megawatt MW; 106 W moving continues to move with uniform velocity, unless an
melting temperature temperature at which a solid changes external force makes it behave differently
to a liquid * Newton’s second law of motion
meniscus curved liquid surface force = mass × acceleration
micrometre µm; 10–6 m non-luminous object which does not make its own light;
it may reflect light from a luminous source
microphone converts sound waves to an electric current
345
non-magnetic materials materials that cannot be polar near the north or south pole of the Earth
magnetised and are not attracted by a magnet
positive charges repel other positive charges, but positive
non-ohmic device which does not obey Ohm’s law charges attract negative charges
non-renewable cannot be replaced when used up potential difference p.d.; the work done by a unit charge
normal line which is perpendicular to a surface passing through a component
nuclear energy energy derived from nuclei potential divider variable resistor connected so that the
p.d. applied to a device can be changed
nuclear fuels radioactive materials such as uranium, used
in the core of a nuclear reactor to produce heat potential energy energy a body has because of its position
or condition (mgh)
nucleon proton or neutron
potentiometer resistor whose resistance can be varied
nucleon number A; number of protons and neutrons in the
nucleus power the work done per unit time and the energy
transferred per unit time
nucleus dense core of an atom containing protons and
neutrons powers of ten way of writing numbers; index gives number
of times number must be multiplied by 10
nuclide atom of an element characterised by the mass
number A and the proton number Z pressure the force per unit area
octave notes are an octave apart if the frequency of one primary main, most important
note is twice that of the other
principal axis line through the optical centre of a lens at
ohm Ω; unit of resistance right angles to the lens
* ohmic conductor conductor which obeys Ohm’s law principal focus (focal point) point on the principal axis
Ohm’s law the current through a metallic conductor is of a lens to which light rays parallel to the principal axis
directly proportional to the p.d. across its ends if the converge, or appear to diverge from
temperature and other conditions are constant principle of conservation of energy energy cannot be
optical centre centre of a lens created or destroyed; it is always conserved
orbit curved path, such as that taken by a moon around progressive wave travelling wave carrying energy from one
a planet place to another
parallel lines with the same direction proportional two variables are proportional if their ratio is
a constant
parallel circuit components are connected side by side
and the current splits into alternative paths and then proton positively charged particle found in the nucleus of
recombines; current from the source is larger than the an atom
current in each branch
proton number Z; number of protons in the nucleus
parallelogram law if two forces acting at a point are
pulse a few cycles of a wave
represented in size and direction by the sides of a
parallelogram drawn from the point, their resultant is pumped storage electricity generated at off-peak periods
represented in size and direction by the diagonal of the is used to pump water from a low-level reservoir to a high-
parallelogram drawn from the point level one
pascal Pa; SI unit of pressure 1 Pa = 1 N/m2 quality or timbre of a sound is determined by the number
period time for one complete oscillation (1/frequency) and strength of the overtones present
permanent magnets made of steel, retain their magnetism radar system which enables the position of a distant object
to be found by the use of microwaves directed at and
perpendicular at 90° reflected from the object
phase vibrating particles transmitting a wave are in phase radial along a radius
if they are moving in the same direction and have the same
displacement; if this is not the case, they are out of phase radiant emits radiation
pitch frequency of a sound wave radiation transfer of thermal energy from one place to
another by electromagnetic waves
346
radio waves electromagnetic waves with the longest * reverse bias p.d. connected across a diode such that it
wavelength has a high resistance and does not conduct
radioactive material which emits α-, β- or γ-radiation rheostat variable resistor connected so that the current in
a circuit can be changed
radioactive decay the emission of α-, β- or γ-radiation
from unstable nuclei right angle 90°
radioisotope isotope of an element which is radioactive right-hand grip rule if the fingers of the right hand grip a
solenoid in the direction of the conventional current, the
radionuclide see radioisotope
thumb points to the N pole
radiotherapy use of ionising radiation to treat cancer
right-hand screw rule if a right-handed screw moves
random irregular, erratic or haphazard forwards in the direction of the conventional current, the
direction of rotation of the screw gives the direction of the
range spread of values
magnetic field
ratemeter instrument which counts the number of current
rotor blades or electromagnets on a rotating shaft
pulses/second (often used with a GM tube)
* scalar a quantity which has magnitude only
ray direction of the path in which light travels
scaler instrument which counts current pulses (often used
reaction force exerted by a support on a body
with a GM tube)
real image an image which can be formed on a screen
second SI unit of time (s)
* rectifier changes a.c. to d.c.
secondary coming later; of less importance
redshift shift in the wavelengths of light from distant
* semiconductor diode electronic device which allows
galaxies towards longer wavelengths (the red end of the
current to flow in one direction but not the other
spectrum)
sensitivity response of a device to a change in input;
reed switch electromagnetic switch
precision
refraction bending of rays when they pass from one
series circuit components connected one after the
medium to another
other; the current is the same at each point in a series
* refractive index n; the ratio of the speeds of a wave in circuit
two different regions
significant figures number of figures to which a value is
regular reflection a parallel beam of light is reflected from given; they indicate the precision of a measurement
a smooth surface such as a mirror, in a parallel beam
sliding friction frictional force acting on a body moving at
relative charges of protons, neutrons and electrons +1, 0, a constant speed
–1, respectively
* slip rings rings attached to the ends of the coil of an a.c.
relative motion motion of one object with respect to another generator which rotate with the coil and to which electrical
contact is made
relay electromagnetic switch
soft in magnetic terms, material such as iron which is easily
renewable can be replaced; cannot be used up
magnetised and demagnetised
resistance opposition of a conductor to the flow of electric
solar cells convert sunlight into electricity
current; symbol R, measured in ohms (Ω)
solar energy energy from the Sun
resistance of a metallic wire directly proportional to its
length and inversely proportional to its cross-sectional area solar panels convert sunlight into thermal energy
resistor conductor designed to have resistance solenoid long cylindrical coil of wire
resultant force the rate of change in momentum per unit time * sonar an echo technique which enables the depth of an
object to be found using ultrasonic waves
* retardation a negative acceleration; velocity decreases
as time increases spectrum band of colours produced when white light is
separated into its component parts
reverberation combination of a sound wave and its echo
which acts to prolong the sound
347
* specific heat capacity the energy required per unit mass thermostat a device which keeps the temperature of a room
per unit temperature increase or appliance constant
speed distance travelled per unit time * thoron radioactive gas which emits α-particles
speed–time graph graph of speed on the vertical axis tidal energy flow of tidal water from a high to a low level
plotted against time on the horizontal axis used to generate electricity
* split-ring commutator split ring of copper which rotates time duration; SI unit is the second (s)
with the coil of an electric motor; it enables the current
total internal reflection occurs when a light ray does
through the coil to be reversed every half-turn
not cross the boundary between two media; it is totally
* spring constant force per unit extension reflected at the boundary
stable equilibrium occurs when a body returns to its * tracer radioisotope injected into a system; the motion or
original position when slightly displaced and then released concentration of the isotope can be monitored, for example
with a GM tube
standard notation writing numbers using powers of ten
transformer two coils (primary and secondary) wound on a
starting friction maximum value of a frictional force which
soft iron core which allow an alternating p.d. to be changed
occurs just as a body starts to move
from one value to another
static friction maximum value of a frictional force which
transverse wave direction of vibration is perpendicular to
occurs just as a body starts to move
the direction of travel of the wave
* stator (or diaphragm) set of fixed blades (or fixed coils 3
H isotope of hydrogen with one proton and two
tritium 1 H;
in an alternator)
neutrons in the nucleus
steam turbine steam is used to turn the blades of a rotor
ultrasound sound wave with a frequency greater than 20 kHz
strain energy energy stored in a compressed spring or
ultraviolet radiation electromagnetic waves having shorter
elastic material
wavelengths than light
stretching force force causing a body to change shape
uniform having the same value
systematic error error introduced by the measuring device
uniform acceleration constant acceleration
(the system)
uniform velocity constant velocity
tangent a line touching, but not intersecting, a curve
unstable equilibrium occurs when a body moves further
temperature determines the direction in which thermal
away from its original position when slightly displaced and
energy flows; kinetic theory regards temperature as a measure
then released
of the average kinetic energy of the molecules of the body
vacuum a space from which all air has been removed
temporary magnets made of soft iron, lose their
magnetism easily vaporisation change of a liquid to a vapour
* terminal velocity constant velocity reached when the air variable quantity that can be changed
resistance upwards equals the downward weight of a falling
variable resistor resistor whose resistance can be changed
body
* variation of magnetic field strength the magnetic field
thermal energy energy of the molecules in a body
decreases with distance from a current-carrying wire and
thermal power station thermal energy is used to turn varies around a solenoid
water into steam to drive a turbine and generate electricity
* vector a quantity which has both magnitude and direction
thermistor semiconductor device in which the electrical
velocity speed in a given direction; change in displacement
resistance decreases when the temperature increases
per unit time
thermometer device for measuring temperature
virtual image an image which cannot be formed on a screen
* thermonuclear fusion the combination of light nuclei
volt V; unit of p.d.
into a heavier nucleus in a reaction which takes place at a
very high temperature (for example in the Sun) voltage p.d.; measured in volts (V)
348
voltmeter instrument used to measure p.d. the crests of waves in a ripple tank are wavefronts. A line
drawn perpendicular to a wavefront is a ray
volume of a cylinder πr 2 × h, where r is the radius and h is
the height of the cylinder wavelength distance between successive crests of a wave
watt SI unit of power; 1 W = 1 J/s weight a gravitational force on an object that has mass
wave energy rise and fall of sea waves used to generate wind turbines convert wind energy into electrical energy
electricity
work measure of amount of energy transferred.
wave equation v = fλ Work done = force × distance moved in the direction of the
force. SI unit is the joule (J)
waveform shape of a wave
X-rays electromagnetic waves with a shorter wavelength
wavefront in two dimensions, it is a line on which the
than ultraviolet radiation
particles transmitting the wave are vibrating in phase;
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350
351
converging beams 137 displacement–distance graphs 129 direct and alternating 192–3
converging lenses 150–2 distance–time graphs 15–16 effects of 190
cooling, rate of 121 falling bodies 20 at a junction 210
cooling by evaporation 112 distance travelled magnetic effect 233–5
cooling curves 109 equations of motion 17 measurement of 190, 191–2
Copernicus, Nicolaus vi speed–time graphs 16 in series and parallel circuits 210
cosmic microwave background diverging beams 137 electric fields 187
radiation (CMBR) 292 diverging lenses 150–1 electric heating 224
cosmic rays 260 Doppler effect 291 electricity
coulomb (C) 190 double insulation 227 paying for 204–5
Crab Nebula 290 drag 40 transmission of 246–7
critical angle 146–7 dwarf planets 279, 280 electricity generation
critical value 257 dynamo rule (Fleming’s right-hand energy sources 69–71
crumple zones 58, 66 rule) 231 see also power stations
cubic centimetre (cm3) 4, 5 electricity meters 204–5
cubic metre (m3) 4 E electric lighting 223
Curie, Marie 260 E = mc2 257 electric motors 239–40
current see electric current Earth 279 power output 203
cylinder, volume of 5 facts and figures 282 practical work 241
magnetic field 182 electric power 202–3
D motion of 276–7 of appliances 204
dams 80 earth (E) wire 224 measurement of 203
day and night 276 earthing 227 electric shock 222–3
d.c. motor 239–40 earthquakes, seismic waves 128, 129, electromagnetic induction 229
practical work 241 173 direction of induced e.m.f. 230–1
decay curves 268 echoes 168–9 experiments 229–30
deceleration (retardation) 13 estimating the speed of sound 169 factors affecting induced e.m.f.
speed–time graphs 14 eddy currents 245 size 230
declination 182 applications 247 generators 231–3
delocalised electrons 116 efficiency 74, 203 mutual induction 243
demagnetisation 180 of power stations 72 electromagnetic radiation 128
density (r) 29 of transformers 245 dangers of 164
calculations 29–30 effort 45 electromagnetic spectrum 160–1
floating and sinking 31 Einstein, Albert 257 gamma rays 164
measurement 30–1 elastic collisions 66 infrared radiation 162
water and ice 103 elastic strain energy 61 light waves 161
density, optical 144 electrical conductors and insulators microwaves 163
dependent variables 298 186–7, 189 radio waves 162–3
depth electrical safety 222–3 ultraviolet radiation 162
real and apparent 145 fuses 225–6 X-rays 163
relationship to pressure 82 trip switches (circuit breakers) 226 electromagnetic waves 161
deuterium 256 electric bell 237 use in communications 164
deviation of a light ray 155–6 electric cells 211–12 electromagnets 181
dichloromethane 112 electric charge 184 uses of 182
diffraction 132 dangers of static electricity 188 electromotive force (e.m.f.) 193,
of radio waves 162–3 explanation of 185 211–12
and wave theory 134 gold-leaf electroscope 186 electromagnetic induction 229–31
diffuse reflection 140 positive and negative 184–5 electron orbits 253
diffusion cloud chambers 264 uses of static electricity 188 electrons 185
digital signals 164–5 electric circuits and conduction of electricity 186–7
diode lasers 218 circuit symbols 209 electrostatic energy 61
diodes 201, 218–19 connecting an ammeter 191 elements, origin of 281
direct current (d.c.) 192–3 connecting a voltmeter 195, 196 elliptical orbits 280
d.c. motor 239–41 house circuits 224–7 endoscopes 148
direction of an electric field 187 model of 194 energy
direct proportion 296 series and parallel 209–13 conservation of 62–3, 65, 230
dispersion of light 155–6, 161 electric current (I) 189 kinetic 63–4
displacement 13 conventional 190 potential 64
displacement can 30 definition 190 energy consumption 73
352
energy density 69 Fleming’s right-hand rule (dynamo gas laws 93, 95–6
energy levels of an atom 254 rule) 231 gas pressure 89, 91
energy sources 68–9 floating and sinking 31 effect of temperature
economic, environmental and fluorescent lamps 223 changes 92, 94
social issues 73 focal length 151 effect of volume changes
non-renewable 69 focal point (principal focus) 151 92–3, 96
power stations 72 force multipliers 80 manometers 83
renewable 69–71 forces gas turbines 72
world use of 73 action-at-a-distance 26 gas volume, effect of temperature
energy stores 61 centripetal 41–2 changes 94, 95
energy transfers 60, 61–2 on charged particles in a magnetic Geiger, Hans 252–3
collisions 66 field 238–9 Geiger–Müller (GM) tube 261
efficiency 74 on a current-carrying generators 61, 231–3
falling bodies 64–5 conductor 237–8 geostationary satellites 42
measurement of 62 effects of 33, 38–9 geothermal energy 71
pendulums 65 extension in springs 34–5 gliding 118
and potential difference 194–5 gas pressure 89 global warming 69
practical work 64 magnetic 178 gold-leaf electroscope 186
pumped storage 72 moments 43–6 gradient (slope) 297
representation of 63 and momentum 57 distance–time graphs 15–16
see also thermal energy transfers Newton’s first law of motion 37 speed–time graphs 15
equations, changing the subject of Newton’s second law of motion 38–9 graphs 297–8
295–6 Newton’s third law of motion 40–1 cooling curves 109
equilibrium 44, 46 paired 40–1 distance–time 15–16, 20
stability 50 resultants 9, 35–6 I–V 201
equinoxes 276, 277 vector nature of 9 load–extension 34
errors forward-biased diodes 218–19 speed–time 14–15, 16
parallax 3 fossil fuels 69 of wave motions 129
systematic 7 power stations 72 gravitational fields 26
zero error 8 freezing (solidification) 108, 109 gravitational field strength 26–7
ether 112 latent heat of fusion 110, 111 of a planet 281
evaporation 87, 112 frequency (f ) 6, 129 gravitational potential
evidence vi of alternating current 193 energy 61, 64
expansion joints 102 and pitch 170 gravity 25–6
explosions 57 friction 37, 40 acceleration of free fall 19–20
extended light sources 138 see also air resistance centre of 47–50
fulcrum 45 of the Moon 277
F fundamental frequency 171 and planetary motion 284
falling bodies 18 fuses 225–6 Great Red Spot, Jupiter 283
acceleration of free fall 19–20 fusion, latent heat of 110 greenhouse effect 69, 120–1
air resistance 22 fusion, nuclear 71, 258
distance–time graphs 20 in stars 286 H
energy transfers 64–5 half-life 267–8
investigation 19 G experimental determination 269
projectiles 21 galaxies 287–8 Halley’s comet 280
Faraday, Michael 229, 230 Galileo Galilei vi, 18 head restraints 66
ferromagnetic materials 176, 177, 180 galvanometers 195, 242 heat conduction 115–16
fields gamma rays 164, 263, 266 heat exchangers 257, 258
electric 187 dangers of 164, 272 heating, electric 224
gravitational 26–7 uses of 270 helium, superfluid 94
magnetic 178–80, 182 gap size, effect on diffraction 132 hertz (Hz) 129, 193
magnetic effect of a current 234 gases high-temperature alarm 217
filament lamps 201 conduction of heat 116 high-voltage transmission of
fire alarms 101 density 29, 31 electricity 246
fire risk, electrical devices 223 properties of 87 Hooke, Robert 34
fission 257 structure 88, 89 house circuits 224–7
fixed points, temperature scales 104 thermal expansion 100–1 Hubble, Edwin 292
Fleming’s left-hand rule gas giants see Jupiter; Neptune; Hubble constant (H0) 292–3
(motor rule) 238 Saturn; Uranus Huygen’s construction 133
353
354
355
356
reflection of light 138–9 ring main circuit 225 field due to 234
image properties 141 ripple tanks 130–2 solidification (freezing) 108, 109
position of the image 140 rockets 57 latent heat of fusion 110, 111
real and virtual images 141 rotors 72 solids
regular and diffuse 140 rulers 3 density 29
total internal reflection 146–9 systematic errors 7 properties of 86
reflection of radio waves 163 Rutherford, Ernest 252–3 structure 88
reflection of sound 168–9 Rutherford–Bohr model of the atom 253 thermal expansion 100
reflection of water waves 131 sonar 172
and wave theory 133 S sound waves 61–2, 129, 167–8
refraction of light 143–4 safety, electrical 222–3 limits of audibility 168
critical angle 146 Sankey diagrams 63 longitudinal nature of 168
by a prism 155–6 satellites 42, 163 musical notes 170–1
real and apparent depth 145 Saturn 279 reflections and echoes 168–9
refraction of water waves 131 facts and figures 282, 283 speed of 169–70
and wave theory 134 scalars 9 ultrasound 171–2
refractive index 145–6 speed 13 south (S) pole, magnets 176–7
and critical angle 147 Schrödinger model of the atom 254 space missions 283
regular reflection 140 scientific enquiry v–vi specific heat capacity 104–6
relays 217, 235–6 sea breezes 118 of aluminium 107
renewable energy sources 69–71 seasons 277 determination of 106–7
economic, environmental and seat belts 58, 66 of water 106–7
social issues 73 second (s) 6 specific latent heat of fusion 110
power stations 72 seismic waves 128, 129, 173 specific latent heat of vaporisation 111
residual current circuit breaker self-righting toys 50 spectacles 154–5
(RCCB) 226 semiconductor diodes 201, 218–19 spectrum
resistance 197–8 semiconductors 216 of an atom 254
effect of temperature 215 series circuits electromagnetic 160–5
measurement of 199–200 cells and batteries 211 visible 156
of a metallic wire 200 current 210 speed 12
Ohm’s law 201 potential difference 210–11 distance–time graphs 15–16
of skin 222 resistors 212 equations of motion 17
resistivity 200 shadows 138 of a wave 129
resistors 198 shooting stars (meteors) 280 speed of light 138, 161
colour code 214 short sight 154 and refraction 145
light-dependent 201, 216–17 SI (Système International d’-Unités) speed of sound 169–70
in series and parallel circuits 212–14 system 2 speed–time graphs 14–15
thermistors 201, 215, 217 significant figures 3 area under 16
variable 199 sliding (dynamic) friction 40 sport, impulse and collision time 58
resultant force 37, 57 smoke alarms 270 spring balances 26
resultant of two forces 9, 35–6 solar cells 69–70 spring constant (k) 35
reverberation 169 solar energy 69, 73 springs, extension in 34–5
reverse-biased diodes 218–19 Solar System 279–80 square, area of 4
rheostats 199 origin of 280–1 square metre (m2) 4
right-hand grip rule 234–5 planets 282 stability 50
right-hand rule, Fleming’s 231 travel times 281 stable equilibrium 50
right-hand screw rule 234 solenoids 180 stable phase of a star 288–9
357
standard notation 2–3 and kinetic energy 89, 105 energy losses 245
stars and rate of emission of step-up and step-down 244
colour of 286, 288 radiation 120 transmission of electricity 246
life cycle 288–90 and thermal energy 105 power loss 247
night sky 287 temperature scales 94, 104 Trans-Neptunian Objects (TNOs) 279
nuclear reactions 286 temporary magnets 177 triangle, area of 4
origin of 288 electromagnets 181 trip switches (circuit breakers) 226
see also Sun terminal velocity 22 tritium 256
starting (static) friction 40 theories vi tsunami waves 129
states of matter 86–7 thermal energy (internal energy) tuning forks 170
static electricity 184 61, 63, 105 turbines 72
dangers of 188 and temperature 105 turning effect of a force see moments
uses of 188 thermal energy transfers 115
see also electric charge applications 122–4 U
stators 72 conduction 115–16 UHF (ultra-high frequency) radio
steam turbines 72 convection 117–18 waves 163
steel, magnetisation of 177 energy loss from buildings 123 ultrasound 171
step-up and step-down radiation 119–20 uses of 172
transformers 244 thermal expansion 100–1 ultraviolet (UV) radiation 162
sterilisation, use of g-radiation 270 bimetallic strips 101–2 dangers of 164
storage heaters 224 linear expansivity 102 umbra 138
straight-line graphs 297 liquid-in-glass uniform (constant) velocity 13
straight wire, field due to 234 thermometers 103 units of electricity 204–5
stroboscope 130 precautions against 102 Universe 290–1
strontium 263 uses 101 age of 292–3
sulfur dioxide 69 water 103 Big Bang theory 291–2
Sun 286, 287 thermal power stations 72, 232–3 expansion of 291–2
as an energy source 71 thermals 118 unstable equilibrium 50
facts and figures 282 thermistors 201, 215, 217 uranium 257, 260
rising and setting of 276–7 thermometers Uranus 279
thermonuclear reactions 258 infrared 124 facts and figures 282, 283
sunlight, protection from 164 liquid-in-glass 103 U-tube manometer 83
superconductors 94 thermonuclear reactions 258
superfluids 94 thermostats 101–2 V
supernovae 290 thickness gauges 270 vacuum 91
as origin of elements 281 thoron, half-life of 269 vacuum flasks 124
superposition see interference three-heat switches 224 van de Graaff generator 189
sweating 112 tickertape timers 6 vaporisation, latent heat of 111
switches 224, 225 tidal energy 70, 71, 73 variable resistors (potentiometers)
systematic errors 7 time 6 198–9
top-pan balance 25 variables 298
T toppling 49 vector addition 9
tangents, gradient of 16 total internal reflection 146–8 vectors 9
temperature optical fibres 148–9 acceleration 13
effect on gas pressure 92 tracers, radioactive 270–1 gravitational field strength 26–7
effect on gas volume 94, 95 transformer equation 244–5 momentum 57
effect on resistance 215 transformers 242–3 velocity 13
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