General Physics 1
General Physics 1
General Physics 1
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GENERAL PHYSICS 1 | MODULE 1
Table 2
Some SI Derived Units Significant figures (sig. figs) are those digits in
a number or measurement that are not being used and
Derived quantity Unit Symbol considered as place-values. Zeroes are not significant
Area square meter mᶻ if they are used only to indicate the position of the
Volume cubic meter mᵌ decimal point. For example, if the length of a computer
Frequency Hertz Hz desk, as measured by a ruler graduated in millimetres,
Density kilogram per cubic kg/m3
metre
was found to be 1564.3mm, the measurement has five
Force Newton N significant figures.
Work, energy Joule J Here are the Rules for Significant Figures
Power Watt W which will help you to understand them better.
Velocity ( speed) metre per second m/s a. All non-zero figures are significant: 25.4 has three
significant figures.
Some derived quantities have been given b. All zeros between non-zeros are significant: 30.08
specific names, such as Newton, Watt and Joule. This has four significant figures.
combination of basic unit can be replaced by the c. Zeros to the right of a non-zero figure but to the left
Newton (N), Joule (J), and Watts (W). 1 Newton = 1
of the decimal point are not significant (unless
kilograms metre per second squared (1N =1kgms-2), 1
Joule = 1 Newton metre (1J= 1Nm), 1 Watt = 1 Joule specified with a bar): 109 000 has three significant
per second (1W=1J/s). figures.
d. Zeros to the right of a decimal point but to the left of
International System of Units a non-zero figure are not significant: 0.050, only the
An internationally agreed system of units is last zero is significant; the first zero merely calls
necessary to standardize measurement of these attention to the decimal point.
quantities, and such a system is now in general use. In e. Zeros to the right of the decimal point and following
1960 the international authority on units agreed to a non-zero figure are significant: 304.50 have five
adopt the Systeme Internationale d’Unites, or the significant figures.
International System of Units. The abbreviation of
which is SI in all languages. The SI is a set of metric
Table 4
units. It is a decimal system in which units are divided
or multiplied by 10 to give smaller or larger units. Significant figures position
Two significant Three significant Four
Examples figure figure significant
1. It would be difficult to give the length of a figure
21000 3250000 42210000
rugby field in millimetres. The length of the rugby field
0.0012 469 1786
is 100 000mm which is equivalent to 100m. Giving it in
1.0 0.00843 508.6
a more appropriate unit that is metres, would give 0.18 0.234 0.6780
people a far better idea of the actual length of the field. 67 65.0 5.060
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GENERAL PHYSICS 1 | MODULE 1
To change this number into scientific notation, from
618.5cm + 145.06cm = 763.56cm where the decimal point is, count how many numbers
you are to move the decimal point to a position where
The least number of significant figures in the original the number is now between 1 and 10;
values is 4, so write the answer to this significance. You have to move the decimal point three places to
The sum is written as 763.6cm. the right, as 3 and 2 are in between 1 to 10.
Now write the number in scientific notation as 3.2 x
Now check what you have just learnt by trying out the 10ˉ³.
exercises below! The -3 shows that the decimal points have to move
Exercises: three places to the right.
Answer the given problem below. Show all your
working out where necessary. 3. Write the following numbers in scientific notation.
1. Give the number of significant figures in each of the (a) 3270 = 3.27 x 10³
following numbers: (b) 0.128 = 1.28 x 10ˉ¹
(a) 4.02 _________________________________ (c) 654 000 = 6.54 x 10⁵
(b) 0.008 ________________________________
(c) 8600 ________________________________ NOTE: In general if the number is greater than
(d) 1049 ________________________________ one, the sign of the index is positive. And if the
(e) 0.0002 ______________________________ number is less than one, the sign of the index
(f) 52.07 _______________________________ is negative.
(g) 0.60 _______________________________
2. The following values are part of a set of
experimental data: 34.7cm and 19.65mm. How many Exercises:
significant figures would be present in the sum of these Read and answer each question. All working out must
two figures? be shown where necessary.
3. Given that the definition of area is Area= length x 1. Convert the following numbers into scientific
width, determine the basic or fundamental unit form of notation:
the unit of the area. (a) 27 000 000 = ___________________________
(b) 0.000 007 12 = __________________________
What is scientific notation?
Scientific notation or standard index notation is a way (c) 821 = __________________________________
of writing any number between 1 and 10 multiplied by (d) 0.000 101 = _____________________________
an appropriate power of 10 notations. It is a shorthand (e) 81 250 000 000 = ________________________
method of writing numbers that are very large or very (f) 0.000 000 002 05 = _______________________
small. 2. Change the following numbers into normal
Let us take for example 1 and 2
notation:
1. The distance from the earth to the nearest star is
about 39 900 000 000 000 000m. In scientific notation (a) 5.80 x 10⁶ = _____________________________
it is written as 3.99 x 10¹⁶m. The exponent tells you (b) 6.32 x 10ˉ⁵ = ____________________________
how many times to multiply by 10. (c) 8.56 x 10⁴ = _______________________________
2. The mass of hydrogen atom is 0.000 000 000 000 (d) 2.52 x 10ˉ³= _______________________________
000 000 000 000 001 7 kilograms. In scientific notation (e) 2.30 x 10¹ᴼ= _______________________________
it is written as 1.7 x 10ˉ²⁷kg. In this case, the exponent
(f) 6.10 x 10ˉ¹¹ = ______________________________
tells you how many times to divide by 10.
3. Rewrite 2800 in scientific notation having 2
Scientific notation involves writing the number in the significant figures to be consistent with uncertainty
form M x 10ⁿ , where M is a number between 1 and 10 2800 ± 10. 4. Write the standard form.
but not 10, and n is an integer. (a) Speed of light in a vacuum = 298 000 000km/s
NOTE: Integer is a positive and negative whole number.
_______________________
Given below are examples on how to change numbers (b) One light year = 10 000 000 000 000km
into scientific notation: _______________________
1. 24 700
To change this number into scientific notation, first put Converting from one unit to another
the decimal point to the right of the last digit. In science, it is important that the standard unit
is used. You must be able to convert from one form of
Now count how many numbers to move the decimal a unit to another.
point to a position where the number is now between 1
and 10. You had to move the decimal point 4 places to Example:
the left. The result is 2, 4700. Change 5m into centimetres. You know that
Now write the number in scientific notation as: 2.47 x there are 100cm in a metre and, therefore, to change
10⁴, where m = 2.47 N = 4 shows that the decimal metres into centimetres you must multiply by 100 that
point was moved 4 places to the left. is:
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GENERAL PHYSICS 1 | MODULE 1
1. First decide if you are converting from a bigger to a Base quantity Name of unit Symbol for
smaller unit or if you are converting from a smaller to a unit
larger unit. length
kg
Case I – Bigger to Smaller
time electric
If you are converting from a bigger to a smaller unit current
(example mega to kilo), then you multiply. K
Case II – Smaller to Bigger mol
If you are converting from a smaller to a bigger unit luminous intensity
(example micro to milli), then you divide.
2. Then find the factor that you are going to multiply or 3. Convert the following values to the indicated units
divide by to make the conversion. If you are moving (a) 330mA = __________ A
(b) 6.3km = __________ m
one step up or down the chart, then the factor is 1000
(c) 2MJ = __________ J
(or 10³ ). If you are moving two steps up or down the
(d) 18mg = __________ g
chart, then the factor is 1000 000 (or 10⁶) etc. (e) 2000g = __________ kg
(f) 18km = __________ m
3. Then multiply or divide your number by the
appropriate factor. Study the chart on the next page to 4. An electric current measures 2 milli-amperes. What
help you convert units. is the current in kilo-amperes?
Measurement of Length
Length is simply defined as the measurement
or extent of something from end to end. The following
are instruments used for measuring length.
Exercises:
Answer the following questions on the spaces In the metric system, the SI unit of length is the
provided. metre (m). For some purposes, the metre is a large
1. Fill in the blanks with the correct words. unit and therefore it is converted into smaller units as
a. All physical quantities consist of a ___ follows:
__ and ____
b. A __________ unit is made up of one or more SI
units.
c. We use __________ to indicate multiples of units.
In dealing with large distances, the kilometre is used
such that 1 kilometre (km) = 1000 metres (m). The
2. Fill in the table below.
conversion in the metric system is essentially a
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GENERAL PHYSICS 1 | MODULE 1
decimal system and it is easy to convert from one unit For example as shown in the figure
to another.
Area ΔABC = ½ x AB x AC
Worked Example = ½ x 4cm x 6cm
= 12cm²
(a)Convert 38m into mm
1m = 1000mm Order of magnitude
You will be converting from a bigger to smaller unit so The order of magnitude of a number is the
you have to multiply by 1000 So 38m= (38 x 1000) mm value of the number rounded to the nearest power of
= 38 000mm ten (no significant figures). It is used if you need to give
(b) Convert 297mm into cm only an indication of how large or small a number is,
In 1cm = 10mm and only the power of ten is given. It also indicates that
You will be converting from a smaller to a bigger unit the accuracy of the measurement is limited.
so you divide by 10. 297mm = (297 ÷ 10) cm = 29.7cm
The instruments you use to measure length depends For example
very much on how large or small the length or distance 1) The velocity of light is 3.0 x 10⁸ metres per second.
is. The order of magnitude of this velocity is 10⁸ .
For an accurate measurement, the eye must 2) The order of magnitude of 142 is 10² . Since 142 in
always be placed vertically above the mark being read. scientific notation you count going to the left it
becomes 1.42 x 10².
. 3) 1 0 0 0 0 = 1.0 x 10⁴ order of magnitude would be
given as 10⁴
4) The average distance between two atoms is 1.6 x
10ˉ¹ᴼm. The order of magnitude for is 10ˉ¹ᴼm.
Exercises:
Answer the following questions on the spaces
provided. Show all your working out.
1. What is the order of magnitude for each of the
following numbers?
(i) 195 000 _________________________________
(ii) 0.00282 ________________________________
(iii) 650 ___________________________________
Application of measurements (iv) 170 million _____________________________
The skill of measuring lengths is the basis of 2. Estimate the order of magnitude of the answer for
finding other measurements such as the each of the following calculations.
measurements of area and volume. (i) 60 x (32 x 10⁶) _______________
(ii) 800000 _______________
Measuring Area 400
The amount of space covered by a body in two
dimensions is called area. The standard unit of area Measurement of Mass
measurement is the square metre (m²). Large areas Mass is the amount of matter in an object. It is
use measurement in square kilometres (km²) or measured in units called grams (g), kilograms (kg) and
hectares (ha), while smaller areas are usually tonnes (t). There are 1000 grams in a kilogram and
measured in square centimeters (cm²). 1000 kilograms in a tonne. Objects with a very small
The following table shows the common units of mass are measured in milligrams (mg) or grams (g).
area measurement. Heavier objects are weighed using kilograms or
tonnes. See table below.
Example 1
Example
The area of a square or rectangle in a formula, is (a) Change 220g to kg
area = length x width. The SI unit of area is the square Solution
metre (m² ) which is the area of a square with sides 1m You will be converting a smaller unit to a bigger unit so
long. Note that by conversion, 1cm² is equal to you divide.
0.0001m² as shown below So in 1kg there are 1000g.
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GENERAL PHYSICS 1 | MODULE 1
Instruments used to measure mass are called The approximate densities of some common
balances or scales. substances are given in Table below.
Example
Solution:
Example 1
An aluminium cube has a mass of 22kg and a volume
of 8.1m³ . Calculate its density.
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GENERAL PHYSICS 1 | MODULE 1
Density of air
The density of air can be found by measuring the mass
and the volume of the air. Using a balance the mass
reading is taken. The air is then removed from the flask
using a vacuum pump, and a second mass reading is
If volume and density are given and the mass is taken. Subtract the two masses and the difference
unknown, rearranging the formula gives: gives the mass of the air which was on the flask. The
volume of the air is found by filling the flask with water
and pouring it into the measuring cylinder. Having the
mass and the volume you can now calculate the
density of air.
Example 4
The density of copper is 9g/cm³, find the volume if the
mass is 63g.
Density of irregularly shaped solid Its volume is 268 x 32 x 25= 214 400m³ . Its mass is 76
The density of irregularly shaped solid is calculated in 800 tonnes = 768 000 x 1000kg.
the same way. The mass of a solid is found on a (Convert tonnes to kg 1 tonne = 1000kg)
balance. Its volume is measured by a method known
as water displacement method. The diagrams below Average density = mass/ volume
illustrate the water displacement method. = 76 800 x 1000 ÷ 214 400
= 358kgmˉ³
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GENERAL PHYSICS 1 | MODULE 1
volume for everyday laboratory work, and it is often Liquid volumes are expressed in litres (l). A litre is
more convenient to measure volumes using the cubic defined as 1000cm³ or 1 x 10ˉ³m. Thus, 1ml = 1cm³.
centimetre (cm³). 1cm³ is the volume of a cube with 1 litre (L) = 100 centilitres (cL)
sides 1cm long. = 1000 millilitres (mL)
Example
How many litres are there in 50 000 millimetres?
There is 1000ml in a 1L. To converting smaller to a
bigger unit, you divide. So 50 000 millilitres = 50 000 ÷
1000 litres = 50 litres
Measurement of Time
Time is the measure of duration of events and the
For a regularly shaped object such as a square or a intervals between them. The unit for time is the second
rectangular block, (s). All clocks and watches make use of some devices
Volume = length x width x height or that ‘beat’ at a steady rate. “Grandfather” clocks used
Volume = area x height the swings of a pendulum. Modern digital watches
count the vibrations made by a tiny quartz crystal. They
are easier to read and capable of measuring to one
hundredth of a second. In using a stopwatch, there is
Example
1. Convert 1 hour to seconds by multiplying
In the diagram on the left the reading of the water
before immersing the object is 250, after immersing the
object the reading became 300.
Example
2. How many milliseconds are there in an hour?
Volume of liquids
The volume of liquid may be obtained by pouring it into
a measuring cylinder. A known volume can be read
accurately. When making a reading, be upright and
your eye must be level with the bottom of the curved
liquid surface, that is, the meniscus.
Generalization:
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GENERAL PHYSICS 1 | MODULE 1
Post test:
Answer the following questions on the spaces
provided.
1. Converting 75.3 grams to kilograms gives
__________ kg.
References: