MAS S ,WE I GHT& D E NS ITY

MASS, WEIGHT & DENSITY

Mass and weight

Gravitational
fields Density
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 MAS S ,WE I GHT& D E NS ITY

MASS &
WEIGHT

State that mass is a measure of the

amount of substance in a body.
State that mass of a body resists
change from its state of rest or motion.

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MASS & INERTIA

• The mass of an object is a measure of the amount substance in the object.

• All bodies with mass posses a property known as inertia.
• The inertia of an object is the reluctant of the object to change either its
state of rest, or if it is moving, its motion in a straight line.

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INERTIA

• The greater the mass of a body the greater will be its

inertia.

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GRAVITATIONAL FIELDS

State that a gravitational field is a

region in which a mass experiences a
force due to gravitational attraction.

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GRAVITATIONAL FIELD

• Gravitational field is a region in which the mass of

an object experiences a force due to gravitational
attraction.
• Any object placed around the Earth experiences a
force pulling it towards the Earth.
• The force is stronger on the surface of the Earth and
gets weaker as we go farther away.

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MASS &
WEIGHT

Calculate weight from the

equation weight = mass x
gravitational field strength.
Explain that weights, and
therefore masses, may be
compared using a balance.
Describe how to measure mass and
weight by using appropriate balances.

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WEIGHT

• The weight of an object is the force of gravity acting

upon the object.

weight = mass × acceleration due to gravity

w = mg

• It is measure in newtons (N)

• The greater the mass of an object, the greater is its
weight.
• Acceleration due to gravity has the same
numerical value as the gravitational field
strength.
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MEASURING MASS &

WEIGHT

triple beam
balance

Spring balance

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electronic balance
 MAS S ,WE I GHT& D E NS ITY

PROBLEM SOLVING

1. A hammer has a mass of 1 kg. What is its weight (i) on Earth (ii) on the
Moon (iii) in outer space.
2. The weight of an object on Earth is 55 N. The gravitational
field strength on Earth is 10 N/kg. What is the mass of the object.
3. A man has a mass of 70 kg. What is his weight on Jupiter where the
field
strength is 26 N/kg.

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EXAMPL
E

4. A spacecraft travels from Earth to Mars, where the gravitational field

strength near the surface is 3.7 N/kg. The spacecraft is carrying a probe
which has a mass of 100 kg when measured on Earth. Assuming that g
= 10 N/kg on Earth.
a) What is the probe’s weight on Earth?
b) What is the probe’s mass in space?
c) What is the probe’s mass in Mars?
d) What is the probe’s weight on Mars?
e) When the probe is falling, near the surface of Mars, what is its
acceleration?

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5. A Saturn V Moon rocket has a mass at lift-off of 3.0 × 106 kg. The
thrust at lift-off is 3.3 × 107 N. Find:
a) the weight of the rocket on Earth
b) the resultant (unbalanced) force at lift-
off
c) the acceleration at lift-off
d) the apparent weight of the rocket in
orbit

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EXAMPL
E

6. What is the acceleration of

the rocket on the right? 3000 N
force from
rocket
engine
mass 200
kg

weight

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MASS &
WEIGHT

Mass Weight
1 is the amount of substance is the force of gravity acting on
in the body
the body
2 is constant at any location depends on acceleration due to
gravity at the location
3 is a scalar quantity is a vector quantity
4 is measured in kilograms is measured in newtons
5 is measured using a beam is measured using a
balance or electronic balance spring balance
(pan balance)
1
6 can never be zero 4
can be zero
 MAS S ,WE I GHT& D E NS ITY

1. The inertia of a body is its resistance to changes in

motion.
2. Which property is a measure of the body’s
inertia?
A. its density
B. its mass
C. the height of its sides
D. the size of its base

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2. Which statement about the mass of a falling object is

correct?
A. It decreases as the object falls.
B. It is equal to the weight of the
object.
C. It is measured in newtons.
D. It stays the same as the object falls.

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3. The mass of a full bottle of cooking oil is 1.30

kg. When exactly half
4. of the oil has been used, the mass of the bottle
plus the remaining oil is 0.90 kg.
What is the mass of the
empty bottle?
A. 0.40 kg
B. 0.50 kg
C. 0.65 kg
D. 0.80 kg

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4. What is the gravitational force that the Earth exerts on an

object?
A. the density of the
object
B. the mass of the object
C. the volume of the
object
D. the weight of the object

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5. What is the meaning of the weight of an

object?
A. the density of the material from which it is
made
B. the force exerted on it by gravity
C. the mass of the matter it contains
D. the pressure it exerts on the floor

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6. Which relationship defines gravitational field

strength?
A. mass x 10
B. mass x
weight
C. mass / weight
D. weight / mass

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7. What are the correct units for force and for

weight?

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8. A body of mass 10 kg falling freely in the gravitational field close to the

Moon’s surface has an acceleration of 1.6 m/s2.
9. What is the gravitational field strength on the
Moon?
A. 0 N/kg
B. 1.6 N/kg
C. 10 N/kg
D. 16 N/kg

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9. An object that has a mass of 15 kg on the Earth is taken to the

Moon.
10. The gravitational field strength on the Earth is 10 N/kg and on the Moon
is 1.6 N/kg.
11. What are the mass and the weight of the object on the Moon?

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10. A person of weight 600 N at the bottom of a mountain climbs to the top.
The gravitational field strength changes from 10.00 N/kg at the bottom
to 9.97 N/kg at the top. His mass is unchanged as he climbs.
11. What are his mass and his weight at the top of the
mountain?

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11. At a point on the surface of the Earth, the gravitational field strength
is 9.8 N/kg.
12. Which pair of values for mass and weight are correct for an object
placed at this point?

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12. The table shows the weight of a 10 kg mass on each of five

planets.

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1. On which planets would an astronaut have a

smaller weight than on Earth?
A. Mercury, Mars and Jupiter
B. Mercury, Venus and Mars
C. Mercury, Venus and
Jupiter
D. Venus, Mars and Jupiter

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13. Two blocks of metal X and Y hang from spring balances as shown in the
diagram.

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1. What does the diagram show about X and

Y?
A. They have the same mass and the same volume but different
weights.
B. They have the same mass and the same weight but different
volumes.
C. They have the same mass, the same volume and the same weight.
D. They have the same weight and the same volume but different
masses.

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14. A passenger is sitting in an aeroplane, which takes off and climbs

to 10000 m.
15. During this time, what happens to the mass and to the weight of
the passenger?

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15. The force of gravity acting on an astronaut in an orbiting spacecraft

is less than when she is on the Earth’s surface.
16. Compared with being on the Earth’s surface, how do her mass and
weight change when she goes into orbit?

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16. A stone is weighed using a newtonmeter (spring balance) and a pair of

scales (pan balance).

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1. This experiment is repeated on the

Moon.
2. Are the readings for each balance the same or different when taken on
Earth and on the Moon?

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17. In a laboratory on Earth, balances show that an object has a mass of 2 kg

and a weight of 20 N.
18. The same balances and object are then taken to the Moon, where the
gravitational field strength is less than on the Earth.
19. Are the mass and weight of the object the same, or less, than before?
mass weight
A. less less
B. less same
C. same less
D. same same C

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18. The reading on a spring balance with a holder and eight identical discs
is 3.0 N.
19. Six discs are removed and the reading becomes 1.2 N.
What is the weight of one
disc?
A. 0.2 N
B. 0.3 N
C. 0.5 N
D. 0.6 N

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19. Which statement about the masses and weights of objects on the Earth is
correct?
A. A balance can only be used to compare weights, not
masses.
B. Heavy objects always have more mass than light ones.
C. Large objects always have more mass than small ones.
D. Mass is a force but weight is not.

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20. Which statement is

correct?
A. The mass of a bottle of water at the North Pole is different from its mass at
the Equator.
B. The mass of a bottle of water is measured in newtons.
C. The weight of a bottle of water and its mass are the same thing.
D. The weight of a bottle of water is one of the forces acting on it.

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DENSITY

Describe how to use a measuring

cylinder to measure the volume of a
liquid or solid.

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VOLUME OF LIQUID

• We use a graduated cylinder to find the volume of liquid.

• Just pour the liquid in and read the measurement on the side of
the cylinder (in ml or cm3).

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DISPLACEMENT METHOD

• Put some water in a graduated cylinder and

write
down the volume of the water, V1.
V2 • Drop in your object and get the new volume, V2.
V1 • Subtract the water's original volume from
the water + object volume, V2 - V1

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DENSITY

Describe how to determine the density

of a liquid, of a regularly shaped solid
and of an irregularly shaped solid
which sinks in water (volume by
displacement).

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EXPERIMENTAL PROCEDURE

1. Aim: To determine the density of liquid

Apparatus
Procedure
Calculatio
n
Precaution
ary
Measure

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APPARATUS

1. Electronic balance
2. Measuring cylinder

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PROCEDURE

1. Measure the mass of the empty measuring cylinder, m1. Take the average
reading.
2. Fill the measuring cylinder with water.
3. Measure the mass of the water inside the measuring cylinder, m2.
Take
average reading.
4. Read the volume of water on the measuring cylinder.

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CALCULATION

1. Mass of the water = m2 – m1

2. Density of water = mass of water / volume of water

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PRECAUTIONARY MEASURE

1. Avoid parallax error when reading the measuring

cylinder
2. To reduce wind interference
3. Always re-zero the electronic balance
4. Take average reading of the mass

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EXPERIMENTAL PROCEDURE

2. Aim: To determine the density of regular solid

Apparatus
Procedure
Calculatio
n
Precaution
ary
Measure

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APPARATU
S

1. Solid
cubeElectronic
2.
balance
3. 30 cm rule

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PROCEDURE

1. Measure the mass of the cube using electronic. Take average reading.
2. Using the rule measure all the length of the side (length,
breadth & height).

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CALCULATION

1. Volume of cube = length x breadth x height

2. Density = mass / volume

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PRECAUTIONARY MEASURE

1. Avoid parallax error

2. Check zero error
3. Reduce wind interference
4. Take average reading of mass and length

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EXPERIMENTAL PROCEDURE

3. Aim: To determine the density of irregular solid

Apparatus
Procedure
Calculatio
n
Precaution
ary
Measure

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APPARATU
S

1.
Plasticine
2. Electronic balance
3. Measuring
cylinder

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PROCEDURE

1. Measuring the mass of the plasticine using the electronic balance.

Take average reading
2. Fill the measuring cylinder with water. Take the initial reading
of the meniscus, V1
3. Submerged the plasticine into the cylinder. Take the new reading of
the
meniscus, V2

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CALCULATION

1. Volume of plasticine = V2 – V1
2. Density of plasticine = mass / volume

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PRECAUTIONARY MEASURE

1. All plasticine must submerge

2. Not to splash out the water when inserting the plasticine inside the
cylinder
3. Take average reading of mass

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DENSITY

Define density and recall and use the

formula density = mass/volume

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DENSITY

• The density of a substance is defined as its mass per unit

volume.

Mass
Density
 Volum
e
• The SI unit for density is kilogram per cubic metre (kg/m3) but
other
units like gram per cubic centimeter (g/cm3) is also commonly used.
1 g/cm3 = 1000 kg/m3
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PROBLEM SOLVING

1. A cylinder has a base of area 100 cm2 and contains water to a height of 10
cm. A piece of rock mass 600 g is lowered into the water and the water
level rises to a height of 12 cm.
a. What is the volume of the piece of rock?

Volume of Rock = Base Area x Height

displaced
Volume of Rock = 100 cm2 x 2 cm2
Volume of Rock = 200 cm3

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PROBLEM SOLVING

1. A cylinder has a base of area 100 cm2 and contains water to a height of 10
cm. A piece of rock mass 600 g is lowered into the water and the water
level rises to a height of 12 cm.
b. Calculate the density of the rock.
mass
Density =
volume

Density = 600 g
200 cm3

Density = 3 g/cm3

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PROBLEM SOLVING

2. The density of a solid is 4 g/cm3. What is the volume of

200 g of the solid.
mass
Density =
volume
200 g
4 g/cm3 =
volume
200
volume =
4
volume = 50 cm3

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PROBLEM SOLVING

3. An empty measuring cylinder has a mass of 200 g. A liquid is poured into

the measuring cylinder until the liquid is at the 80 cm3 mark. The total
mass is now 272 g. What is the density of the liquid in g/cm3?
mass
Density =
volume
72 g
Density =
80 cm3
Densi
ty = 0.9 g/cm3

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PROBLEM SOLVING

4. A sample of ethanol has a volume of 240 cm3. Its mass is found to

be
190.0 g. What is the density of ethanol.
mass
Density =
volume
190 g
ty = Densi
240 cm3

Densit
y = 0.792 g/cm3

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PROBLEM SOLVING

5. Calculate the density of mercury if 500 cm3 has a mass of 6.60 kg. Give
your answer in g/cm3.
mass
Density =
volume
6600 g
ty = Densi
500 cm3

Densi
ty = 13.2 g/cm3

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PROBLEM SOLVING

6. A steel block has a mass of 40 g. It is in the form of a cube. Each edge

of the cube is 1.74 cm long. Calculate the density of the steel.
mass
Density =
volume
40
Density =

1.74 × 1.74 × 1.74

Density
= 7.59 g/cm3

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PROBLEM SOLVING

7. What is the volume of a storage tank which will hold 3200 kg of petrol?
Density of petrol = 800 kg/m3.
mass
Density =
volume
3200 kg
800 kg/m =3
volume
3200
volume =
800
volume = 4 m3

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PROBLEM SOLVING

8. A small rectangular block of steel measures 2 cm by 4 cm by 5 cm and

has a mass of 312 g. Calculate its density
mass
Density =
volume
3
12 g
ty = Densi
2 ×=
312
4×5
Density
40
Density = 7.8 g/cm3

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PROBLEM SOLVING

9. The mass of a small metal statue is found to be 90 g. A measuring

cylinder is filled with water to the 82 cm3. The statue is lowered into the
measuring cylinder and the water rises to the 91 cm3. What is the
density of the metal.
mass
Density =
volume
90 g
Density =
9 cm3
Density = 10 g/cm3

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PROBLEM SOLVING

10. What mass of lead has the same volume of 1600 kg of petrol? Density
of petrol = 800 kg/m3 & density of lead = 11400 kg/m3.
mass of petrol mass of lead
Density of petrol = Density of lead =
volume of petrol volume of lead
1600 kg mass of petrol
800 kg/m3= 11400 kg/m3 =
volume of petrol 2 m3
1600 mass of lead = 11400 × 2
volume of petrol = = 2 m3
800
mass of lead = 22800 kg
volume of petrol = volume of lead

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PROBLEM SOLVING

11. An engineer needs to know the mass of steel girder which is 20 cm

long,
0.1 m wide and 0.1 m high. (Density of steel = 8000 kg/m3)
mass
Density =
volume
mass
8000 =
0.2 × 0.1 × 0.1
mass =
8000 × 0.2 × 0.1 × 0.1
mass =
16 kg

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PROBLEM SOLVING

12. A contractor wants to load some bricks into his van. There
are 1000 bricks, and when stacked neatly they measure 2 m by 1 m by 1
m.
a) What is the volume of the stack?
volume of stack = 2 × 1 × 1
volume of stack = 2 m3

b) If the density of brick is 2500 kg/m3, what is the mass of the

stack?
mass of stack
density of stack = mass of stack
2500 = volume of stack
2
mass of stack = 2500 × 2 = 5000 kg
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PROBLEM SOLVING

12. A contractor wants to load some bricks into his van. There
are 1000 bricks, and when stacked neatly they measure 2 m by 1 m by 1
m.
c) If his van’s maximum load is 1000 kg, how many bricks can he
load?

1000 bricks = 5000 kg

how many bricks = 1000 kg
1000 × 1000
no. of bricks =
5000
no. of bricks = 200 bricks

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1. The diagrams show an experiment to determine the volume of a

stone.
What is the volume of the
stone?
A. 3 cm3
B. 4 cm3
C. 7 cm3
D. 11 cm3

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2. Which of the following is a unit of

density? 3
A. cm /g
B. g/cm2
C. g/cm3
D. kg/m2

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3. Which items ofapparatus are required to determine

the density of a liquid?
A. balance and measuring cylinder
B. balance and thermometer
C. metre rule and measuring
cylinder
D. metre rule and thermometer

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4. A student is trying to find the density of water and of a large,

regularly shaped concrete block.
5. Which apparatus is needed to find the density of both the water and the
concrete block?
A. balance, clock, measuring cylinder
B. balance, clock, ruler
C. balance, measuring cylinder, ruler
D. clock, measuring cylinder, ruler

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5. A student needs to find the density of a cubic block of

wood.
6. Which two pieces of apparatus should she
use?
A. balance and metre rule
B. balance and thermometer
C. measuring cylinder and metre rule
D. measuring cylinder and thermometer

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6. A student does an experiment to estimate the density of an

irregularly- shaped stone.
7. Which items of equipment are needed?
A. a balance and a measuring cylinder containing
water
B. a balance and a ruler
C. a ruler and a measuring cylinder containing water
D. only a measuring cylinder containing water

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7. A scientist needs to determine the volume of a small, irregularly shaped

rock sample. Only a rule and a measuring cylinder, partially filled with
water, are available.

To determine the volume,

which apparatus should the
scientist use?
A. both the measuring
cylinder and the rule
B. neither the measuring
cylinder nor the rule
C. the measuring cylinde
only r
D. the rule only
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8. A student is trying to find the density of a stone, but he has mixed up the
instruction cards.

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What order should the cards be

in? 5 → 3 → 6 → 2 → 1 → 4→ 7
A.
B. 1 → 5 → 3 → 6 → 2 → 7 →
4
C. 5 → 6 → 3 → 2 → 1 → 7 →
4
D. 1 → 4 → 5 → 3 → 6 → 2 →
7

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9. The mass of a measuring cylinder is measured before and after pouring

a liquid into it.

What is the density of the

liquid?
A. 0.79 g/cm3
B. 1.3 g/cm3
C. 1.4 g/cm3
D. 2.2 g/cm3

8
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10. A metal drum has a mass of 200 kg when empty and 1000 kg when
filled with 1.0 m3 of methylated spirit.
11. What is the density of methylated
spirit?
A. 0.0050 kg/m3
B. 0.11 kg/m3
C. 800 kg/m3
D. 1000 kg/m3

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11. The diagram shows a rectangular block of density 2

g/cm3.
What is the mass of the
block?
A. 2 g
B. 6 g
C. 14 g
D. 24 g

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12. The diagrams show a rectangular box with inside measurements of 5

cm
× 6 cm × 4 cm.

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 MAS S ,WE I GHT& D E NS ITY

The box has a mass of 40 g when empty. When filled with a liquid, it has a
total mass of 220 g.
What is the density of the
liquid?

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13. A room measures 4.0 m × 3.0 m × 2.0 m. The density of the air in the
room is 1.3 kg/m3.
1. What is the mass of air in the
room?
A. 0.054 kg
B. 18 kg
C. 24 kg
D. 31 kg

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14. A box has an internal volume of 1000 cm3. When a solid object is
placed in the closed box, the volume of air in the box is 520 cm3.
15. The density of the object is 8.00 g/cm3.

What is the mass of the

object? A.

60.0 g
B.

3840 g
C.
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15. A lump of metal has a mass of 210 g. It is lowered into a

measuring cylinder containing water.
16. The level of the water rises from 35 cm3 to 140 cm3.

What is the density of the

metal? A.

0.67 g/cm3
B. 1.5 g/cm3
C. 2.0 g/cm3
D. 6.0 g/cm3

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16. An object of mass 100 g is immersed in water as shown in the

diagram.
What is the density of the material from
which the object is made?
A. 0.4 g/cm3
B. 0.9 g/cm3
C. 1.1 g/cm3
D. 2.5 g/cm3

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17. A measuring cylinder contains 118 cm3 of water. When a small object is
fully immersed in the water, the reading goes up to 132 cm3. The object
has a mass of 42 g.
18. What is the density of the
object?

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18. Three objects are cut from the same sheet of steel. They are
different shapes but they all have the same mass.

Which object has the

greatest density?
A. the disc
B. the L-shape
C. the square
D. they all have the same
density

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19. Some students measure the masses and the volumes of different
sized samples of a type of wood.
20. Which graph shows their
results?

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20. Two identical measuring cylinders containing different liquids are

placed on a simple balance.
21. They balance as
shown.

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How does the density of X compare with the density of

Y?

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