Discover PHYSICS
for GCE ‘O’ Level Science
Unit 4: Mass, Weight and Density
Unit 4.1 Mass and Weight
Learning Outcomes
In this section, you’ll be able to:
• define mass, gravitational field and
gravitational field strength g
• differentiate between mass and weight
• recall and apply weight W = m x g to solve
problems
23 March 2016
Unit 4.1: Mass and Weight
What is mass?
• Mass is a measure of the amount of matter or
substance in a body.
• The SI unit of mass is the kilogram (kg)
Fig 4.1 The number and composition of atoms and molecules make
up the mass of a body.
23 March 2016
Unit 4.1: Mass and Weight
What is weight?
• Weight is a force and has direction pointing
towards the centre of the earth (downwards).
• Its SI unit is the Newton (N).
• This force is called gravitational force or
gravity.
23 March 2016
Unit 4.1: Mass and Weight
What is gravitational field?
• The Earth’s gravity is experienced by any
object near it.
• The region surrounding the Earth where
gravity is experienced is called the
gravitational field.
• The force experienced is strongest on the
surface of the earth and gets weaker further
away.
Fig 4.3 Earth is surrounded
by a gravitational field. Field
lines are drawn to represent
the gravitation field.
23 March 2016
Unit 4.1: Mass and Weight
What is gravitational field strength?
• Gravitational field strength g is defined as the
gravitational force acting per unit mass on an object.
• On Earth, the gravitational field strength is about
10 N kg-1
• A mass of 1 kg will weigh 10 N on Earth.
• On Moon, the gravitational field strength is about
1.6 N kg-1
• A mass of 1 kg will weigh 1.6 N on Moon.
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Unit 4.1: Mass and Weight
• The Moon’s gravitational pull causes high and
low tides of the Earth’s ocean.
23 March 2016
Unit 4.1: Mass and Weight
How are mass and weight related?
• The weight or amount of gravitational force
acting on an object is dependent on its mass.
• The weight W can be found by
W = mg
where
m = mass of object (in kg)
g = gravitational field strength in (N kg-1)
23 March 2016
Unit 4.1: Mass and Weight
How are mass and weight related?
• Common weighing instruments such as electronic
balance, spring balance and bathroom scales
actually measure the weight and not the mass
of an object.
• Using the scale on Moon will give different
readings.
Fig 4.7 The fastest way to
lose weight.
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Unit 4.1: Mass and Weight
How is mass measured?
• Mass of an object does not depend on the
gravitational field strength.
• It can be measured using the beam balance.
• The beam balance compares the gravitational
force acting on an object with standard
masses. (Unit 5)
23 March 2016
Unit 4.1: Mass and Weight
Differences between mass and weight
Table 4.1 Differences between mass and weight.
23 March 2016
Unit 4.1 Mass and Weight
23 March 2016
Unit 4.1 Mass and Weight
23 March 2016
Unit 4.1 Mass and Weight
Key Ideas
1. Mass measures the amount of matter or
substance in a body. The SI unit is kilograms (kg)
2. Weight is the gravitational force acting on a body.
The SI unit is newtons (N).
3. The weight of a body is related to its mass by the
equation:
W = mg
4. Gravitational field strength, in N kg-1 is the same
as the acceleration of free fall in m s-2.
5. The weight of an object varies according to the
gravitational field strength. The mass of an object
is a physical property of the object that does not
change.
23 March 2016
Unit 4.1: Mass and Weight
Test Yourself 4.1
1. List four differences between mass and
weight.
23 March 2016
Unit 4.1 Mass and Weight
Test Yourself 4.1
2. Why is the mass of a body not affected by
changes in the physical environment such as
location?
Answer:
Mass is the amount of matter in the object.
It does not change with physical
environment.
23 March 2016
Unit 4.1: Mass and Weight
Test Yourself 4.1
3. We have learnt that Earth’s gravitational field
strength g (10 N kg-1) is the same as its
acceleration due to free fall, ag (10 m s-2).
Even though their unit are different, N kg-1 vs
m s-2, they are said to be dimensionally the
same. Prove that N kg-1 is the same as m s-2.
Answer:
By the definition of newton N, it can be written
as:
N = kg m s-2
Hence N kg-1 = (kg m s-2) x kg-1
= m s-2 (shown)
23 March 2016
Unit 4.1: Mass and Weight
Test Yourself 4.1
4. The gravitational field strength of Jupiter is
22.9 N kg-1. An astronaut weighs 1200 N on
Earth. What will his weight on Jupiter be?
Answer:
First, we deduce the mass of the astronaut.
Wearth = m gearth
1200 = m x 10
 m = 1200 / 10 = 120 kg
Hence his weight on Jupiter (if he managed to
reach Jupiter) is
WJupiter = m gjupiter
= 120 x 22.9
= 2750 N
23 March 2016
Unit 4.1: Mass and Weight
Test Yourself 4.1
5. What is the difference between gravitational
field strength and gravitational pull?
Answer:
Gravitation field strength g is the
gravitational force acting per unit mass on an
object.
g has SI units N kg-1.
Gravitational pull is the gravitational force
acting on the object and this is equivalent to
its weight. The weight is given by
W = mg
Weight has SI units of N.
23 March 2016
Unit 4.2: Inertia
Lesson Outcomes
In this section, you’ll be able to:
• understand and define inertia.
23 March 2016
Unit 4.2: Inertia
What is inertia?
• Inertia of an object refers to the reluctance of
the object to change its state of motion.
• The inertia of an object depends on its mass.
An object with more mass has greater inertia.
Fig. 4.13 Driver not wearing the seat belt.
Fig. 4.14 Driver wearing the seat belt.
23 March 2016
Unit 4.3 Density
Lesson Outcomes
In this section, you’ll be able to:
• recall and apply density = mass/volume to
solve problems
23 March 2016
Unit 4.3: Density
• Density of a substance is defined as its mass
per unit volume
m
r =
V
where
r = density (in kg m-3)
m = mass of object (in kg)
V = volume of object (in m3)
The SI unit of density is kilogram per cubic metre
(kg m-3)
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Unit 4.3: Density
Table. 4.2 Densities of common substances.
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Unit 4.3 Density
Floating
• Substances that float on water have lower
densities than water.
eg. Ice (rice = 917 kg m-3) has a lower density
than water (rwater = 1000 kg m-3). Hence we
can observe that ice floats on water.
Do you know what would happen if we place
the ice in turpentine?
Fig 4.16
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Unit 4.3: Density
23 March 2016
Unit 4.3: Density
23 March 2016
Unit 4.3: Density
23 March 2016
Unit 4.3: Density
23 March 2016
Unit 4.3 Density
Key Ideas
1. The density of a substance is defined as its mass
per unit volume.
2. The SI units for density is kg m-3.
3. The density of a substance is a fixed physical
property.
4. Substances that are less dense than water will
float on water.
5. To measure density of a substance, we measure
its:
a) Mass, eg. With a beam balance, and
b) Volume, eg. Using mathematical formulae of
volume (for regular objects) or measuring the
volume of water it displaces (for irregular
objects).
23 March 2016
Unit 4.2,4.3: Inertia & Density
Test Yourself 4.2-4.3
1. Two groups of people get into two identical cars. One group
consists of five Sumo wrestlers while the other group consists
of five marathon runners. Assuming both drivers step on the
accelerator with equal force, state and explain
a) which car takes off faster from rest, and
b) which car will need a longer braking distance, once in
motion.
Answer:
(a) The car with marathon runners has smaller mass. It is
said to have smaller inertia. Hence it will take off faster.
We can also see that by Newton’s 2nd Law,
a = F/m
Hence the car with smaller mass will have a larger
acceleration.
(b) The car with the Sumo wrestlers will have a larger
breaking distance since they have a larger inertia and
hence greater reluctance to come to a stop.
23 March 2016
Unit 4.3: Density
Test Yourself 4.3
3. The density of water is 1000 kg m-3. What is the
mass of 1 cm3 of water in grams?
Answer:
1000 kg
Density of water rwater =
1 m3
1000 kg 1000 g
1 m3
=
x
x
3
1m
1 kg
(100)3 cm3
= 1 g cm 3
Hence 1 cm3 of water has a mass of 1 g.
23 March 2016
Unit 4: Mass, Weight and Density
23 March 2016