CHAPTER 4
Mass, Weight
and Density
© 2013 Marshall Cavendish International (Singapore) Private Limited
Chapter 4 Mass, Weight and Density
4.1
Mass and Weight
4.2
Inertia
4.3
Density
4.1 Mass and Weight
Learning Outcomes
At the end of this section, you should be able to:
• define mass, gravitational field and
gravitational field strength;
• differentiate between mass and weight;
• recall and apply the formula weight = mass ×
gravitational field strength to solve problems.
4.1 Mass and Weight
Recall
• Weight is a gravitational force
exerted by Earth on an object.
• Weight is a vector.
What is mass? How is it
different from weight?
W
What is gravitational field and
gravitational field strength?
4.1 Mass and Weight
What is Mass?
Mass is the amount of matter in a body.
The SI unit of mass is the kilogram (kg).
What is Weight?
The weight of an object is the gravitational force,
or gravity, acting on it.
The SI unit of weight is the newton (N).
4.1 Mass and Weight
What is a Gravitational Field?
A gravitational field is a region in which a mass
experiences a force due to gravitational attraction.
• When a mass is placed in a
gravitational field, it experiences
a gravitational force.
• This gravitational force is also
known as weight.
Earth’s gravitational force acts
towards the centre of Earth.
4.1 Mass and Weight
Earth’s Gravitational Field
• The strength of this field is strongest at the surface of Earth
and gets weaker farther away.
• In other words, the gravitational force experienced by the
object due to the Earth’s gravitational field gets stronger as
the object moves closer to Earth.
say, 50 N
>50 N
4.1 Mass and Weight
What is Gravitational Field Strength?
Gravitational field strength is defined as the
gravitational force acting per unit mass.
• It tells us how strong the gravitational field is.
• On Earth, the gravitational field strength is
approximately 10 N kg–1.
Note: N kg–1 is the dimensionally the same as m s–2.
By the definition of the newton (N), it can be
written as: N = kg m s–2
Hence, N kg–1 = (kg m s–2) × kg–1= m s–2
4.1 Mass and Weight
Mass versus Weight
Mass
The amount of matter
in a body
Weight
A gravitational force
A scalar quantity
A vector quantity
SI unit: kg
SI unit: N
Independent of
gravitational field
strength
Dependent on
gravitational field
strength
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.
• From Chapter 3,
force = mass × acceleration
Weight W is the
gravitational force
acting on an object.
• Hence,
W = mg
• The acceleration of free fall
is a constant.
• The acceleration of free fall
is equal to the gravitational
field strength g.
4.1 Mass and Weight
What do Common Weighing
Instruments Measure?
• Common weighing instruments such as the electronic
balance and bathroom scale actually measure the weight
of an object and not its mass.
• However, they are calibrated to give mass readings.
• Since they are calibrated
according to Earth’s
gravitational field strength,
they cannot be used in
places with different
gravitational field strengths.
4.1 Mass and Weight
How is Mass Measured?
• The mass of an object does not depend on the
gravitational field strength.
• It can be measured using a beam
balance.
• The beam balance compares the
gravitational force acting on an
object with standard masses.
• Since both the object and the
standard masses experience the
same gravitational field strength,
the mass readings obtained
whether on Earth or the Moon, will
be the same.
URL
4.1 Mass and Weight
Question
The weight of a 1 kg object is measured at A, B, C, D and E.
A
B
D
C
E
1. At which point will the weight of the object be the smallest?
2. At which points are the weights of the object approximately
the same?
Chapter 4 Mass, Weight and Density
4.1
Mass and Weight
4.2
Inertia
4.3
Density
4.2 Inertia
Learning Outcome
At the end of this section, you should be able to:
• define inertia.
4.2 Inertia
Recall
Newton’s First Law of Motion states that an object
will continue in its state of rest or uniform motion
in a straight line unless a resultant force acts on it.
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URL2
What is inertia?
4.2 Inertia
What is Inertia?
• The inertia of an object refers to the reluctance
of the object to change its state of motion, due
to its mass.
• In other words, a stationary object tends to stay
at rest. A moving object tends to continue in its
state of motion.
• Newton’s First Law of Motion is also known as
the law of inertia.
4.2 Inertia
What is Inertia?
• Mass is a measure of
inertia.
• The greater the mass
of an object, the
greater its inertia.
The man is trying to
escape a charging
elephant. Should he run
in a straight line or in a
zigzag manner?
4.2 Inertia
Inertia in Everyday Life
• Observe what happens to the passengers in the
MRT train when the train stops.
• The passengers tend to continue moving in the
direction that the train was moving in.
• This is due to inertia!
Question
Can you predict what will happen to the
passengers in a stationary MRT train when it
starts moving? Check if your prediction is right on
your next train ride!
Chapter 4 Mass, Weight and Density
4.1
Mass and Weight
4.2
Inertia
4.3
Density
4.3 Density
Learning Outcome
At the end of this section, you should be able to:
• recall and apply the formula density =
to solve problems.
mass
volume
4.3 Density
What is Density?
The density of a substance is defined as its mass
per unit volume.
 =
m
V
where  = density;
m = mass of the object;
V = volume of the object.
The SI unit of density is the kilogram per cubic metre
(kg m–3).
4.3 Density
Different Densities
of Substances
Different substances have
different densities.
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URL2
4.3 Density
What Floats?
Based on our understanding of density, we can
determine what substances float on water.
Examples
•Water (ρwater = 1000 kg m−3) has a higher density than
ice (ρice = 917 kg m–3).
 Hence, we observe that ice floats on water.
•Turpentine (ρturpentine = 868 kg m-3) has a lower density
than ice (ρice = 917 kg m–3).
 Hence, ice will sink in turpentine.
4.3 Density
Why does a Steel ship
Float on Water?
• Even though steel has a higher density than
water, a steel ship is able to float. Why?
• The ship is made of more than one material. To
check if a steel ship will float or sink in water, we
need to calculate its average density.
4.3 Density
Worked Example
A rectangular block of wood has the dimensions 0.1 m by
0.02 m by 0.01 m. Given that this wood has a density of
500 kg m–3, determine its mass.
Solution
Volume V of wood = 0.1 m × 0.02 m × 0.01
m
= 0.00002 m3
Mass m of wood = density  × volume V
= 500 kg m–3 × 0.00002 m3
= 0.01 kg
4.3 Density
Worked Example
The following data shows the measurements of the volume of
water in a measuring cylinder. Use the data to determine the
density of the rock in g cm–3.
Initial volume V1 of water
= 10.0 cm3
Final volume V2 of water (after the rock
is lowered into the measuring cylinder)
= 12.4 cm3
Mass m of rock
= 50.2 g
Solution
Volume of the rock = 12.4 cm3 – 10.0 cm3
= 2.4 cm3
Therefore, density  =
50.2 g = 20.9 g cm–3
2.4 cm3
4.3 Density
Worked Example
A metal cylinder has a radius of 1.0 cm. It weighs 50 N
when measured near the surface of the Earth. Given that its
density  is approximately 7800 kg m–3, and g = 10 m s–2,
determine the length of this cylinder.
Solution
We can determine the volume of the cylinder from its density and mass.
To find mass, we use
m=W÷g
= 50 N ÷ 10 N kg–1
= 5 kg
Volume V of cylinder
=m÷
= 5 kg ÷ 7800 kg m–3
= 6.4 × 10–4 m3
Volume of cylinder is also given by
= area × length
= ( × r2) ×
l
Hence, length of cylinder
= (6.4 × 10–4 m3) ÷ ( × (0.01
2)
m)
= 2.04
m
Remember to use
the right units
Chapter 4 Mass, Weight and Density
Amount of
substance
in a body
Mass m
(SI unit: kg)
Inertia
is related to
The gravitational
force acting on
an object
defined
as
Weight W
(SI unit: kg)
Density 
(SI unit: kg m–3)
by the
equation
W=m×
g
Gravitational field strength g
is the gravitational force
acting per unit mass.
defined
as
Mass per
unit volume
by the
equation
 =
m
V
Gravitational field is a region where
a mass experiences a force due to
gravitational attraction.
Chapter 4 Mass, Weight and Density
The URLs are valid as at 15 October 2012.
Acknowledgements
(slides 1−36) ship © Nishapl | Dreamstime.com
(slides 6, 7, Earth © Tonygers | Dreamstime.com
13, 15)
(slide 13) Moon © Tonygers | Dreamstime.com
(slide 14) beam balance © Marshall Cavendish International
(Singapore) Private Limited
(slide 26) Archimedes © Wikimedia Commons | Public
Domain
(slide 28) ice cube © Reshavskyi | Dreamstime.com
(slide 28) glass © Royalspirite| Dreamstime.com
(slide 29) Titanic © F.G.O Stuart © Wikimedia Commons |
Public Domain