Mass, Weight and Density
Lesson Objectives
At the end of this lesson, you should be able to:
1. State that mass is a measure of the amount of substance in
a body.
2. State that mass of a body resists a change in the state of
rest or motion of the body.
3. State that a gravitational field is a region in which a mass
experiences a force due to gravitational attraction.
4. Define gravitational field strength as gravitational force per
unit mass.
5. Recall the relationship weight = mass x gravitational field
strength.
6. Recall the relationship density = mass / volume.
Mass




Mass is a measure of the amount of
substance in a body.
SI Unit: Kilogram (kg)
Mass cannot be changed by the location,
shape and speed of the body.
Large masses are measured in tonnes while
small masses are measured in grams.
Examples of Masses of Objects
Object
Mass in
kilogram (kg)
Electron
10-30
A fine grain of sand
10-6
A pea
10-3
An apple
10-1
A medium-sized car
103
Earth
1024
Sun
1030
Measurement Instruments
Mass is measured using a balance such
as the
beam balance
electronic balance
Beam Balance
Electronic Balance
Newton’s First Law
An object at rest tends to stay at rest
and an object in motion tends to
continue in motion at constant speed in
a straight line (uniform velocity)
unless
an external resultant force acts on it.
Inertia
Inertia
The inertia of an object is its reluctance to
move when it is at rest or to slow down or
stop when it is moving.
That is, it is its reluctance to change its state
of rest or motion
The car and the wall
Inertia is ...
measured by mass
The more massive an object, the more inertia
it has, hence, the larger the force is required
to change its motion
Conversely ...
Gravitational Field Strength



The gravitational field is a region in which a
mass experiences a force due to gravitational
attraction.
Gravitational field strength is gravitational
force acting per unit mass on an object.
On earth, the gravitational field strength is
10 N kg-1 or 10 ms-2.
Weight is . . .
gravitational force acting on an object
W = mg
where m is the mass of the object
g is the gravitational field strength.
Weight is measured in newtons (N)
Measurement Instruments
Weight is measured using a balance such as the
spring balance
compression balance
Spring Balance
Compression Balance
Differences between Weight and Mass
Weight
 pull of gravity on the body
 has both magnitude and
direction
 measured in newtons
 changes from place to place
Mass
 amount of matter in the
body
 has only magnitude but no
direction
 measured in kilograms
 is constant regardless of
place or location
Weight
Planets
Sun
Mercury
Venus
Earth
Earth
Moon
Mars
Jupiter
Saturn
Uranus
Neptune
Pluto
Acceleration Due to Gravity Comparison
Acceleration Due
Mass [kg] Radius [m]
g / g-Earth
to Gravity, "g" [m/s2 ]
1.99 x 1030
3.18 x 1023
4.88 x 1024
5.98 x 1024
7.36 x 1022
6.42 x 1023
1.90 x 1027
5.68 x 1026
8.68 x 1025
1.03 x 1026
1.40 x 1022
6.96 x 108
2.43 x 106
6.06 x 106
6.38 x 106
1.74 x 106
3.37 x 106
6.99 x 107
5.85 x 107
2.33 x 107
2.21 x 107
1.50 x 106
274.13
3.59
8.87
9.81
9.81
1.62
3.77
25.95
11.08
10.67
14.07
0.42
27.95
0.37
0.90
1.00
0.17
0.38
2.65
1.13
1.09
1.43
0.04
Story of a naked man
In the first century BC the Roman architect Vitruvius
related a story of how Archimedes uncovered a fraud
in the manufacture of a golden crown commissioned
by Hiero II, the king of Syracuse. The crown (corona
in Vitruvius’s Latin) would have been in the form of a
wreath. Hiero would have placed such a wreath on the
statue of a god or goddess. Suspecting that the
goldsmith might have replaced some of the gold given
to him by an equal weight of silver, Hiero asked
Archimedes to determine whether the wreath was
pure gold. And because the wreath was a holy object
dedicated to the gods, he could not disturb the wreath
in any way.
Story of a naked man
The solution which occurred when he stepped into his
bath and caused it to overflow was to put a weight of
gold equal to the crown, and known to be pure, into a
bowl which was filled with water to the brim. Then the
gold would be removed and the king’s crown put in, in its
place. An alloy of lighter silver would increase the bulk of
the crown and cause the bowl to overflow.
Density
What is density?
Density is defined as mass per unit volume
Density = mass/volume
M
Units
SI units: kg/m3
Other units: g/cm3
The floating orange
D
V
My Dear Valentine
Density
A cylindrical steel rod has a diameter of 0.2 m and
length of 3m. Its mass is 3.5kg. Calculate its density.
d
2
Volume of rod =  ( ) 2 l
0.2 2
=(
) 3
2
= 0.094 m3
Mass
3.5
3


37
.
2
kg
m
Density =
Volume
0.094
Density
Object
Mass/g Vol/cm3
Aluminium
sheet
Gold bracelet
50
18.52
150
Water
Density
g/cm3
Sink or
Float?
2.70
Sink
7.89
19.0
Sink
500
500
1
---
Ice
10
10.87
0.92
Float
Block of
pinewood
800
1600
0.5
Float
Concept Map
kg/m3
Densit
y
Mass per unit
volume
defined as
related to
mass by
D = M/V
related to
density by
Mass, m
defined
as
kg
related to
weight by
is a
measure of
W=mxg
related
to mass
by
N
Weight
where
defined
as
Amount of
substance in a
body
inertia
g is the gravitational force
per unit mass acting on an
object
Gravitational force
acting on an object