Unit 4: Mass, Weight and Density

Discover PHYSICS for GCE ‘O’ Level Science

April 19, 2023

Unit 4.1 Mass and WeightLearning OutcomesIn 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

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Unit 4.1: Mass and WeightWhat 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.

April 19, 2023

Unit 4.1: Mass and WeightWhat 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.

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Unit 4.1: Mass and WeightWhat 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.

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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.

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Unit 4.1: Mass and WeightHow 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 byW = mg

where m = mass of object (in kg)g = gravitational field strength in (N kg-

1)

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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)

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Unit 4.1: Mass and Weight

Table 4.1 Differences between mass and weight.

Differences between mass and weight

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Unit 4.1 Mass and Weight

April 19, 2023

Unit 4.1 Mass and Weight

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Unit 4.1 Mass and WeightKey Ideas1. 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.

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Unit 4.1: Mass and WeightTest Yourself 4.11. List four differences between mass and

weight.

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Unit 4.1 Mass and WeightTest Yourself 4.12. 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.

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Unit 4.1: Mass and WeightTest 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)

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Unit 4.1: Mass and WeightTest Yourself 4.14. 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

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Unit 4.1: Mass and WeightTest Yourself 4.15. 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 = mgWeight has SI units of N.

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Unit 4.2: Inertia

Lesson OutcomesIn this section, you’ll be able to:• understand and define inertia.

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Unit 4.2: InertiaWhat 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.

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Unit 4.3 Density

Lesson OutcomesIn this section, you’ll be able to:• recall and apply density = mass/volume to

solve problems

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Unit 4.3: Density• Density of a substance is defined as its mass

per unit volume

V

m

The SI unit of density is kilogram per cubic metre (kg m-3)

where = density (in kg m-3)m = mass of object (in kg)V = volume of object (in m3)

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Unit 4.3: Density

Table. 4.2 Densities of common substances.

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Unit 4.3 DensityFloating• Substances that float on water have lower

densities than water.eg. Ice (ice = 917 kg m-3) has a lower density than water (water = 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

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Unit 4.3: Density

April 19, 2023

Unit 4.3: Density

April 19, 2023

Unit 4.3: Density

April 19, 2023

Unit 4.3 DensityKey Ideas1. 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, andb) Volume, eg. Using mathematical formulae of

volume (for regular objects) or measuring the volume of water it displaces (for irregular objects).

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Unit 4.2,4.3: Inertia & DensityTest Yourself 4.2-4.31. 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 explaina) which car takes off faster from rest, andb) 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/mHence 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.

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Unit 4.3: DensityTest Yourself 4.33. The density of water is 1000 kg m-3. What is the

mass of 1 cm3 of water in grams?Answer:Density of water water

3

33

3

3

3

cm g 1

cm (100)

m 1x

kg 1

g 1000x

m 1

kg 1000m 1

kg 1000

Hence 1 cm3 of water has a mass of 1 g.

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Unit 4: Mass, Weight and Density