Unit 4: Mass, Weight and Density

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Unit 4 Mass, Weight and Density
Discover PHYSICS for GCE O Level Science
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Unit 4.1 Mass and Weight

• Learning Outcomes
• In this section, youll 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 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.
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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.

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Unit 4.1 Mass and Weight

• What is gravitational field?
• The Earths 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 Moons gravitational pull causes high and low
  tides of the Earths ocean.

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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)

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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
Differences between mass and weight
Table 4.1 Differences between mass and weight.
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Unit 4.1 Mass and Weight
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Unit 4.1 Mass and Weight
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Unit 4.1 Mass and Weight

• Key Ideas
• Mass measures the amount of matter or substance
  in a body. The SI unit is kilograms (kg)
• Weight is the gravitational force acting on a
  body. The SI unit is newtons (N).
• The weight of a body is related to its mass by
  the equation
• W mg
• Gravitational field strength, in N kg-1 is the
  same as the acceleration of free fall in m s-2.
• 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 Weight

• Test Yourself 4.1
• List four differences between mass and weight.

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Unit 4.1 Mass and Weight

• Test Yourself 4.1
• 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 Weight

• Test Yourself 4.1
• We have learnt that Earths 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 Weight

• Test Yourself 4.1
• 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 Weight

• Test Yourself 4.1
• 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.

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Unit 4.2 Inertia

• Lesson Outcomes
• In this section, youll be able to
• understand and define inertia.

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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.
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Unit 4.3 Density

• Lesson Outcomes
• In this section, youll 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

where ? 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 (?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
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Unit 4.3 Density
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Unit 4.3 Density
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Unit 4.3 Density

• Key Ideas
• The density of a substance is defined as its mass
  per unit volume.
• The SI units for density is kg m-3.
• The density of a substance is a fixed physical
  property.
• Substances that are less dense than water will
  float on water.
• To measure density of a substance, we measure
  its
• Mass, eg. With a beam balance, and
• 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 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 Newtons 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.
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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
• Density of water ?water

Hence 1 cm3 of water has a mass of 1 g.
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Unit 4 Mass, Weight and Density