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Physics · Forces

Gravity, mass and weight

Use \(W = mg\) to calculate weight, and describe how weight and mass are related.

  • 6 key terms
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Teacher resources

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Student handouts

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Warm-up

Answer each one, then check.

  1. 1

    What is the unit of mass?

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    Kilogram

  2. 2

    What is the unit of weight?

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    Newton

  3. 3

    What does g stand for?

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    Gravitational field strength

  4. 4

    What is gravity?

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    An attractive force between objects with mass

  5. 5

    What instrument measures force?

    Show answerHide answer

    A newtonmeter (spring balance)

Learning Objectives

  1. 1Define weight and explain how it depends on gravitational field strength.
  2. 2Recall and apply \(W = mg\).
  3. 3Explain that weight and mass are directly proportional.
  4. 4Describe the centre of mass.

WEIGHT

weight \(=\) mass \(\times\) gravitational field strength \(W = mg\)

Weight is the force on an object due to gravity. On Earth g is about 9.8 N/kg, but in any calculation the value of g will be given.

Gravitational Field Strength

g varies from place to place.

  • Earth

    g (N/kg): 9.8

  • Moon

    g (N/kg): 1.6

  • Mars

    g (N/kg): 3.7

  • Jupiter

    g (N/kg): 25

Weight on Earth

A person has a mass of 60 kg. Calculate their weight on Earth. g = 9.8 N/kg.

Show the solutionHide the solution
  1. 1 Write the equation \(W = mg\)
  2. 2 Substitute \(W = 60 \times 9.8\)
  3. 3 Answer \(W = 588\) N

Answer588 N

Weight on the Moon

The same person goes to the Moon, where g = 1.6 N/kg. Calculate their mass and weight.

Show the solutionHide the solution
  1. 1 Mass Mass does not change: 60 kg
  2. 2 Weight \(W = 60 \times 1.6 = 96\) N

AnswerMass 60 kg; weight 96 N.

Finding g

An object of mass 3.0 kg has a weight of 12 N on a planet. Calculate g.

Show the solutionHide the solution
  1. 1 Rearrange \(g = W \div m\)
  2. 2 Substitute \(g = 12 \div 3.0\)
  3. 3 Answer \(g = 4.0\) N/kg

Answer4.0 N/kg

Key Ideas

Mass and weight are different.

  • Mass

    The amount of matter in an object; in kg; does not change with place.

  • Weight

    A force in newtons; depends on g; measured with a newtonmeter.

  • Proportional

    \(W \propto m\): doubling the mass doubles the weight.

  • Centre of mass

    The single point at which the weight of an object may be considered to act.

Weigh It

A rock has a mass of 5.0 kg. Calculate its weight on Earth (g = 9.8 N/kg), on the Moon (g = 1.6 N/kg) and on Jupiter (g = 25 N/kg).

1. Use W = mg.

2. Compare the answers.

A good answer shows: Earth 49 N; Moon 8.0 N; Jupiter 125 N. The mass is 5.0 kg everywhere.

Can I...?

  1. 1Define weight.
  2. 2Use \(W = mg\).
  3. 3Rearrange for g or m.
  4. 4Say why weight changes but mass does not.
  5. 5Recall the unit of weight.
  6. 6Describe a newtonmeter.
  7. 7Explain proportionality.
  8. 8Describe the centre of mass.

Summary & Exam Focus

  • \(W = mg\).
  • Mass in kg; weight in N.
  • Weight is proportional to mass.
  • Mass is the same everywhere; weight depends on g.

Exam focus

A person has a mass of 60 kg. Calculate their weight. g = 9.8 N/kg. (2 marks) (2 marks)

Substitute into W = mg and include N.

Key terms

The vocabulary this lesson expects you to use. Each one is linked from the first place it appears above.

Weight
The force acting on an object due to gravity.
Mass
The amount of matter in an object.
Gravitational field strength
The force per kilogram near a planet.
Newtonmeter
A calibrated spring balance for measuring force.
Centre of mass
The point where the weight of an object may be considered to act.
Directly proportional
Doubling one quantity doubles the other.

Questions and answers

10 questions set on this lesson, with the mark schemes and model answers open.

1. Exam question Calculate 2 marks Easier

A person has a mass of 60 kg. Gravitational field strength = 9.8 N/kg. Calculate the weight of the person. Use the equation: weight = mass × gravitational field strength

Mark scheme — 2 marks available

  • Correct substitution — 1 mark
  • 588 N — 1 mark

Model answer

\(60 \times 9.8 = 588\) N

2. Exam question Explain 3 marks Easier

An astronaut travels from Earth to the Moon. Explain what happens to the astronaut's mass and weight.

Mark scheme — 3 marks available

  • Mass unchanged — 1 mark
  • Weight decreases — 1 mark
  • Moon has a weaker gravitational field — 1 mark

Model answer

The mass stays the same because it is the amount of matter. The weight decreases because the gravitational field strength on the Moon is less than on Earth.

3. Exam question Use the graph 4 marks Easier

The graph shows how the weight of objects on a planet depends on their mass. (a) Describe the relationship between weight and mass. (b) Use the graph to calculate the gravitational field strength of the planet.

A straight line graph of weight against mass through the origin for objects on a planet.

Mark scheme — 4 marks available

  • Straight line through the origin — 1 mark
  • Directly proportional — 1 mark
  • Uses the gradient — 1 mark
  • 3.7 N/kg (accept 3.5 to 3.9) — 1 mark

Model answer

(a) Weight is directly proportional to mass (a straight line through the origin). (b) Gradient \(= 18.5 \div 5.0 = 3.7\) N/kg

4. Exam question Calculate 3 marks Easier

A rock has a weight of 12 N on a planet. Its mass is 3.0 kg. Calculate the gravitational field strength of the planet.

Mark scheme — 3 marks available

  • Rearranges to g = W ÷ m — 1 mark
  • Correct substitution — 1 mark
  • 4.0 N/kg — 1 mark

Model answer

\(g = W \div m = 12 \div 3.0 = 4.0\) N/kg

5. Exam question Explain 2 marks Easier

A newtonmeter is used to measure the weight of an object. State what the newtonmeter actually measures and the unit used.

Mark scheme — 2 marks available

  • Force or weight — 1 mark
  • In newtons — 1 mark

Model answer

The force (weight) acting on the object due to gravity, in newtons.

6. Multiple choice 1 mark Easier

Weight is measured in...

  1. A kilograms
  2. B joules
  3. C newtons Correct
  4. D watts

Why: It is a force.

7. Multiple choice 1 mark Core

Weight is calculated using...

  1. A \(W = m \div g\)
  2. B \(W = m + g\)
  3. C \(W = g \div m\)
  4. D \(W = mg\) Correct

Why: Mass times g.

8. Multiple choice 1 mark Core

A 2 kg mass where g = 10 N/kg weighs...

  1. A 20 N Correct
  2. B 5 N
  3. C 12 N
  4. D 0.2 N

Why: 2 × 10.

9. Multiple choice 1 mark Core

On the Moon an object's mass is...

  1. A less than on Earth
  2. B the same as on Earth Correct
  3. C more than on Earth
  4. D zero

Why: Mass does not change.

10. Multiple choice 1 mark Stretch

Weight and mass are...

  1. A inversely proportional
  2. B unrelated
  3. C directly proportional Correct
  4. D equal

Why: W ∝ m.