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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
  • All boards
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Warm-up

Answer each one, then check.

  1. 1

    What is the unit of mass?

    Show answerHide answer

    Kilogram

  2. 2

    What is the unit of weight?

    Show answerHide answer

    Newton

  3. 3

    What does g stand for?

    Show answerHide answer

    Gravitational field strength

  4. 4

    What is gravity?

    Show answerHide answer

    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.

Practice questions

Have a go at each one before you open its answer.

  1. Question 1 Calculate 2 marks

    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

    Show answerHide answer

    Model answer

    \(60 \times 9.8 = 588\) N

    Mark scheme

    • Correct substitution — 1 mark
    • 588 N — 1 mark
  2. Question 2 Explain 3 marks

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

    Show answerHide answer

    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.

    Mark scheme

    • Mass unchanged — 1 mark
    • Weight decreases — 1 mark
    • Moon has a weaker gravitational field — 1 mark
  3. Question 3 Use the graph 4 marks

    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.
    Show answerHide answer

    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

    Mark scheme

    • 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
  4. Question 4 Calculate 3 marks

    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.

    Show answerHide answer

    Model answer

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

    Mark scheme

    • Rearranges to g = W ÷ m — 1 mark
    • Correct substitution — 1 mark
    • 4.0 N/kg — 1 mark
  5. Question 5 Explain 2 marks

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

    Show answerHide answer

    Model answer

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

    Mark scheme

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

Quick check

  1. Weight is measured in...

    1. Akilograms
    2. Bjoules
    3. Cnewtons
    4. Dwatts
    Show answerHide answer

    C: newtons

    It is a force.

  2. Weight is calculated using...

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

    D: \(W = mg\)

    Mass times g.

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

    1. A20 N
    2. B5 N
    3. C12 N
    4. D0.2 N
    Show answerHide answer

    A: 20 N

    2 × 10.

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

    1. Aless than on Earth
    2. Bthe same as on Earth
    3. Cmore than on Earth
    4. Dzero
    Show answerHide answer

    B: the same as on Earth

    Mass does not change.

  5. Weight and mass are...

    1. Ainversely proportional
    2. Bunrelated
    3. Cdirectly proportional
    4. Dequal
    Show answerHide answer

    C: directly proportional

    W ∝ m.

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