Gravitational potential energy exam questions with worked answers

By Mehmood Kakar · Updated

Quick answer

Every GPE question uses Ep = mgh. Convert mass to kg and height to m, use the value of g given in the question, and rearrange when you need mass or height. The six questions below go from 2-mark substitutions to multi-step questions that combine GPE with power.

The method

GPE questions reward care more than cleverness. Write Ep = mgh. Convert grams to kilograms and centimetres to metres. Use the g value from the question. Then substitute and give the answer in joules.

When the question asks for height or mass, rearrange before you substitute. Both rearrangements divide by a product, so work out the bottom first: m × g, or g × h.

Q1: Find GPE

A 5.0 kg box is lifted onto a shelf 1.2 m high. g = 9.8 N/kg. Calculate the GPE gained. (2 marks)

  1. Ep = m g h
  2. Ep = 5.0 × 9.8 × 1.2
  3. Ep = 58.8 J
  4. Ep = 59 J (2 s.f.)

58.8 J would also be accepted. Rounding to 59 J matches the 2 significant figures of the data.

Q2: Grams and centimetres

A 650 g book is lifted 80 cm. g = 9.8 N/kg. Calculate the GPE gained. (3 marks)

  1. Convert: m = 650 ÷ 1000 = 0.65 kg; h = 80 ÷ 100 = 0.80 m
  2. Ep = 0.65 × 9.8 × 0.80
  3. Ep = 5.096 J
  4. Ep = 5.1 J (2 s.f.)

Two conversions this time. Miss both and the answer comes out at 509,600 J, a hundred thousand times too big.

Q3: Find height

A 45 kg child climbs a tree and gains 3.5 kJ of GPE. g = 9.8 N/kg. Calculate how high the child climbs. (3 marks)

  1. Rearrange: h = Ep ÷ (m × g)
  2. Convert: Ep = 3.5 × 1000 = 3500 J
  3. m × g = 45 × 9.8 = 441; h = 3500 ÷ 441 = 7.936…
  4. h = 7.9 m (2 s.f.)

On a calculator, 3500 ÷ 45 × 9.8 gives 762 m, because it divides by 45 and then multiplies by 9.8. Work out 45 × 9.8 first, or use brackets.

Q4: Find mass

Lifting a sack of flour through 2.5 m gives it 1470 J of GPE. g = 9.8 N/kg. Calculate its mass. (3 marks)

  1. Rearrange: m = Ep ÷ (g × h)
  2. g × h = 9.8 × 2.5 = 24.5
  3. m = 1470 ÷ 24.5
  4. m = 60 kg

Q5: On the Moon

An astronaut lifts a 2.0 kg rock through 1.5 m on the Moon, where g = 1.6 N/kg. Calculate the GPE gained, and compare it with lifting the same rock through the same height on Earth (g = 9.8 N/kg). (4 marks)

  1. Moon: Ep = 2.0 × 1.6 × 1.5 = 4.8 J
  2. Earth: Ep = 2.0 × 9.8 × 1.5 = 29.4 J
  3. 29.4 ÷ 4.8 = 6.125
  4. Lifting the rock on the Moon needs 4.8 J, about 6 times less energy than on Earth, because g on the Moon is about 6 times smaller.

The mass of the rock is the same in both places. Only g changes, and GPE is directly proportional to g.

Q6: GPE and power

A crane lifts a 400 kg load through 15 m in 20 s. g = 9.8 N/kg. Calculate the useful power output of the crane. (4 marks)

  1. Step 1, energy: Ep = m g h = 400 × 9.8 × 15 = 58,800 J
  2. Step 2, power: P = E ÷ t
  3. P = 58,800 ÷ 20
  4. P = 2940 W (2.94 kW)

The GPE gained is the useful energy output, so dividing it by the time gives the useful power. If the question then gives the crane's input power, you can go on to find its efficiency with the efficiency calculator.

Check each step with the GPE calculator and the power calculator.

Practice

Try these before opening the answers.

1. A 70 kg diver stands on a 10 m board. g = 9.8 N/kg. Calculate her GPE relative to the water.

Ep = 70 × 9.8 × 10 → Ep = 6860 J (6900 J to 2 s.f.)

2. A 0.20 kg apple falls and loses 2.94 J of GPE. g = 9.8 N/kg. Calculate the height it fell.

h = 2.94 ÷ (0.20 × 9.8) = 2.94 ÷ 1.96 → h = 1.5 m

3. A lift raises a 600 kg load through 12 m in 30 s. g = 9.8 N/kg. Calculate the useful power.

Ep = 600 × 9.8 × 12 = 70,560 J → P = 70,560 ÷ 30 → P = 2352 W (2400 W to 2 s.f.)

Frequently asked questions

What is the equation for gravitational potential energy?

GPE = mass × gravitational field strength × height (Ep = mgh). GPE is in joules (J), mass in kilograms (kg), g in newtons per kilogram (N/kg) and height in metres (m).

What value of g should I use?

Use the value given in the question. AQA questions usually give 9.8 N/kg for Earth. If a question is set on another planet or the Moon, it will give you that value of g.

How do I find height from GPE?

Rearrange to h = Ep ÷ (m × g). Multiply mass by g first, then divide the energy by that result.

Is the height the distance fallen or the height above the ground?

It is the change in height. For an object lifted from a table to a shelf, use the vertical distance between the table and the shelf.

Written by Mehmood Kakar

Physics teacher and engineer (MSc Physics, M.Ed) with 8 years of hands-on teaching, from college students to teacher training. About the author · LinkedIn (opens in a new tab)

Checked against the AQA GCSE Physics (8463) specification on 14 November 2026.