Gravitational potential energy

When an object is lifted in a gravitational field, energy is transferred to a gravity store. This store is called gravitational potential energy.

gravitational potential energy = mass × height × gravitational field strength (g)

This is when:

  • gravitational potential energy is measured in joules (J)
  • mass is measured in kilograms (kg)
  • height is measured in metres (m)
  • gravitational field strength (g) is measured in newtons per kilogram (N/kg)

Example

Calculate the energy transferred to the gravity store when a woman of mass 60 kg climbs 4 rungs up a ladder. Each rung is 15 cm high.

First calculate the distance climbed in metres:

15 cm is 0.15 m

0.15 × 4 = 0.6 m

Then calculate the gravity store increase (the gravitational potential energy), remembering that g is 10 N/kg on Earth:

gravitational potential energy = mass × height × gravitational field strength (g)

gravitational potential energy = 60 × 0.6 × 10

gravitational potential energy = 360 J

Question

Calculate the energy transferred to the gravity store when a rocket of mass 4000 kg reaches 10 km up in the atmosphere. Express your answer in megajoules (MJ).

Convert the units to metres:

10 km is 10,000 m

Then calculate the gravity store increase:

10,000 × 4,000 × 10 = 400,000,000 J

Finally, convert to MJ:

400,000,000 ÷ 1,000,000 = 400 MJ

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