# Gravitational potential energy

An object that is lifted from the ground gains energy since it can go on to do something else. A glass on the floor stays stable, one on a table can drop and smash.

The amount of stored by an object at height can be calculated using the equation:

Gravitational potential energy = mass × gravitational field strength × height

This is when:

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

### Example

A 5 kg object is taken to the top of a building. The building is 56 m high. How much gravitational potential energy has the object gained? ( = 10 N/kg)

= 5 × 10 × 56

= 2,800 J

Question

How much gravitational potential energy does a 500 g book gain when it is lifted up 1.5 m onto a shelf?

= 0.5 × 10 × 1.5

= 7.5 J

For any of these equations you may need to change the subject of the formula.