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 gravitational potential energy stored by an object at height can be calculated using the equation:

Gravitational potential energy = mass × gravitational field strength × height

\text{E}_{p} = \text{mgh}

This is when:

  • gravitational potential energy ( \text{E}_{p}) is measured in joules (J)
  • mass ( \text{m}) is measured in kilograms (kg)
  • gravitational field strength ( \text{g}) is measured in newtons per kilogram (N/kg)
  • height ( \text{h}) 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? ( \text{g} = 10 N/kg)

\text{E}_{p} = \text{mgh}

\text{E}_{p} = 5 × 10 × 56

\text{E}_{p} = 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?

\text{E}_{p} = \text{mgh}

\text{E}_{p} = 0.5 × 10 × 1.5

\text{E}_{p} = 7.5 J

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