Gravitational potential energy (GPE)

On Earth we always have the force of gravity acting on us. When we are above the Earth's surface we have potential (stored) energy. This is called gravitational potential energy (GPE).

The amount of GPE an object on Earth has depends on its:

  • mass
  • height above the ground
Book A and book B stand on a bookshelf. Book B is twice as thick as book A. Book C sits on a second bookshelf. It is directly below book A and has a similar thickness.

In the diagram:

  • all the books on a shelf have GPE
  • book A has more than book C because it is higher
  • book B has more than book A because it has a greater mass

Calculating change in gravitational potential energy

If an object is lifted, work is done against gravitational force. The object gains energy. For example, Book C would gain GPE if it were lifted onto the higher book shelf alongside Books A and B.

Here is the equation for calculating gravitational potential energy:

GPE = mgh~~or~~GPE = m \times g \times h

where:

GPE is the gravitational potential energy in joules, J

m is the mass in kilograms, kg

g is the gravitational field strength in newtons per kilogram, N/kg

h is the change in height in metres, m

For example, a book with a mass of 0.25 kg is lifted 2 m onto a book shelf. If g is 10 N/kg, how much gravitational potential energy does it gain?

GPE = 0.25 × 10 × 2 = 5 J