Gravitational potential energy

An object can possess energy as a result of its motion, position and deformation.

On Earth, the force of gravity is always acting upon you. When you are above the Earth's surface you 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 GPE than book C because it is higher
  • book B has more GPE than book A because it has a greater mass

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 bookshelf alongside books A and B.

Calculating change in GPE (higher tier)

Here is the equation for calculating gravitational potential energy.

\text{GPE} = {\text{m}}\times{\text{g}}\times{\text{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)

Question

Use the above information to answer the question.

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

GPE = 0.25 × 10 × 2 = 5 J