# 5.2.1 Gravitational Potential Energy

### Derivation of GPE = mgh

• Gravitational potential energy is energy stored in a mass due to its position in a gravitational field
• When a heavy object is lifted, work is done since the object is provided with an upward force against the downward force of gravity
• Therefore energy is transferred to the object
• This equation can therefore be derived from the work done

### Gravitational Potential Energy

• Gravitational potential energy (GPE) is energy stored in a mass due to its position in a gravitational field
• If a mass is lifted up, it will gain GPE (converted from other forms of energy)
• If a mass falls, it will lose GPE (and be converted to other forms of energy)
• The equation for gravitational potential energy for energy changes in a uniform gravitational field is: Equation for GPE

• The potential energy on the Earth’s surface at ground level is taken to be equal to 0
• This equation is only relevant for energy changes in a uniform gravitational field (such as near the Earth’s surface)

#### GPE v Height graphs

• The two graphs below show how GPE changes with height for a ball being thrown up in the air and when falling down Graphs showing the linear relationship between GPE and height

• Since the graphs are straight lines, GPE and height are said to have a linear relationship
• These graphs would be identical for GPE against time instead of height

#### Exam Tip

This equation only works for objects close to the Earth’s surface where we can consider the gravitational field to be uniform. In A2 level, you will consider examples where the gravitational field is not uniform such as in space, where this equation for GPE will not be relevant. ### Author: Ashika

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.
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