Gravitational potential energy revision notes

Edexcel International GCSE Physics (4PH1), chapter 16: Work and power, specification point 4.13. Free lesson.

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Gravitational potential energy (GPE) is the energy gained when an object is raised. Use the object's mass and its vertical change in height to calculate the gain, or rearrange the equation to find a height.

What gravitational potential energy measures

Lifting an object transfers energy to its gravitational store. The equation is GPE = m × g × h. It is on the equation list, so you need to know how to use it and what each symbol means. GPE is energy in the gravitational store, measured in joules (J). m is mass in kilograms (kg). g is gravitational field strength, measured in newtons per kilogram (N/kg). On Earth, use 10 N/kg. h is the change in height in metres (m), meaning how far the object is raised or lowered.

How to calculate a gain in GPE

Substitute the mass, gravitational field strength and change in height into GPE = m × g × h. Use the vertical change in height, not the distance travelled along a slope.

Use the vertical rise, not the slope length

For stairs or a ramp, only the vertical rise changes the object's height. The route length does not affect the GPE gained, so the same rise gives the same energy gain. For the stairs example, the stairs are 7 m long but rise by 4 m. Use h = 4 m, not 7 m.

Convert units before substituting

The equation needs mass in kilograms and height in metres. Convert the measurements first, or the calculated energy will be wrong. Convert grams to kilograms by dividing by 1,000. Convert centimetres to metres by dividing by 100. For example, 250 g = 0.25 kg and 80 cm = 0.8 m.

Rearrange the equation to find height

If you know the energy gained and the mass, rearrange GPE = m × g × h to find h. Divide the energy by m × g. The result is a height in metres.