Define gravitational potential energy.

The gravitational potential energy of an object is the energy it has because of its position in a gravitational field, measured by the work done against gravity in moving it to that position from a chosen reference level.

Show how Δp.e. = mgΔh follows from the definition of work done.

Lifting a mass m at a steady speed needs an upward force equal to the weight mg, and this force acts through a vertical distance Δh, so the work done and hence the gain in gravitational potential energy is mgΔh.

Under what condition is Δp.e. = mgΔh a valid equation?

It is valid only where the gravitational field is effectively uniform, which means the height change must be small compared with the radius of the Earth so that g does not change appreciably.

How does the gain in gravitational potential energy change if the height an object is raised through is doubled?

The gain in gravitational potential energy also doubles, because Δp.e. is directly proportional to Δh for a fixed mass in a uniform field.

CCEA A-Level Physics 1210

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Work, Energy and Power

Gravitational potential energy

3 things to know
Unit AS 1

Overview

Gravitational potential energy and sign of Δp.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Key term

State the equation for the change in gravitational potential energy near the Earth's surface and define every symbol.

Numbers

A climber of mass 65 kg ascends a vertical height of 850 m. Calculate the gain in gravitational potential energy.

Key term

Why can g be quoted either as 9.81 m s⁻² or as 9.81 N kg⁻¹?

Questions from this subtopic

Each one with the model answer underneath.

1
Define gravitational potential energy.
Model answer
The gravitational potential energy of an object is the energy it has because of its position in a gravitational field, measured by the work done against gravity in moving it to that position from a chosen reference level.
2
State the equation for the change in gravitational potential energy near the Earth's surface and define every symbol.
Model answer
The change is Δp.e. = mgΔh, where Δp.e. is the change in gravitational potential energy in joules, m the mass in kilograms, g the acceleration of free fall of 9.81 m s⁻² and Δh the change in vertical height in metres.
3
Show how Δp.e. = mgΔh follows from the definition of work done.
Model answer
Lifting a mass m at a steady speed needs an upward force equal to the weight mg, and this force acts through a vertical distance Δh, so the work done and hence the gain in gravitational potential energy is mgΔh.
4
Under what condition is Δp.e. = mgΔh a valid equation?
Model answer
It is valid only where the gravitational field is effectively uniform, which means the height change must be small compared with the radius of the Earth so that g does not change appreciably.
5
A climber of mass 65 kg ascends a vertical height of 850 m. Calculate the gain in gravitational potential energy.
Model answer
The gain is Δp.e. = 65 × 9.81 × 850 = 5.42 × 10⁵ J, and 542 000 ÷ (65 × 850) = 9.81 m s⁻², confirming the result.
6
How does the gain in gravitational potential energy change if the height an object is raised through is doubled?
Model answer
The gain in gravitational potential energy also doubles, because Δp.e. is directly proportional to Δh for a fixed mass in a uniform field.

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