Gravitational Potential Energy

Extended tier only

Energy in an object's gravitational potential energy store is defined as:

The energy an object has due to its height in a gravitational field

Work is done against the weight force exerted on the object; therefore, energy is transferred
This means that:
- if an object is lifted up, energy will be transferred to its gravitational potential store
- if an object is lowered, energy will be transferred away from its gravitational potential store

Gravitational potential energy of an object lifted through a gravitational field

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Energy is transferred to the mass's gravitational store as it is lifted through the gravitational field

Gravitational potential energy equation

The change in energy in an object's gravitational potential energy store can be calculated using the equation:

$∆ E_{p} = m g ∆ h$

Where:
- $∆ E_{p}$ = change in gravitational potential energy, measured in joules (J)
- $m$ = mass, measured in kilograms (kg)
- $g$ = gravitational field strength, measured in newtons per kilogram (N/kg)
- $∆ h$ = change in height, measured in metres (m)

Worked example

A man climbs a flight of stairs that is, in total, 3.0 m higher than the floor. The man has a mass of 72 kg, and the gravitational field strength on Earth is approximately 9.8 N/kg.

Calculate the energy transferred to the man's gravitational potential energy store.

Answer:

Step 1: List the known quantities

Mass of the man, $m = 72 kg$
Gravitational field strength, $g = 9.8 N / kg$
Change in height, $∆ h = 3.0 m$

Step 2: Write down the equation for gravitational potential energy

$∆ E_{p} = m g ∆ h$

Step 3: Calculate the gravitational potential energy

$∆ E_{p} = 72 \times 9.8 \times 3.0$

$∆ E_{p} = 2116.8 J$

Step 4: Round to an appropriate number of significant figures

The input values are to 2 s.f. therefore, the output value must be to 2 s.f.

$∆ E_{p} = 2100 J (2 s . f .)$

Examiner Tip

In your IGCSE Co-ordinated Sciences exam, you will generally be expected to round your answers to an appropriate number of significant figures.

Your answer can only be as accurate as your least accurate input value. Therefore, your final answer should round to the lowest number of significant figures of all your input values.

Gravitational Potential Energy (CIE IGCSE Physics: Co-ordinated Sciences (Double Award))

Revision Note