What gravitational potential energy means

Gravitational potential energy is energy associated with an object's position in a gravitational field. In GCSE questions, this usually means the energy an object gains when it is lifted to a greater height above ground level.

The word "gained" matters. If a box starts on the floor and is lifted onto a shelf, you calculate the energy gained from the increase in height. If a question gives a starting height and a final height, use the vertical height gained, not the total height from the ground unless that is what the question asks for.

The energy gained depends on three things:

• mass: a larger mass gains more gravitational potential energy for the same lift
• gravitational field strength: the same mass and height give different energies in different gravitational fields
• height: a greater vertical height gives a greater energy gain

The equation and units

For AQA GCSE Physics, you need to recall and apply this equation:

In words:

gravitational potential energy = mass x gravitational field strength x height

Each symbol has a specific meaning and unit:

The value of g will be given in any calculation. Use the value in the question, even if you have seen common values such as 9.8 N/kg or 10 N/kg before.

This equation is a multiplication relationship. If the height is doubled while mass and g stay the same, the gravitational potential energy gained doubles. If the mass is tripled while height and g stay the same, the energy gained triples.

Direct calculations

A calculation answer should show the equation, substitute the numbers, calculate the answer, and include the unit. This gives the examiner your method as well as your final value.

Example: A 2.0 kg box is lifted 1.5 m. The gravitational field strength is 9.8 N/kg. Calculate the gravitational potential energy gained.

1. Write the equation: E_p = m g h
2. Substitute values: E_p = 2.0 x 9.8 x 1.5
3. Calculate: E_p = 29.4
4. Add the unit: E_p = 29.4 J

The answer is 29.4 J.

Unit conversions are a common trap. Mass must be in kilograms and height must be in metres before you substitute into the equation. For example, 50 cm is 0.50 m, and 200 g is 0.200 kg.

Rearranging the equation

Sometimes the question gives the energy gained and asks for the mass or the height. The value of g is still supplied in the question. Start from the same equation, then rearrange it before substituting.

To find height:

h = E_p / (m g)

Example: An object of mass 4.0 kg gains 120 J of gravitational potential energy. The gravitational field strength is 10 N/kg. Calculate the height raised.

h = E_p / (m g)

h = 120 / (4.0 x 10)

h = 3.0 m

To find mass:

m = E_p / (g h)

The same pattern works each time: divide the energy by the two quantities you already know.

Exam care and boundaries

For this lesson, the calculation is only about the gravitational potential energy gained by an object raised above ground level. Kinetic energy and elastic potential energy have their own separate equations, so do not bring those equations into this calculation.

AQA may use a falling or dropping context to describe an energy transfer. In that kind of context, a raised object has a gravitational potential energy store. As it falls, energy is transferred away from that store and may be transferred to a kinetic energy store, but this lesson only calculates the gravitational potential energy using E_p = m g h.

Use these checks before finalising an answer:

• Did you use the vertical height gained?
• Did you convert mass to kg and height to m?
• Did you use the value of g given in the question?
• Did you include the unit J for gravitational potential energy?
• Does the size of the answer make sense? Bigger mass, bigger g, or bigger height should mean bigger E_p.