Changes in energy: gravitational potential energy, E_p, in joules, J

The idea

Gravitational potential energy, E_p, is the energy a mass stores because of its height in a gravitational field. Lifting an object means a force equal to its weight, W = m × g, moves it upward through a vertical distance, so the energy transferred to the gravitational store is E_p = m × g × h. E_p is measured in joules, J, the same unit as every other energy form, because one joule is one newton-metre. For example, lifting a 2 kg bag by 3 m with g = 9.8 N/kg gives E_p = 2 × 9.8 × 3 = 58.8 J. Only the vertical height change matters, not the path taken. When the object falls, that stored energy is transferred to kinetic and thermal stores, so E_p lost equals energy gained elsewhere if no energy is dissipated.

What earns the marks

• State that E_p is energy stored in the gravitational store of an object because of its position in a gravitational field.
• Recall and apply E_p = m × g × h, identifying m in kilograms, g in newtons per kilogram and h in metres.
• Recognise that the vertical height change h is measured from a chosen reference level and that only the vertical component counts.
• Give the unit of E_p as the joule, J, and explain that 1 J = 1 N m.
• Use E_p calculations to describe energy transfers, for example gravitational store to kinetic store as an object falls.

Common mistakes and how to put them right

• Using the sloping distance along a ramp instead of the vertical height.

  Put it right: Resolve to the vertical height change, because E_p depends only on vertical displacement.

• Substituting mass in grams or height in centimetres without converting.

  Put it right: Convert to kg and m before multiplying so the answer is in joules.

• Treating g as 10 N/kg automatically.

  Put it right: Use the value of g given in the question, which may be 9.8 N/kg or another stated value.

Exam tips

• Write the equation, substitute the values with units, then give the answer with the unit J.
• Check whether the question asks for energy stored, energy transferred or height, and rearrange E_p = m × g × h before substituting.
• For a falling object, compare E_p lost with kinetic energy gained to explain any difference caused by air resistance or friction.