3.4.1.7
Gravitational potential energy depends on mass, g, and height change
Work, Energy & Power — AQA A-Level Physics
Key Definition
Gravitational potential energy (near Earth's surface) — The energy stored in a mass due to its position in a uniform gravitational field. delta-E_p = mg delta-h.
$$\Delta E_p = mg \Delta h$$
- $ΔE_p$: change in gravitational potential energyThe capacity to do work. Measured in joules (J).The energyThe capacity to do work. Measured in joules (J). an object possesses due to its position in a gravitational fieldA region of space in which a mass experiences a gravitational force.. (J)
- $m$: mass (kg)
- $g$: gravitational field strengthThe gravitational force per unit mass at a point in a gravitational fieldA region of space in which a mass experiences a gravitational force.. Measured in N kg⁻¹. (9.81 N kg⁻¹)
- $Δh$: change in height (m)
- Lifting a mass increases its GPE. Lowering it decreases GPE.
- $GPE = 0 can be defined at any convenient height; only changes in GPE\;\text{m}atter.$
- This equation applies only in a uniform gravitational fieldA region of space in which a mass experiences a gravitational force. (near Earth's surface).
- GPE and height have a linear relationship: the graph is a straight line.
Worked Example
A man of mass 74 kg climbs five flights of stairs, each 3.7 m high. Find the change in GPE.
Show Solution
1
Calculate total height
$$\Delta h = 5 \times 3.7 = 18.5 \text{ m}$$
2
Calculate GPE change
$$\Delta E_p = 74 \times 9.81 \times 18.5 = 13400 \text{ J} \approx 13000 \text{ J (2 s.f.)}$$
Answer
$\Delta E_p \approx 13000$ J
Examiner Tips and Tricks
- In your equations, write ΔE_p (not GPE).
- At A-Level you may encounter problems where the gravitational field is non-uniform (e.g. in space), where this equation does not apply.