Gravitational potential energy E = mgh, elastic potential energy E = ½ke², and using conservation of energy for falls, swings and springs.
What you will learn
- Calculate gravitational potential energy and rearrange E = mgh
- Calculate the energy stored in a spring, in metres
- Use energy conservation to find a speed or a height
Gravitational potential energy
Lift something up and you fill its gravitational potential store.
gravitational potential energy = mass × gravitational field strength × height
Ep = m g h
Energy in J, mass in kg, g in N/kg, height in m. On Earth, g = 9.8 N/kg: the question will tell you which value to use. Recall it: none of the three boards puts it on the sheet.
- A 50 kg climber climbs 12 m. Take g = 9.8 N/kg.
- E = 50 × 9.8 × 12
- E = 5880 J
To find a height: h = E ÷ (m g). To find a mass: m = E ÷ (g h). If the energy is in kJ, multiply by 1000 first.
Some questions ask you to estimate: you choose sensible values yourself. A teenager or adult has a mass of about 50 to 80 kg, and one storey of a building (one flight of stairs) is about 3 m high.
- Estimate the energy gained by an adult climbing two floors. Take g = 9.8 N/kg.
- mass about 70 kg, height about 2 × 3 = 6 m
- E = 70 × 9.8 × 6 = 4116 J
- so about 4000 J
The rest of this lesson and its 10 practice questions are locked.
In this lesson
- Gravitational potential energy
- Elastic potential energy
- Energy is conserved
- Try it: Watch the stores swap in a pendulum
- Try it: Energy in a bouncing spring
- Try it: Your first potential energy calculation
10 practice questions, marked as you go; about 25 minutes in all.
Key terms
Limit of proportionality, Metres
In this unit: Energy stores, transfers and efficiency
Energy stores and how energy moves between them, kinetic and potential energy, specific heat capacity, power, efficiency and the energy resources that make our electricity.