Gravitational potential energy · Year 9
In Year 9 you learn: gravitational potential energy = mgh.
Lifting something up gives it energy in its gravitational potential store. The energy gained is ΔGPE = mgh: mass × gravitational field strength × the change in height. Twice the mass or twice the height means twice the energy, and on the Moon, where g is smaller, the same lift stores less. Falling back down, the object loses that energy again.
Key facts
- Gravitational potential energy ΔGPE = mgh (g = 9.8 N/kg on Earth).
- Gravitational potential energy depends on mass, height and g: on the Moon (g = 1.6 N/kg) the same lift gains far less.
Worked examples
Example 1
A 2 kg book is lifted 1.5 m onto a shelf. How much gravitational potential energy does it gain? (g = 10 N/kg)
Answer: 30 J
Example 2
A 0.20 kg apple falls 2.0 m from a branch. How much gravitational potential energy does it lose? (g = 9.8 N/kg)
Answer: 3.92 J
Example 3
A crane lifts a 500 kg crate 12 m. How much gravitational potential energy does the crate gain? (g = 9.8 N/kg)
Answer: 58,800 J
Example 4
Which gains more gravitational potential energy: a 2 kg bag lifted 3 m, or a 3 kg bag lifted 1.5 m? (g = 9.8 N/kg)
Answer: the 2 kg bag (58.8 J, compared with 44.1 J)