Gravitational potential energy · Grade 11
In Grade 11 you get fluent with: finding height or mass from GPE.
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.
- To find a height from GPE, rearrange: h = GPE ÷ (mg).
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)
Example 5
A hiker of mass 72 kg gains 67,032 J of gravitational potential energy. How high does it rise? Give your answer to 1 decimal place. (Take g = 9.8 N/kg.)
Answer: 95 m
Example 6
A lift with passengers of mass 1,100 kg gains 1,379,840 J of gravitational potential energy. How high does it rise? Give your answer to 1 decimal place. (Take g = 9.8 N/kg.)
Answer: 128 m