2.2 - Gravitational Potential Energy

The gravitational potential energy store

• Lifting an object higher off the ground transfers energy to its gravitational potential energy store.
• Any object raised above the ground has energy in this store, and the higher it is, the more energy it holds.
• Lifting takes a force acting against gravity - this is what transfers the energy into the store.
• When the object is lowered or allowed to fall, energy is transferred back out of the store again.

What gravitational potential energy depends on

• Mass - A heavier object has more energy in its gravitational potential energy store than a lighter one at the same height.
• Height - The higher an object is raised, the more energy is transferred to its gravitational potential energy store.
• Gravitational field strength - The stronger the gravitational field the object is in, the more energy is stored for the same mass and height.

The gravitational potential energy formula

For a change in height, the same equation is written $\mathrm{\Delta }{E}_p=mg\mathrm{\Delta }h$.

Where:

• $E_p$ (or $\mathrm{\Delta }{E}_p$) = Gravitational potential energy (or change in gravitational potential energy), in joules (J)
• $m$ = Mass, in kilograms (kg)
• $g$ = Gravitational field strength, in newtons per kilogram (N/kg)
• $h$ (or $\mathrm{\Delta }h$) = Height (or change in vertical height), in metres (m)

Gravitational field strength on Earth is about 9.8 N/kg (sometimes rounded to 10 N/kg or given as 9.81 N/kg), so always use the value given in the question.

Worked example - GPE of a rucksack

A rucksack of mass 4.0 kg is lifted onto a luggage rack 1.8 m above the floor. Gravitational field strength is 9.8 N/kg. Calculate the energy in the rucksack's gravitational potential energy store.