4.13 - Gravitational Potential Energy

Gravitational potential energy and what it depends on

• Lifting an object higher off the ground gives it gravitational potential energy.
• Any object raised above the ground has gravitational potential energy, and the higher it is, the more it has.
• Lifting takes a force acting against gravity - this is what gives the object its gravitational potential energy.
• When the object is lowered or allowed to fall, this energy changes into other forms again.

What it depends on

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

The gravitational potential energy formula

Where:

• $E_p$ = Gravitational potential energy, in joules (J)
• $m$ = Mass, in kilograms (kg)
• $g$ = Gravitational field strength, in newtons per kilogram (N/kg)
• $h$ = Height, in metres (m)

Gravitational field strength on Earth is taken as 10 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 10 N/kg. Calculate the rucksack's gravitational potential energy.