Learn about kinetic and gravitational potential energy.

Part of

Any object lifted above the ground has gravitational potential energy ( or GPE).

The amount of gravitational potential energy an object has on Earth depends on its:

- mass;
- height above the ground.

In the diagram:

- all the books on a shelf have GPE
- books A and B have more GPE than book C because they are higher
- book B has more GPE than book A because it has a greater mass

The gravitational potential energy of an object raised above the Earth’s surface can be calculated using the equation:

Gravitational potential energy=mass x gravitational field strength x vertical height raised

gravitational potential energy = mgh

or

= mgh

where:

is the gravitational potential energy in joules, J

*m* is the mass in kilograms, kg

*g* is the gravitational field strength in newtons per kilogram, N/kg

*h* is the change in height in metres, m

- Question
A book with a mass of 0.25 kg is lifted 2 m onto a bookshelf. If g is 10 N/kg, how much gravitational potential energy does it gain?

= mgh

m = 0.25 kg

g = 10 N/kg

h = 2 m

= 0.25 kg x 10 N/kg x 2 m

= 5 J

The gravitational potential energy gained by the book is 5 J.

- Question
A book of mass 600 g has 12 J of gravitational potential energy. How high is it above the Earth’s surface? (g = 10 N/kg)?

The book has mass 600 g.

This must be converted into kg to use in the equation for gravitational potential energy.

600 g = = 0.6 kg

= mgh

= 12 J

m = 0.6 kg

g = 10 N/kg

12 J = 0.6 kg x 10 N/kg x h

h =

h = 2 m

The book is 2 m above the surface of the Earth.