Gravitational potential energy

Any object lifted above the ground has gravitational potential energy ( E_{p} or GPE).

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

  • mass;
  • height above the ground.
Book A and book B stand on a bookshelf. Book B is twice as thick as book A. Book C sits on a second bookshelf. It is directly below book A and has a similar thickness.

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

Calculating change in gravitational potential energy

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

E_{p} = mgh

where:

E_{p} 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?

E_{p} = mgh

m = 0.25 kg

g = 10 N/kg

h = 2 m

E_{p} = 0.25 kg x 10 N/kg x 2 m

E_{p} = 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 = \frac{600 kg}{1000} = 0.6 kg

E_{p} = mgh

E_{p} = 12 J

m = 0.6 kg

g = 10 N/kg

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

h = \frac {12~J}{{0.6~kg} x {10~N/kg}}

h = 2 m

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