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.
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.
