# Calculating energy changes

## Calculating kinetic energy

The amount of of a moving object can be calculated using the equation:

This is when:

• kinetic energy (KE) is measured in joules (J)
• mass (m) is measured in kilograms (kg)
• speed (v) is measured in metres per second (m/s)

### Example

Question

How much kinetic energy does a 30 kg dog have when it runs at 4 m/s?

## Calculating gravitational potential energy

The amount of stored by an object at height can be calculated using the equation:

change in gravitational potential energy = mass × graviational field strength × change in vertical height

This is when:

• change in gravitational potential energy (∆GPE) is measured in joules (J)
• mass (m) is measured in kilograms (kg)
• gravitational field strength (m) is measured in newtons per kilogram (N/kg)
• change in vertical height (∆ℎ) is measured in metres (m)

### Example

Galileo takes a 5 kg cannonball to the top of the Tower of Pisa for one of his experiments. The tower is 56 m high. How much gravitational potential energy has the cannonball gained? (g = 10 N/kg)

Question

How much gravitational potential energy does a 500 g book gain when it is lifted up 1.5 m onto a shelf?

For any of these equations you may need to change the subject of the formula.