# Calculation of energy changes

## Calculating kinetic energy

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

This is when:

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

### Example

An apple of mass 100 g falls from a tree. It reaches a speed of 6 m/s before landing on Isaac’s head. What is the gain of kinetic energy of the apple?

Question

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

## Calculating elastic potential energy

The amount of stored in a stretched spring can be calculated using the equation:

This is when:

• elastic potential energy (Ee) is measured in joules (J)
• spring constant (k) is measured in newtons per metre (N/m)
• extension (e) is measured in metres (m)

### Example

Robert stretches a spring with a spring constant of 3 N/m until it is extended by 50 cm. What is the elastic potential energy stored by the spring?

Question

How much elastic potential energy does a spring store when it is compressed by 0.2 m if it has a spring constant of 5 N/m?

## Calculating gravitational potential energy

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

Gravitational potential energy = mass × gravitational field strength × height

This is when:

• gravitational potential energy (Ep) is measured in joules (J)
• mass (m) is measured in kilograms (kg)
• gravitational field strength (g) is measured in newtons per kilogram (N/kg
• 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.

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