Calculating energy changes

Calculating kinetic energy

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

 Kinetic \ energy = \frac{1}{2} \times mass \times velocity^{2}

 KE = \frac{1}{2} \times m \times v^{2}

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

 KE = \frac{1}{2} \times m \times v^{2}

 KE = \frac{1}{2} \times 0.1 \times 6^{2}

 KE = \frac{1}{2} \times 0.1 \times 36

 KE = 1.8 \ J

Question

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

 KE = \frac{1}{2} \times m \times v^{2}

 KE = \frac{1}{2} \times 30 \times 4^{2}

 KE = \frac{1}{2} \times 30 \times 16

 KE = 240 \ J

Calculating gravitational potential energy

The amount of gravitational potential energy 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

 ∆GPE = m \times g \times ∆h

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)

 ∆GPE = m \times g \times ∆h

 ∆GPE = 5 \times 10 \times 56

 ∆GPE = 2,800 \ J

Question

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

∆GPE = m \times g \times ∆h

∆GPE = 0.5 \times 10 \times 1.5

∆GPE = 7.5 \ J

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