Calculating energy changes

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

change in gravitational potential energy = mass x gravitational field strength x change in vertical height

\Delta GPE = m \times g \times \Delta h

This is when:

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

Example

A 3.5 kg cat climbs a tree. The tree is 5.6 m high. How much gravitational potential energy has the cat gained? (g = 10 N/kg)

\Delta GPE = m \times g \times \Delta h

E^{p} = m \times g \times h

\Delta GPE = 3.5 \times 10 \times 5.6

\Delta GPE = 196 \ J

Question

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

\Delta GPE = m \times g \times \Delta h

\Delta GPE = 0.5 \times 10 \times 1.5

\Delta GPE = 7.5 \ J

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

A dancer with a mass of 90 kg moves at a speed of 6 m/s across the stage. What is his kinetic energy?

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

KE = \frac{1}{2} \times 90 \times  6^{2}

KE = \frac{1}{2} \times 90 \times  36

KE = 1,620 \ J

Question

How much kinetic energy does a 300 g kitten have when it runs at 4 m/s to chase a butterfly?

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

KE = \frac{1}{2} \times 0.30 \times 4^{2}

KE = \frac{1}{2} \times 0.30 \times 16

KE = 2.4 \ J

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

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