Calculating energy changes
Calculating kinetic energy
The amount of kinetic energyEnergy which an object possesses by being in motion. 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 energyThe energy stored by an object lifted up against the force of gravity. Also known as GPE. 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.
