Energy calculations
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 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 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
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.
