Calculation of energy changes
Calculating kinetic energy
The amount of kinetic energyEnergy which an object possesses by being in motion. in a moving object can be calculated using the equation:
\(kinetic~energy= \frac{1}{2}\times mass \times speed^2\)
\(E_{k} = \frac{1}{2}~m~v^{2}\)
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 Isaacâs head. What is the gain of kinetic energy of the apple?
\(E_{k} = \frac{1}{2}~m~v^{2} \)
\(E_{k} = \frac{1}{2} \times 0.1 \times6^{2} \)
\(E_{k} = \frac{1}{2} \times 0.1 \times 36\)
\(E_{k} = 1.8~J \)
Question
How much kinetic energy does a 30 kg dog have when it runs at 4 m/s?
\(E_{k} = \frac{1}{2}~m~v^{2}\)
\(E_{k} = \frac{1}{2} \times 30 \times 4^{2}\)
\(E_{k} = \frac{1}{2} \times 30 \times 16 \)
\(E_{k} = 240~J\)
Calculating elastic potential energy
The amount of elastic potential energyEnergy stored in squashed, stretched or twisted materials. stored in a stretched spring can be calculated using the equation:
\(elastic~potential~energy= \frac{1}{2} \times spring~constant \times extension^{2}\)
\(E_{e}=\frac{1}{2}~k~e^{2}\)
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?
\(E_{e} = \frac{1}{2}~k~e^{2}\)
\(E_{e} = \frac{1}{2} \times 3\times 0.5^{2}\)
\(E_{e} = \frac{1}{2} \times 3\times 0.25\)
\(E_{e} = 0.375~J\)
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?
\(E_{p} = \frac{1}{2}~k~e^{2}\)
\(E_{e} = \frac{1}{2} \times 5 \times 0.2^{2}\)
\(E_{e} = \frac{1}{2} \times 5 \times 0.04\)
\(E_{e} = 0.1~J\)
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:
Gravitational potential energy = mass Ă gravitational field strength Ă height
\(E_{p}=m~g~h\)
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)
\(E_{p}=m~g~h\)
\(E_{p}= 5 \times 10 \times 56\)
\(E_{p}= 2,800 J\)
Question
How much gravitational potential energy does a 500 g book gain when it is lifted up 1.5 m onto a shelf?
\(E_{p}= m~g~h\)
\(E_{p}= 0.5 \times 10 \times 1.5\)
\(E_{p}= 7.5~J\)
For any of these equations you may need to change the subject of the formula.