Forces & Energy Notes

Q: How do we calculate elastic potential energy?

Energy stored in a stretched spring is Ee = \tfrac{1}{2} k e^2. Here Ee is elastic potential energy (J), k the spring constant (N/m) and e the extension (m). It only applies within the limit of proportionality.

Q: How do we calculate gravitational potential energy?

Gravitational potential energy is Ep = m \times g \times h. The gravitational potential energy is the energy an object has because of its height above a reference point. Here m is mass (kg), g the gravitational field strength (N/kg) and h the height (m).

Q: How do we calculate kinetic energy?

Kinetic energy is Ek = \tfrac{1}{2} m v^2, so doubling the speed quadruples it. The kinetic energy of an object is the energy it has because it is moving. Here m is mass (kg) and v is speed (m/s).

Oxford AQA IGCSE Physics: Revision notes

Key facts

Work done $W = F \times d$ , with $d$ in the direction of the force.
Elastic energy $E_e = \tfrac{1}{2} k e^2$ ; gravitational energy $E_p = m g h$ ; kinetic energy $E_k = \tfrac{1}{2} m v^2$ .
Doubling speed quadruples kinetic energy.
Power $P = E \div t = W \div t$ .
Work done against friction transfers energy by heating.

Work done

Work done is the energy transferred when a force moves an object.

Here $W$ is the work done (J), $F$ is force (N) and $d$ is the distance moved in the direction of the force (m). Work done against friction transfers energy by heating, so the object and its surroundings warm up.

A constant force of 50 N over 4 m: the shaded area under the graph is the work done, 50 × 4 = 200 J.

Work done $W = F \times d$

Worked example

A force of 50 N pushes a box 4 m along the floor. How much work is done?

1
Use $W = F \times d$ .
2
$W = 50 \times 4$ .
3
$W = 200$ J.

Work is done against friction. Where does the energy go?

Elastic potential energy

Energy stored in a stretched spring is $E_e = \tfrac{1}{2} k e^2$ .

Here $E_e$ is elastic potential energy (J), $k$ the spring constant (N/m) and $e$ the extension (m). It only applies within the limit of proportionality.

k = 100spring constant (N/m)

Elastic energy against extension: change the spring constant k

Worked example

A spring with a spring constant of 50 N/m is stretched by 0.1 m. How much energy is stored?

1
Use $E_e = \tfrac{1}{2} k e^2$ .
2
$E_e = 0.5 \times 50 \times 0.1^2$ .
3
$E_e = 0.5 \times 50 \times 0.01 = 0.25$ J.

If the extension of a spring is doubled (within the limit of proportionality), what happens to the stored energy?

Gravitational potential energy

Gravitational potential energy is $E_p = m \times g \times h$ .

The gravitational potential energy is the energy an object has because of its height above a reference point. Here $m$ is mass (kg), $g$ the gravitational field strength (N/kg) and $h$ the height (m).

GPE of a 2 kg object (g = 10 N/kg): the energy is directly proportional to height

Worked example

A 2 kg book is lifted 5 m. Taking g = 10 N/kg, how much gravitational potential energy does it gain?

1
Use $E_p = m \times g \times h$ .
2
$E_p = 2 \times 10 \times 5$ .
3
$E_p = 100$ J.

A 3 kg object is raised 2 m. Taking g = 10 N/kg, what is the increase in GPE?

Kinetic energy

Kinetic energy is $E_k = \tfrac{1}{2} m v^2$ , so doubling the speed quadruples it.

The kinetic energy of an object is the energy it has because it is moving. Here $m$ is mass (kg) and $v$ is speed (m/s). Because speed is squared, a small increase in speed gives a much larger increase in stopping energy, which is why higher speeds are so dangerous.

m = 2mass (kg)

Kinetic energy against speed: change the mass with the slider

Worked example

A 1500 kg car travels at 20 m/s. Find its kinetic energy, then at 40 m/s.

1
At 20 m/s: $E_k = 0.5 \times 1500 \times 400 = 300\,000$ J.
2
At 40 m/s: $E_k = 0.5 \times 1500 \times 1600 = 1\,200\,000$ J.
3
Doubling the speed multiplied the energy by $1\,200\,000 \div 300\,000 = 4$ .

A cyclist triples her speed. By what factor does her kinetic energy increase?

Power

Power is the rate of transferring energy or doing work.

Here $P$ is the power (W), $E$ is energy transferred (J), $W$ is work done (J) and $t$ is time (s). A more powerful device transfers the same energy in less time, or more energy in the same time.

Work done against time: the gradient is the power. The motor does 600 J in 20 s, so P = 30 W.

Power $P = \dfrac{E}{t}$ or $P = \dfrac{W}{t}$

Worked example

A motor does 600 J of work in 20 s. What is its power?

1
Use $P = W \div t$ .
2
$P = 600 \div 20$ .
3
$P = 30$ W.

Two machines each lift the same load by the same height. Machine A takes 5 s and machine B takes 10 s. Which has the greater power?

Try an exam question

A 1000 kg car travels at 10 m/s. Calculate its kinetic energy and state what happens to the kinetic energy if the speed doubles.

[4 marks]

That's the notes covered.

Carry on to the next subtopic.