Work, Power & Efficiency Notes

Edexcel GCSE Physics: Revision notes

Key facts

Work done = force × distance moved in the direction of the force: $E = F \times d$ . Work done in joules equals energy transferred in joules.
A system's energy changes by work done by forces, electrical equipment or heating.
Energy is always dissipated: it spreads out, usually as thermal energy, and becomes less useful.
Power = energy transferred ÷ time: $P = \dfrac{E}{t}$ . 1 watt = 1 joule per second.
Efficiency = useful energy transferred ÷ total energy supplied. No device is 100% efficient.

Work done $E = F \times d$
Power $P = \dfrac{E}{t}$

Work done

Work done is the energy transferred when a force moves an object, found by multiplying force by distance.

Work done is the energy transferred when a force causes something to move. $E$ is in joules (J), $F$ in newtons (N) and $d$ in metres (m), measured in the direction of the force.

Work done and energy transferred are the same quantity. If there is no movement in the direction of the force, no work is done by that force.

A constant force of 20 N over 3 m: the shaded area under the graph is the work done, 20 × 3 = 60 J.

Work done (J) $E = F \times d$

Worked example

A force of 20 N pushes a box 3 m. How much work is done?

1
Write the equation: $E = F \times d$ .
2
Substitute: $E = 20 \times 3$ .

A 50 N force moves a trolley 4 m in the direction of the force. How much work is done?

Changing a system's energy

Energy changes by work done by forces, by electrical equipment or by heating.

In a closed system, energy moves between stores but the total does not change.

Two related equations:

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

$KE = \tfrac{1}{2} \times m \times v^2$

m = 2mass (kg)

Kinetic energy rises with the square of the speed. Drag m to change the mass.

Work done by forces

Lifting, pushing, stretching

Electrical equipment

Electrical energy transferred to other stores

Heating

Thermal energy transferred directly, without mechanical work

A kettle heats water with its element. Which route changes the energy of the water?

Wasted energy

In every energy change some energy is dissipated into the surroundings, where it is no longer useful.

Energy is dissipated in all system changes: it ends up in less useful stores, typically the thermal store of the surroundings.

Mechanical processes waste energy when they cause a rise in temperature, such as friction between moving parts. Dissipated energy is not destroyed, because energy is always conserved.

1
Energy supplied
The total put into the device.
2
Useful transfer
The part that does the job.
3
Dissipated
Spread out as thermal energy in the surroundings.

Energy supplied is shared out

Is dissipated energy destroyed?

Power

Power is the rate at which energy is transferred: energy divided by time, in watts.

Power is the rate at which energy is transferred or work is done. It is in watts (W), with energy in joules (J) and time in seconds (s). One watt is one joule per second.

Energy transferred against time: the gradient is the power. The motor transfers 300 J in 5 s, so P = 60 W.

Power (W) $P = \dfrac{E}{t}$

Worked example

A motor transfers 300 J of energy in 5 s. What is its power?

1
Write the equation: $P = E \div t$ .
2
Substitute: $P = 300 \div 5$ .

A lamp transfers 600 J in 20 s. What is its power?

Efficiency

Efficiency is the useful energy transferred divided by the total energy supplied, as a decimal or percentage.

Efficiency compares the useful energy a device transfers with the total energy supplied to it. Give it as a decimal from 0 to 1, or as a percentage.

No real device is 100% efficient, because some energy is always dissipated.

Energy for the device in the worked example: 200 J supplied, 50 J useful, 150 J wasted. Efficiency = 50 ÷ 200 = 0.25.

Efficiency $\dfrac{\text{useful energy transferred}}{\text{total energy supplied}}$

Efficiency example

A device is supplied with 200 J and usefully transfers 50 J. What is its efficiency?

1
Write the equation: efficiency = useful energy ÷ total energy.
2
Substitute: $50 \div 200 = 0.25$ .

Why can no real device be 100% efficient?

Try an exam question

A motor is supplied with 500 J of energy in 10 s and usefully transfers 400 J. Calculate its power and its efficiency.

[4 marks]

That's the notes covered.

Carry on to the next subtopic.