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7.1.6Energy – Forces Doing Work

Power

5 min read 9 parts Lesson 7 of 14 1 quiz

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Section 1 of 9What power is

Power is the rate at which energy is transferred, or equivalently the rate at which work is done. A powerful machine transfers a lot of energy each second. Two people can lift the same box to the same shelf, doing the same work, but the one who does it in half the time has twice the power.

Power is a scalar measured in watts (W). One watt is one joule per second: 1 W = 1 J s−1. Larger units are the kilowatt (1 kW = 1000 W) and megawatt (1 MW = 106 W).

Section 2 of 9The equations

1
power = work done ÷ time taken, P = W ÷ t
2
power = energy transferred ÷ time taken, P = E ÷ t
3
where P is power in watts (W), W or E is work done or energy transferred in joules (J) and t is time in seconds (s).
  • RearrangedE = P t and t = E ÷ P.
  • Always convert minutes and hours into seconds before substituting, unless working in kilowatt-hours.
4
For a moving object pushed by a steady force F at speed v, the power is P = Fv,
  • but at this level you are mostly expected to use the energy and time form.

Section 3 of 9Typical powers

A human climbing stairs outputs about 200 W.

1
A kettle is about 2000 W (2 kW).
2
A car engine delivers tens of kilowatts, and a large power station produces about 1000 MW.
3
A small LED bulb is about 5 W, a mobile phone charger about 10 W, and a household oven about 3 kW.
4
Appliance ratings on labels give the power drawn when running.

The household bill uses a unit of energy called the kilowatt-hour (kWh): the energy transferred by a 1 kW device in 1 hour. 1 kWh = 1000 W × 3600 s = 3.6 × 106 J.

Section 4 of 9Power, work and efficiency

Power links closely with other ideas.

Power, work and efficiency
When a motor lifts a weight at constant speed, its useful power equals the GPE gained per second: P = mgh ÷ t.
Because energy is wasted, the electrical power input is bigger than the useful power output, and the efficiency is the ratio of the two.
A machine rated at 500 W that is 60% efficient delivers 300 W of useful power.

On an energy-time graph, the gradient is the power. A steeper line means a faster rate of transfer, and a straight line means constant power.

Section 5 of 9Common problem types

You may be asked to compare two machines doing the same job in different times, to calculate how long a heater takes to transfer a given amount of energy, or to work out the cost of running an appliance (energy in kWh × price per kWh).

Common problem types
In each case: identify the energy or work, find the time in seconds, then apply P = E ÷ t.
State the unit with the answer: W for power, J for energy, s for time.
If the numbers are large, giving the answer in kW or MW is neater.

Section 6 of 9Power in everyday devices and cost

The kilowatt-hour is how electricity is sold.

1
To find cost, multiply energy in kWh by the price per kWh.
2
A 3 kW electric shower used for 10 minutes uses 3 × (10 ÷ 60) = 0.5 kWh; at 28 pence per kWh that costs 14 pence.
3
A 10 W LED lamp left on for 10 hours uses only 0.1 kWh.
4
Comparing these helps people choose where to save energy: high-power devices used for long periods,
  • such as heaters, matter far more than small chargers.

Power also matters for choosing equipment.

1
A winch that must raise a 500 kg load through 20 m in 40 s needs a useful output of 500 × 9.8 × 20 ÷ 40 = 2450 W.
2
If its motor is 70% efficient it must be supplied with 3500 W.
3
Two motors can transfer the same total energy, but the one with more power does it faster.
4
Do not confuse "more powerful" with "more energy": a 100 W lamp on for a minute uses less energy than a 10 W lamp on for an hour.

Section 7 of 9Worked examples

  1. A student of mass 55 kg climbs a flight of stairs 3.5 m high in 5.0 s. Calculate the useful power. (g = 9.8 N kg−1)

  2. A 2.4 kW kettle runs for 3 minutes. How much energy does it transfer?

  3. A pump needs to raise 600 kg of water through 8.0 m. If the pump has a useful power of 400 W, how long does it take?

Section 8 of 9Key terms

TermMeaning
PowerRate of energy transfer or rate of doing work.
WattUnit of power, one joule per second.
Kilowatt-hourEnergy transferred by a 1 kW device in one hour (3.6 MJ).
Useful powerPower transferred to the desired store.
RatingThe power an appliance is designed to use.

Section 9 of 9Exam technique

1
Using minutes or hours in P = E ÷ t without converting to seconds.
2
Confusing power and energywatts are not joules.
3
Forgetting to include g when the work comes from lifting a mass.
4
Saying power is the "amount of energy"; it is the rate of transfer.
5
Mixing up kW and kWhkW measures power, kWh measures energy.
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