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Physics · Energy

Power

Define power as the rate of transfer of energy or of doing work, and use \(P = E \div t\) and \(P = W \div t\).

  • 6 key terms
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Teacher resources

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Student handouts

The same files the students see, to print or hand out.

Warm-up

Answer each one, then check.

  1. 1

    What is the unit of energy?

    Show answerHide answer

    Joule

  2. 2

    What is the unit of time used in power calculations?

    Show answerHide answer

    Seconds

  3. 3

    Convert 2 minutes to seconds.

    Show answerHide answer

    120 s

  4. 4

    What is work done?

    Show answerHide answer

    Energy transferred by a force

  5. 5

    Write 1.5 kW in watts.

    Show answerHide answer

    1500 W

Learning Objectives

  1. 1Define power.
  2. 2Recall and apply both power equations.
  3. 3Explain that 1 W is 1 J/s.
  4. 4Compare two devices doing the same work at different rates.

POWER

Power is the rate at which energy is transferred or the rate at which work is done.

\(P = \dfrac{E}{t}\) and \(P = \dfrac{W}{t}\). Power is in watts (W), energy and work in joules (J), time in seconds (s). 1 W = 1 J/s.

Power Equations

Learn both and the units.

  • \(P = \dfrac{E}{t}\)

    Meaning: Power is energy transferred divided by time. Units: W, J, s

  • \(P = \dfrac{W}{t}\)

    Meaning: Power is work done divided by time. Units: W, J, s

Energy Transferred by a Kettle

A kettle transfers 360 000 J of energy in 2.0 minutes. Calculate its power.

Show the solutionHide the solution
  1. 1 Convert time \(2.0\) min \(= 120\) s
  2. 2 Substitute \(P = 360\,000 \div 120\)
  3. 3 Answer \(P = 3000\) W

Answer3000 W (3 kW)

Work and Power of a Climber

A person of mass 60 kg climbs 3.0 m in 5.0 s. g = 9.8 N/kg. Calculate the power.

Show the solutionHide the solution
  1. 1 Work done = energy gained \(W = mgh = 60 \times 9.8 \times 3.0 = 1764\) J
  2. 2 Power \(P = W \div t = 1764 \div 5.0\)
  3. 3 Answer \(P = 352.8\) W

AnswerAbout 350 W (2 s.f.)

Rearranging

A 1500 W heater is switched on. How long does it take to transfer 450 000 J?

Show the solutionHide the solution
  1. 1 Rearrange \(t = E \div P\)
  2. 2 Substitute \(t = 450\,000 \div 1500\)
  3. 3 Answer \(t = 300\) s

Answer300 s (5 minutes)

Watch Out

Common ways to lose marks.

  • Time in seconds

    Always convert minutes and hours to seconds.

  • Power, not energy

    Power is a rate: it tells you how quickly, not how much.

  • Unit

    1 W is 1 joule per second, not 1 joule.

Fair Race

Two students run up the same flight of stairs. Student A takes 8.0 s and student B takes 5.0 s. Both have a weight of 600 N and the stairs are 3.0 m high. Calculate the work done and the power of each student.

1. Work done first.

2. Then divide by each time.

A good answer shows: Work done by each = 600 × 3.0 = 1800 J. Power A = 225 W. Power B = 360 W.

Can I...?

  1. 1Define power.
  2. 2Use \(P = E \div t\).
  3. 3Use \(P = W \div t\).
  4. 4Convert minutes to seconds.
  5. 5Explain what a watt is.
  6. 6Rearrange for time.
  7. 7Compare two devices with the same work.
  8. 8Give the unit.

Summary & Exam Focus

  • \(P = E \div t\) or \(P = W \div t\).
  • 1 W = 1 J/s.
  • Higher power means energy transferred faster.
  • Time must be in seconds.

Exam focus

A motor transfers 6000 J of energy in 30 s. Calculate its power. (2 marks) (2 marks)

Write the equation, substitute, and give the unit W.

Key terms

The vocabulary this lesson expects you to use. Each one is linked from the first place it appears above.

Power
The rate at which energy is transferred or work is done.
Watt
The unit of power; one joule per second.
Work done
Energy transferred by a force moving an object.
Rate
How much something changes in each unit of time.
Kilowatt
1000 watts.
Energy transferred
The amount of energy moved from one store to another.

Questions and answers

11 questions set on this lesson, with the mark schemes and model answers open.

1. Exam question Calculate 2 marks Easier

A motor transfers 6000 J of energy in 30 s. Calculate the power of the motor. Use the equation: power = energy transferred ÷ time

Mark scheme — 2 marks available

  • Correct substitution — 1 mark
  • 200 W — 1 mark

Model answer

\(6000 \div 30 = 200\) W

2. Exam question Calculate 2 marks Easier

A machine does 900 J of work in 12 s. Calculate the power.

Mark scheme — 2 marks available

  • Correct substitution — 1 mark
  • 75 W — 1 mark

Model answer

\(900 \div 12 = 75\) W

3. Exam question Compare 3 marks Easier

Motor A lifts a 20 N weight through 3.0 m in 6.0 s. Motor B lifts the same weight through the same height in 3.0 s. Compare the power of the two motors. Show your calculations.

Mark scheme — 3 marks available

  • Work done = 60 J — 1 mark
  • A = 10 W and B = 20 W — 1 mark
  • B has twice the power — 1 mark

Model answer

Work done = 20 × 3.0 = 60 J. Power A = 60 ÷ 6.0 = 10 W. Power B = 60 ÷ 3.0 = 20 W. Motor B has twice the power of motor A.

4. Exam question State 1 mark Easier

State what is meant by a power of 1 watt.

Mark scheme — 1 mark available

  • 1 joule per second — 1 mark

Model answer

An energy transfer of 1 joule each second.

5. Exam question Calculate 4 marks Easier

A person of mass 60 kg climbs stairs of height 3.0 m in 5.0 s. Calculate the power developed by the person. Gravitational field strength = 9.8 N/kg. Give your answer to 2 significant figures.

Mark scheme — 4 marks available

  • Work done = mgh — 1 mark
  • 1764 J — 1 mark
  • 352.8 W — 1 mark
  • 350 W — 1 mark

Model answer

\(W = 60 \times 9.8 \times 3.0 = 1764\) J; \(P = 1764 \div 5.0 = 352.8\) W = 350 W

6. Exam question Calculate 2 marks Easier

A 1500 W heater is switched on until it has transferred 450 000 J. Calculate the time it is switched on for.

Mark scheme — 2 marks available

  • Rearranges to t = E ÷ P — 1 mark
  • 300 s — 1 mark

Model answer

\(t = 450\,000 \div 1500 = 300\) s

7. Multiple choice 1 mark Easier

Power is the rate of...

  1. A energy transfer Correct
  2. B energy storage
  3. C force
  4. D movement

Why: Power is how quickly energy is transferred.

8. Multiple choice 1 mark Core

The unit of power is...

  1. A joule
  2. B watt Correct
  3. C newton
  4. D second

Why: The watt (W).

9. Multiple choice 1 mark Core

A 100 W lamp transfers how much energy in 10 s?

  1. A 10 J
  2. B 100 J
  3. C 1000 J Correct
  4. D 10 000 J

Why: \(E = Pt = 100 \times 10\).

10. Multiple choice 1 mark Core

Two motors do the same work. Motor X takes half the time. Motor X has...

  1. A half the power
  2. B the same power
  3. C four times the power
  4. D twice the power Correct

Why: Power = work ÷ time.

11. Multiple choice 1 mark Stretch

An appliance is rated 2 kW. In watts this is...

  1. A 2000 W Correct
  2. B 20 W
  3. C 200 W
  4. D 20 000 W

Why: 1 kW = 1000 W.