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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 \(P = W \div t\).
Warm-up
Answer each one, then check.
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1
What is the unit of energy?
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Joule
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2
What is the unit of time used in power calculations?
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Seconds
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3
Convert 2 minutes to seconds.
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120 s
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4
What is work done?
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Energy transferred by a force
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5
Write 1.5 kW in watts.
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1500 W
Learning Objectives
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.
Same Work, Different Power
Same work, half the time means twice the power.
Power Equations
Learn both and the units.
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\(P = \dfrac{E}{t}\)
Meaning: Power is energy transferred divided by time. Units: W, J, s
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\(P = \dfrac{W}{t}\)
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.
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- 1 Convert time \(2.0\) min \(= 120\) s
- 2 Substitute \(P = 360\,000 \div 120\)
- 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.
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- 1 Work done = energy gained \(W = mgh = 60 \times 9.8 \times 3.0 = 1764\) J
- 2 Power \(P = W \div t = 1764 \div 5.0\)
- 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?
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- 1 Rearrange \(t = E \div P\)
- 2 Substitute \(t = 450\,000 \div 1500\)
- 3 Answer \(t = 300\) s
Answer300 s (5 minutes)
Watch Out
Common ways to lose marks.
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Time in seconds
Always convert minutes and hours to seconds.
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Power, not energy
Power is a rate: it tells you how quickly, not how much.
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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...?
- 1Define power.
- 2Use \(P = E \div t\).
- 3Use \(P = W \div t\).
- 4Convert minutes to seconds.
- 5Explain what a watt is.
- 6Rearrange for time.
- 7Compare two devices with the same work.
- 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.
Practice questions
Have a go at each one before you open its answer.
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Question 1 Calculate 2 marks
A motor transfers 6000 J of energy in 30 s. Calculate the power of the motor. Use the equation: power = energy transferred ÷ time
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Model answer
\(6000 \div 30 = 200\) W
Mark scheme
- Correct substitution — 1 mark
- 200 W — 1 mark
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Question 2 Calculate 2 marks
A machine does 900 J of work in 12 s. Calculate the power.
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Model answer
\(900 \div 12 = 75\) W
Mark scheme
- Correct substitution — 1 mark
- 75 W — 1 mark
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Question 3 Compare 3 marks
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.
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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.
Mark scheme
- Work done = 60 J — 1 mark
- A = 10 W and B = 20 W — 1 mark
- B has twice the power — 1 mark
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Question 4 State 1 mark
State what is meant by a power of 1 watt.
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Model answer
An energy transfer of 1 joule each second.
Mark scheme
- 1 joule per second — 1 mark
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Question 5 Calculate 4 marks
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.
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Model answer
\(W = 60 \times 9.8 \times 3.0 = 1764\) J; \(P = 1764 \div 5.0 = 352.8\) W = 350 W
Mark scheme
- Work done = mgh — 1 mark
- 1764 J — 1 mark
- 352.8 W — 1 mark
- 350 W — 1 mark
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Question 6 Calculate 2 marks
A 1500 W heater is switched on until it has transferred 450 000 J. Calculate the time it is switched on for.
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Model answer
\(t = 450\,000 \div 1500 = 300\) s
Mark scheme
- Rearranges to t = E ÷ P — 1 mark
- 300 s — 1 mark
Quick check
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Power is the rate of...
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A: energy transfer
Power is how quickly energy is transferred.
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The unit of power is...
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B: watt
The watt (W).
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A 100 W lamp transfers how much energy in 10 s?
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C: 1000 J
\(E = Pt = 100 \times 10\).
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Two motors do the same work. Motor X takes half the time. Motor X has...
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D: twice the power
Power = work ÷ time.
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An appliance is rated 2 kW. In watts this is...
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A: 2000 W
1 kW = 1000 W.
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