💪 A force moves something
Step 1: work done = force × distance moved in the direction of the force.
Step 2: power = work done ÷ time taken.
Work and Power » Power
What you'll learn this session
Study time: 30 minutes
Edexcel spec: 4.16, 4.17
- What power means: the rate of transfer of energy, or the rate of doing work
- How to use power = work done ÷ time taken, and how to rearrange it
- How to solve two-step problems where you find the work done first
- How you could measure your own power by running up stairs
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Unlock This CourseWhat is power?
Two friends carry identical boxes up the same flight of stairs. One takes 10 seconds and the other takes 30 seconds. They do the same amount of work on the boxes, because the weight of the boxes and the height are the same. But the first friend does the work three times as quickly. In physics we say the first friend has three times the power.
You met power in the electricity lessons as the energy an appliance transfers each second. The same idea works for any energy transfer, including work done by a force. The specification gives two ways to describe it:
- power is the rate of transfer of energy
- power is the rate of doing work
These say the same thing, because doing work is one way of transferring energy. Doing 500 J of work transfers 500 J of energy.
Power is measured in watts (W). One watt is one joule per second. So a person working at 200 W transfers 200 J of energy every second. Large powers are given in kilowatts (kW), where 1 kW = 1000 W.
Key terms:
- Rate: how quickly something happens. A rate is always an amount divided by a time.
- Rate of doing work: the work done each second. This is the power.
The power equation
power = work done ÷ time taken
P = W ÷ t
This equation is given on the formulae page of the exam paper, so you do not have to memorise it. You do have to use it with the right units.
| Quantity | Symbol | Unit |
|---|---|---|
| power | P | watt (W) |
| work done (energy transferred) | W | joule (J) |
| time taken | t | second (s) |
Take care with the letter W. In the equation, W stands for work done. After a number, W is the unit watt.
Worked example 1: finding power
An athlete on a rowing machine does 9000 J of work in 60 s. Calculate her power.
P = W ÷ t
P = 9000 ÷ 60
P = 150 W
Rearranging the equation
| To find | Use |
|---|---|
| power | P = W ÷ t |
| work done | W = P × t |
| time taken | t = W ÷ P |
Worked example 2: finding work done
A motor has a power of 2 kW. Calculate the work it does in 30 s.
Convert first: 2 kW = 2000 W
W = P × t
W = 2000 × 30
W = 60 000 J
Worked example 3: finding time
An electric drill has a power of 500 W. Calculate how long it takes to transfer 45 000 J of energy.
t = W ÷ P
t = 45 000 ÷ 500
t = 90 s
Two-step problems
Many exam questions do not give you the work done. You have to calculate it first, then divide by the time. There are two common starting points.
🏔 Something is lifted
Step 1: work done = GPE gained = m × g × h. If you are given the weight, use weight × height.
Step 2: power = work done ÷ time taken.
Worked example 4: force and distance first
A boy drags a kayak 30 m up a beach in 40 s. He pulls with a force of 200 N in the direction the kayak moves. Calculate his power.
W = F × d = 200 × 30 = 6000 J
P = W ÷ t = 6000 ÷ 40
P = 150 W
Worked example 5: m × g × h first
A pump lifts 300 kg of water up 8 m from a well in 2 minutes. Calculate the power of the pump.
W = m × g × h = 300 × 10 × 8 = 24 000 J
Convert the time: 2 minutes = 2 × 60 = 120 s
P = W ÷ t = 24 000 ÷ 120
P = 200 W
Comparing people and machines
A machine usually does not do more work than a person on the same job. It does the same work in less time. Suppose 600 kg of bricks must be lifted 2 m onto a platform. The work done is 600 × 10 × 2 = 12 000 J, whoever does it.
| Who lifts the bricks | Work done | Time taken | Power |
|---|---|---|---|
| A worker carrying a few bricks at a time | 12 000 J | 10 minutes = 600 s | 12 000 ÷ 600 = 20 W |
| An electric hoist | 12 000 J | 24 s | 12 000 ÷ 24 = 500 W |
The hoist has 25 times the power, so it does the job in one twenty-fifth of the time (24 s instead of 600 s). There are two fair ways to compare power:
- same work done: the one that takes less time is more powerful
- same time: the one that does more work is more powerful
Measuring your own power
Suggested investigation (optional)
You can find your own power by running up a flight of stairs. You need three measurements.
- Your weight. Find your mass in kg on bathroom scales, then multiply by 10 N/kg.
- The vertical height of the stairs. Measure the height of one step with a ruler and multiply by the number of steps.
- The time taken. Ask a helper to time your run from the bottom step to the top with a stopwatch.
Then work done = weight × vertical height, and power = work done ÷ time taken. Repeat the run a few times and take a mean of the times. Wear shoes with good grip and make sure the stairs are clear and dry.
Worked example 6: power on the stairs
A student of mass 55 kg runs up 20 steps in 5.0 s. Each step is 0.15 m high.
weight = 55 × 10 = 550 N
vertical height = 20 × 0.15 = 3.0 m
work done = 550 × 3.0 = 1650 J
power = 1650 ÷ 5.0 = 330 W
You can do the same thing with your arms by lifting objects of different weights. Lift a 20 N bag from the floor onto a shelf 0.5 m high, 30 times in 60 s. Each lift does 20 × 0.5 = 10 J of work, so the total is 300 J and your power is 300 ÷ 60 = 5 W. If you manage the same with a 40 N bag, the work is 600 J and your power is 10 W.
Common mistakes
- Leaving time in minutes. Time must be in seconds. Multiply minutes by 60.
- Leaving power in kilowatts. Multiply by 1000 to get watts before you calculate.
- Using the length of the stairs or slope. When something is lifted, use the vertical height.
- Thinking more power means more work. A more powerful machine does the same job in less time. The work done can be the same.
Exam-style question
A goods lift in a furniture shop carries a sofa to an upper floor. The lift and the sofa have a total mass of 800 kg. The lift rises 15 m in 12 s at a steady speed.
(a) State what is meant by the term power. [1 mark]
(b) Calculate the work done in raising the lift and the sofa. [2 marks]
(c) Calculate the power needed to raise the lift and the sofa. Give your answer in kilowatts. [3 marks]
(d) The motor is replaced by one that raises the same load through the same height with a power of 8 kW. Calculate the time this lift takes. [3 marks]
(e) A student says that the first motor does more work on this journey because it is more powerful. Explain why the student is wrong. [2 marks]
Model answer
(a) Power is the rate of doing work, or the rate of transfer of energy. (1)
(b) work done = m × g × h = 800 × 10 × 15 (1) = 120 000 J (1)
(c) P = W ÷ t = 120 000 ÷ 12 (1) = 10 000 W (1) = 10 kW (1)
(d) 8 kW = 8000 W (1). t = W ÷ P = 120 000 ÷ 8000 (1) = 15 s (1)
(e) Both motors lift the same load through the same height, so they do the same work, 120 000 J. (1) The first motor does this work in less time, so it transfers energy at a greater rate. (1)
Exam tip
In a 'lift' question like this, write the work done on its own line before you touch the power equation. Parts (c), (d) and (e) all reuse the 120 000 J, so getting it clearly on the page saves time and keeps your method marks safe.