Work, power and efficiency Cambridge International AS & A Level Physics revision
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In plain words
Work is how a force transfers energy, and it only counts the part of the force that points along the motion. Power is how fast that transfer happens. And because no machine is perfect, efficiency tells you how much of the energy you put in ends up doing something useful.
4 things to know
- Work done = force × displacement in the direction of the force: W = Fs cos θ, where θ is the angle between the force and the displacement. Units: joules.
- Energy is conserved. It can be transferred from one form to another, but the total stays the same.
- Power = work done ÷ time (or energy transferred ÷ time), in watts. Because work = force × distance, power is also force × velocity: P = Fv.
- Efficiency = useful energy (or power) output ÷ total energy (or power) input.
Worked example
A 1000 kg car travels at a constant 20 m/s against a total resistive force of 500 N. Find the power its engine delivers to the wheels.
- Constant speed means the driving force equals the resistive force: 500 N.
- P = Fv.
- = 500 × 20 = 10 000 W = 10 kW.
Tips and tricks
- A force at right angles to the motion does no work: cos 90° = 0.
- Efficiency can never be more than 1 (100%). If yours is, you have the fraction upside down.
It lands in your notebook with its questions as flashcards.
Work, power and efficiency: 5 questions and answers
These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.
How much work is done by a 20 N force moving an object 3.0 m in the direction of the force?
W = Fs.
A force acts at right angles to the direction of motion. How much work does it do?
There is no component of the force along the displacement.
An engine provides a driving force of 2000 N at a speed of 15 m/s. What is its power output?
P = Fv.
A machine has an input of 500 J and a useful output of 400 J. What is its efficiency?
400 ÷ 500.
A motor does 600 J of work in 20 s. What is its power?
600 ÷ 20.
Quiz
5 questions
Tap an answer and you’ll see straight away whether it’s right, and why.
Worksheet
3 questions, 7 marks. Write your answers on paper, then check them.
Work, power and efficiency
Cambridge International AS & A Level Physics 9702 · 7 marks · papermunch.org
Name ______________________________ Date ______________
A 50 N force acts at 60° to the direction of motion as an object moves 4.0 m. Find the work done.[2]
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100 J. 50 × 4.0 × cos 60°.
A motor lifts a 300 N load through 5.0 m in 10 s. Its input power is 200 W. Find its efficiency.[3]
Show answerHide answer
75%. Output power = 1500 J ÷ 10 s = 150 W.
A crane lifts a 2000 N load at a steady 0.50 m/s. Find its useful output power.[2]
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1000 W.
Answers: Work, power and efficiency
- 1. 100 J. 50 × 4.0 × cos 60°.
- 2. 75%. Output power = 1500 J ÷ 10 s = 150 W.
- 3. 1000 W.