Work and powerIB MYP Physics: Revision notes
Section 1
Work done
Work is done when a force moves an object. The work done is the force multiplied by the distance moved in the direction of the force:
W = F × s
where W is work in joules (J), F is force in newtons (N) and s is distance in metres (m). So 1 J = 1 N m: one joule is the work done when a force of 1 N moves an object 1 m.
Worked example: a force of 40 N pulls a sledge 5.0 m. W = 40 × 5.0 = 200 J.
Only the distance moved in the direction of the force counts. A force acting at right angles to the movement, such as the upward force when you carry a bag horizontally, does no work.
Section 2
Work is energy transferred
When work is done, energy is transferred. The work done equals the energy transferred, in joules.
- Lifting a 10 kg box (weight 100 N) up 3.0 m: W = 100 × 3.0 = 300 J, so its gravitational potential energy increases by 300 J.
- Pushing a crate at steady speed across a rough floor: the work done against friction is transferred to thermal energy, which warms the crate and floor.
So you can say: energy transferred (J) = work done (J).
Section 3
Power
Power is the rate of doing work, or the rate at which energy is transferred:
P = W ÷ t = E ÷ t
where P is power in watts (W), W or E is work or energy in joules and t is time in seconds. 1 watt = 1 joule per second (1 W = 1 J/s).
Rearranged: W = P × t and t = W ÷ P.
Worked example: a motor does 600 J of work in 12 s. P = 600 ÷ 12 = 50 W.
Two machines can do the same work, but the more powerful one does it in a shorter time.
Always change minutes and hours into seconds before using P = W ÷ t. For example, 3 minutes is 180 s.
Section 4
Typical power ratings
Power is often large, so we use larger units:
- 1 kilowatt (kW) = 1000 W
- 1 megawatt (MW) = 1 000 000 W
Typical values:
- LED light bulb: about 8 W
- Person running upstairs: a few hundred watts
- Electric kettle: about 2 kW
- Car engine: about 70 kW
- Large wind turbine: about 2 MW
- Power station: hundreds of MW
Section 5
Calculations with kW and MW
Convert to watts first, then calculate.
- 3.5 kW = 3.5 × 1000 = 3500 W
- 2.0 MW = 2.0 × 1 000 000 = 2 000 000 W
Worked example 1: a 2.0 kW kettle runs for 3 minutes. t = 3 × 60 = 180 s, so E = P × t = 2000 × 180 = 360 000 J.
Worked example 2: a lift motor does 240 000 J of work in 30 s. P = 240 000 ÷ 30 = 8000 W = 8.0 kW.
Worked example 3: a power station with an output of 500 MW transfers 500 000 000 J of electrical energy every second.
Do not forget to convert. 8000 W is 8.0 kW, not 8000 kW.
Must know
- W = F × s; 1 J = 1 N m
- Work done = energy transferred
- P = W ÷ t = E ÷ t; 1 W = 1 J/s
- 1 kW = 1000 W; 1 MW = 1 000 000 W
- Same work in less time means greater power
That's the notes covered.
Carry on to the next subtopic.
Exam questions on Work and power
- A removal worker in Lagos pushes a crate across a warehouse floor with a constant horizontal force of 150 N. The crate moves 8.0 m in 20 s at a steady speed.The crate moves at a steady speed, so its kinetic energy does not change. Explain where the energy transferred by the worker goes.2 marks
- A motor in a lift at an office tower in Singapore raises the lift car and its passengers, which have a total weight of 8000 N, through a height of 30 m in 40 s.Explain why the new motor has a greater power than the original motor even though it does not do more work.2 marks
- A student investigates whether carrying a bag changes the power she develops when she runs up a staircase. The staircase rises 4.0 m vertically and the student has a weight of 500 N. Without a bag, she completes the climb in 5.2 s, 4.8 s and 5.0 s on three trials, timed with a stopwatch.Identify the independent variable, the dependent variable and one control variable in an investigation into the effect of carrying a bag on her power.3 marks
Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).