Sign up to access the complete lesson and track your progress!
Unlock This CourseIn everyday life, 'work' can mean anything that makes you tired. In physics it has one exact meaning. Work is done when a force moves something in the direction of that force.
Push a pushchair along a path and you do work on it. Lift a bag of cement onto a truck and you do work on it. In both cases a force acts and the object moves the way the force is pointing.
You need to know this relationship by heart. It is not given on the formulae page of the exam paper.
work done = force × distance moved
W = F × d
| Quantity | Symbol | Unit |
|---|---|---|
| Work done | W | joule (J) |
| Force | F | newton (N) |
| Distance moved in the direction of the force | d | metre (m) |
Key terms:
So 1 J = 1 N × 1 m. Lifting something that weighs 1 N straight up through 1 m takes 1 J of work.
Set out every calculation in three lines: the equation, the numbers, then the answer with its unit.
A man pushes a pushchair with a steady force of 30 N. It moves 50 m along a level path. Calculate the work done.
W = F × d
W = 30 × 50
W = 1500 J
A builder lifts a bag of cement of mass 25 kg through a height of 1.2 m onto a truck. Calculate the work done.
To lift something at a steady speed, the upward force must equal its weight. Remember, weight = mass × g.
Force = 25 × 10 = 250 N
W = F × d
W = 250 × 1.2
W = 300 J
The brakes on a mountain bike give a friction force of 150 N. The bike stops in a distance of 12 m. Calculate the work done by the brakes.
W = F × d
W = 150 × 12
W = 1800 J
| To find | Use |
|---|---|
| Work done | W = F × d |
| Force | F = W ÷ d |
| Distance moved | d = W ÷ F |
Check the units before you put any numbers in. The force must be in newtons and the distance in metres to give work in joules.
| Given | Change it to | How |
|---|---|---|
| 2 kN | 2000 N | multiply by 1000 |
| 300 kJ | 300 000 J | multiply by 1000 |
| 40 cm | 0.40 m | divide by 100 |
A horse does 90 000 J of work pulling a cart 200 m along a level road. Calculate the force the horse pulls with.
F = W ÷ d
F = 90 000 ÷ 200
F = 450 N
A tow truck pulls a broken-down car with a force of 2 kN. It does 300 kJ of work. Calculate the distance the car is pulled.
2 kN = 2000 N and 300 kJ = 300 000 J
d = W ÷ F
d = 300 000 ÷ 2000
d = 150 m
The distance in the equation is the distance moved in the direction of the force. That gives two cases where the work done is zero, however hard the force is.
A weightlifter holds a heavy bar still above her head. The force is large but the distance moved is 0 m, so W = F × 0 = 0 J. Her muscles get tired, but no work is done on the bar. The same is true if you push hard on a parked van that does not move.
A waiter carries a tray across a level room. His force on the tray is upwards, but the tray moves sideways. The tray moves no distance in the direction of the upward force, so that force does no work on the tray.
A girl of weight 500 N climbs a staircase. She walks 5 m along the slope of the stairs and ends up 3 m higher than she started. Calculate the work she does against her weight.
Weight acts vertically, so use the vertical distance: 3 m, not 5 m.
W = F × d
W = 500 × 3
W = 1500 J
Doing work is one way of transferring energy. Remember, energy can be transferred mechanically, which means by a force moving something. The amount of energy transferred is exactly the same as the work done:
work done = energy transferred
This is why work and energy share the same unit, the joule. If you do 1500 J of work, you transfer 1500 J of energy. Where the energy goes depends on what the force is working against.
| Situation | Work done | Where the energy goes |
|---|---|---|
| Pushing the pushchair at a steady speed | 1500 J against friction | 1500 J is transferred to the thermal stores of the wheels, the path and the air. The surroundings heat up a little. |
| Lifting the bag of cement | 300 J against its weight | 300 J is transferred to the gravitational store of the bag. |
| Braking on the mountain bike | 1800 J by friction | 1800 J is transferred from the kinetic store of the bike and rider to the thermal stores of the brakes and the surroundings. |
In the first two rows the energy comes from the chemical store of the person doing the work.
Rub your hands together quickly and you can feel this happen. You do work against friction and your hands warm up.
A farmer uses a tractor to drag a log across a level field. The tractor pulls the log with a horizontal force of 600 N. The log moves 40 m at a steady speed.
(a) State the equation linking work done, force and distance moved. [1 mark]
(b) Calculate the work done by the tractor on the log. [2 marks]
(c) State the amount of energy transferred as the log is dragged. [1 mark]
(d) Describe what happens to this energy. [2 marks]
(e) The tractor then lifts the log straight up. The log has a weight of 1500 N and the tractor does 3000 J of work lifting it. Calculate the height the log is lifted through. [3 marks]
(f) The tractor now holds the log still in the air. Explain why no work is being done on the log. [2 marks]
(a) work done = force × distance moved, or W = F × d (1)
(b) W = 600 × 40 (1) = 24 000 J (1)
(c) 24 000 J (1), because work done is equal to energy transferred.
(d) The work is done against friction (1). The energy is transferred to the thermal stores of the log, the ground and the surroundings, so they heat up (1).
(e) d = W ÷ F (1) = 3000 ÷ 1500 (1) = 2 m (1)
(f) The log is not moving, so the distance moved is zero (1). Work done = force × distance moved, so the work done is zero (1).
When a question asks for the energy transferred straight after a work done calculation, as in part (c), no new calculation is needed. Write the same number of joules and say that work done is equal to energy transferred.