Work & Energy
Push, pull, lift or drag: whenever a force moves something, it does work and transfers energy. Master W = F × s, the joule, and why friction always warms things up.
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Work & Energy
In physics, work has an exact meaning, and it is narrower than the everyday one. Work is done whenever a force moves an object, and doing work transfers energy. Lift a box, drag a sledge, stretch a spring: in each case a force does work. Hold a heavy box still until your arms ache and, in the physicist's sense, you have done none at all. This module is about why.
The words for it
Five terms, and the third one is the condition that most work-done questions are really testing:
Work out the work done
A force of 20 N drags a box 5 m in the direction of the force. How much work is done, in joules (J)?
What exactly is a joule?
Work is force multiplied by distance, force is measured in newtons and distance in metres. So what must one joule be?
- The work done when a force of 1 newton moves an object 1 metre, which is why the joule can also be written as a newton-metre
- The work done when a mass of 1 kilogram is lifted
- The energy transferred when a current of 1 amp flows for 1 second
- The energy used when a power of 1 watt runs for 1 hour
When is work actually done?
A force being present is not enough, and neither is the object moving. Both are needed, and the movement has to be along the line the force acts in:
The carried box
A student carries a box weighing 40 N along a level corridor for 10 m, holding it at a constant height. How much work does the upward force she applies do on the box?
- None at all, because the box does not move in the direction of her upward force: it only moves horizontally
- 400 J, because 40 N acts over 10 m
- It depends how fast she walks: the quicker she goes, the more work she does
- 40 J, one joule for each newton of weight
Turning the equation round
W = F s can be rearranged two ways, and exam questions use all three forms: • Force from work and distance: F = W ÷ s • Distance from work and force: s = W ÷ F A quick check that costs nothing: the units have to work out. Joules divided by newtons must give metres, because a joule is a newton-metre. If your rearrangement would give you newtons per joule, you have divided the wrong way round. And always write the unit on the answer. A bare number is not a physical quantity.
Find the distance
A force of 12 N does 60 J of work moving an object along its line of action. How far did the object move, in metres (m)?
Where the energy goes
When work is done against friction, the energy transferred does not end up anywhere useful. It goes into the thermal store of the object and its surroundings, which simply get warmer. Rub your hands together and they warm up. That warmth is the work your muscles did against friction, and there is no mystery about where it went. A car braking from motorway speed is the same process at a much larger scale. All of the car's kinetic energy has to go somewhere, and it goes into the brake discs, which is why they can reach several hundred degrees on a long descent, and why brakes can fade when they get too hot to absorb any more.
The braking cyclist
A cyclist freewheels down a hill and brakes hard at the bottom. Follow the energy through four questions.
- The bike slows from fast to stationary. Where has its kinetic energy gone?
- The brake blocks are noticeably hot afterwards. What does that tell you?
- On a longer, steeper hill the brakes get very much hotter. Why?
- Could the cyclist get that energy back and use it to climb the next hill?
How much work, and where does it go?
- A 10 N force pushes a box 3 m along its own line of action
- A person pushes hard on a wall, which does not move
- A box is carried 10 m along a level corridor at constant height
- A sledge is dragged 20 m across rough ground
- 30 J of work is done on the box
- No work is done, because nothing moves
- No work is done against gravity, because the movement is perpendicular to the lifting force
- Work is done against friction, and the energy ends up in the thermal store
Which are true?
Select ALL THREE statements that are TRUE.
- Doing work and transferring energy are the same thing, which is why both are measured in joules
- A force can act on a moving object and still do no work on it, if the movement is perpendicular to the force
- Energy dissipated to the thermal store has not been destroyed: it has been spread among the surroundings, where it is no longer useful
- If you push hard enough on a stationary wall you do a large amount of work
- Work done against friction destroys energy
- The joule is a unit of force
The work rules
Work done equals the energy _____, which is why both are measured in _____. It is calculated with work = force × distance, where the distance must be measured along the _____ of the force, so a box carried horizontally has no work done on it against gravity. Work done against friction is transferred to the _____ store, warming things up.
Explain the hot brakes
Exam practice. In about 50 words, explain what happens to a car's energy when the driver brakes to a stop, and why the brakes get hot. Include:
- which energy store the car empties as it slows
- what the braking force does, and against what
- where that energy ends up, and why it cannot be recovered and used again