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4.2.1Energy Resources and Energy Transfers

Work Done — Edexcel International GCSE Science Double Award 4SD0 - Physics Revision Notes & Topical Questions

5 min read 9 parts Lesson 8 of 12

📚 Edexcel International GCSE Science Double Award 4SD0 - Physics Hub / Topical Revision
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Part 1 of 7Work as energy transfer

In physics, work done is the energy transferred when a force moves an object.

1
If you push a box across the floor, chemical energy in your muscles is transferred to the box (and to the floor by friction).
2
The amount of energy transferred equals the work done.
3
Work is therefore measured in the same unit as energy, the joule (J).
4
One joule is the work done when a force of 1 newton moves an object through 1 metre in the direction of the force.

Work is a scalar. It has size but no direction, though it can be positive (the force speeds the object up) or negative in advanced work (the force slows it down).

Part 2 of 7The equation

work done = force × distance moved in the direction of the force

W = F d

What the symbols mean: W = work done = energy transferred (J) · F = force (N) · d, s or x = distance moved in the direction of the force (m)

where W is work done in joules (J), F is the force in newtons (N) and d is the distance in metres (m) moved along the line of the force.

The equation
If the force and movement are in the same direction, use the force directly.
If you hold a heavy bag still, you feel tired but you do no work on the bag in the physics sense, because the distance moved is zero.
Carrying a bag horizontally at constant height also does no work against gravity,
  • because the force you exert is upwards while the movement is horizontal and perpendicular to it.

Part 3 of 7Where the energy goes

The work done on an object equals the energy transferred to it. Different situations show different destinations:

1
Lifting a load at steady speed: work done by you becomes gravitational potential energy.
2
Pushing a trolley that speeds up: work done becomes kinetic energy.
3
Pushing a box at steady speed along a rough floor: work done against friction becomes thermal energy in the box and floor.
  • There is no gain in kinetic energy because the speed is constant.
4
Stretching a spring: work done becomes elastic potential energy.

Because work is a way of describing a transfer, we can also say the energy transferred equals the work done by the force when the force does the transferring.

Part 4 of 7Working with forces and distances

Often you are not given F directly.

Working with forces and distances
For a lift at constant speed the force needed equals the weight, W = mg, where m is mass in kg and g is 9.8 N kg−1.
So the work done in lifting through height h is mgh, which links directly to the gravitational potential energy equation of the next sub-topic.
For friction, the work done by the pushing force equals the frictional force multiplied by the distance moved, provided the speed is steady and so the pushing force matches friction.

On a force-distance graph, the area under the line is the work done. A constant force gives a rectangle; a force that grows steadily, like stretching a spring, gives a triangle whose area is ½Fd.

Part 5 of 7Typical sizes and pitfalls

A person climbing a flight of stairs of height 3 m with mass 60 kg does about 60 × 9.8 × 3 ≈ 1800 J of work against gravity.

Typical sizes and pitfalls
A car engine does millions of joules over a short journey.
When using W = Fd, check that the distance is in metres (change cm and km first) and that the force is in newtons (change kN to N or work out weight from mass).
Watch for questions where a force acts but the movement is at right angles to it: the work done by that force is zero.

Part 6 of 7Work, direction and the idea of a

The phrase "in the direction of the force" is easy to overlook.

1
Suppose you lift a suitcase and then walk across a room carrying it.
2
During the lift, your upward force and the upward movement are in the same direction, so you do work and the suitcase gains GPE.
3
During the walk, the suitcase moves sideways, at right angles to your upward force, so the force you apply does no work on it.
4
The suitcase's energy does not change, which agrees with what we observe: its height and speed are unchanged.

A planet orbiting in a circle, or a satellite at constant height, is a similar case: the gravitational force acts at right angles to the motion, so it does no work and the speed stays constant.

Work, direction and the idea of a
When you do a calculation, ask yourself what the force does to the object: speeds it up, lifts it, stretches it or heats it.
That tells you which energy store receives the energy and lets you check that your answer is sensible.

Part 7 of 7Worked examples

  1. A student pushes a box with a constant force of 40 N across a floor for 6.0 m. Calculate the work done.

  2. A crane lifts a 250 kg container through 12 m at constant speed. Find the work done by the crane. (g = 9.8 N kg−1)

  3. A 15 N force moves a trolley 80 cm along a bench. How much energy is transferred to the trolley?

Key terms

TermMeaning
Work doneEnergy transferred when a force moves an object through a distance.
JouleUnit of work and energy: 1 N × 1 m.
ForceA push or pull measured in newtons.
WeightForce of gravity on a mass, W = mg.
FrictionForce opposing relative motion between surfaces.
Force-distance graphGraph whose area under the line equals work done.

Avoid these mistakes

1
Using distance in centimetres or kilometres without converting to metres.
2
Calculating work with weight when the object is moved horizontally against friction; the force you must use is the pushing force (equal to friction at steady speed).
3
Saying a person holding a heavy object still is doing work on it; there is no distance moved.
4
Forgetting that work and energy share the same unit (joule) and that W is not a force.
5
Taking the full distance when the force acts at right angles to the movement, which gives zero work.

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