Pearson Edexcel International GCSE in Physics · 4PH1

Work Done

The precise meaning of a word everybody thinks they already know — and why holding something still is not work at all.

Topic 4 · Energy resources and energy transfers — one of 7 lessons in this topic, and one of 65 in Physics.

What this lesson covers in the specification

Incandio is aligned to this specification. It is not published by, endorsed by or affiliated with Pearson, and it reproduces none of Pearson's wording — the statement numbers are given so you can check every lesson against your own copy.

  • 4.11 — Use W = F × d
  • 4.12 — Work done is equal to energy transferred

1 · Understand it

No exam language yet. The only question this section answers is: do I actually understand what is happening?

In physics WORK has an exact meaning, and it is narrower than the everyday one. Work is done when a FORCE MOVES AN OBJECT THROUGH A DISTANCE, and the amount of work is the force multiplied by the distance moved in the direction of the force: W = F × d. Both parts are required. A force with no movement does no work at all, however hard it feels.

Stand holding a heavy suitcase and you will be exhausted within a minute, and you will have done no work on the suitcase whatever. The suitcase has not moved, so the distance is zero, so the work is zero. Your muscles are certainly transferring energy — they are contracting and relaxing continuously to hold the weight, and that energy goes into your thermal store — but none of it has gone into the suitcase, which is exactly where the equation says it has not gone.

Think of it like being paid by the metre

Imagine a removal firm that pays by the load and by the distance carried, and by nothing else. Carry a heavy box a long way and you are paid well. Carry a light box the same distance and you are paid less. Stand in the doorway holding the heaviest box in the van for an hour and you are paid nothing at all, because you did not move it. You will still be tired, and the firm will still be sympathetic, but the arithmetic does not care how tired you are — only about the load and the distance. Physics is that firm. Work is force multiplied by distance moved, and effort with no movement earns nothing.

Now statement 4.12, which is the most useful sentence in the whole topic: WORK DONE IS EQUAL TO ENERGY TRANSFERRED. They are not merely related — they are the same quantity, measured in the same unit, the joule. Doing 50 J of work on an object transfers exactly 50 J of energy to it. One joule is the work done when a force of one newton moves an object one metre.

Why that identity is so useful

  1. If you know the FORCE and the DISTANCE, you can find the ENERGY TRANSFERRED without knowing anything else about what happened.
  2. LIFTING: the force needed is the object's weight, and the distance is the height, so the work done equals the gravitational potential energy gained.
  3. PUSHING AGAINST FRICTION: the work done against the friction force equals the energy transferred to the thermal store of the surfaces, which is why brakes get hot.
  4. STRETCHING: the work done on a spring equals the elastic potential energy stored in it.
  5. BRAKING: the work done against friction equals the energy taken OUT of the car's kinetic store, which is why the discs get hot as the car slows.
  6. In every case the same calculation, W = F × d, answers a question about energy — which is why work done is the bridge between the forces of Topic 1 and the energy of Topic 4. None of it creates or destroys anything: the conservation of energy holds throughout, and a machine can only change how a given amount of work is delivered.

Work done, and the energy it accounts for

(a) A crate is pushed 8.0 m along the floor against a friction force of 45 N. Find the work done against friction. (b) A 12 kg box is lifted 1.5 m. Take g as 10 N/kg. Find the work done.

  1. (a) W = F × d = 45 × 8.0 = 360 J. All of it is transferred to the thermal store of the floor and the crate.
  2. (b) The force needed to lift the box is its weight: W = m × g = 12 × 10 = 120 N.
  3. Work done = F × d = 120 × 1.5 = 180 J.
  4. That 180 J is now in the gravitational potential store of the box.

Answer: 360 J against friction, and 180 J to lift the box.

The lifting case has a step that catches people out and is worth naming. The force in W = F × d is the force needed to move the object, and to lift something at a steady speed that force is its WEIGHT, not its mass. A question giving you a mass in kilograms wants you to multiply by g before you go anywhere near the distance. Using the mass directly gives an answer ten times too small, and it will look perfectly reasonable.

One final refinement the specification implies rather than states. The distance in the equation is the distance moved IN THE DIRECTION OF THE FORCE. Push a trolley horizontally and it moves horizontally, so the two agree and there is nothing to think about. But carry a suitcase horizontally along a level platform and the force you exert on it is upward while the motion is horizontal — so you do no work on the suitcase at all, even though you are certainly moving. That is the same result as standing still with it, arrived at from a different direction.

2 · Grade 9 Notes

A different job from the section above. You have already understood it; this is the precise set of things to LEARN — definitions to reproduce word for word, processes in order, equations with units, and the answers that score full marks.

W = F × d

W is work done in joules (J), F is the force in newtons (N), d is the distance moved in the direction of the force, in metres (m)

Units: J, N, m. Rearranged: F = W ÷ d and d = W ÷ F. One joule is the work done when a force of one newton moves an object one metre.

Learn this definition · Work done

The energy transferred when a force moves an object through a distance, equal to the force multiplied by the distance moved in the direction of the force. It is measured in joules.

Statement 4.12 — work done IS energy transferred

  • Work done and energy transferred are the SAME QUANTITY in the same unit, the joule
  • LIFTING at a steady speed: work done = gravitational potential energy gained
  • PUSHING against friction: work done = energy transferred to the thermal store, which is why brakes heat up
  • STRETCHING a spring: work done = elastic potential energy stored
  • So W = F × d answers an energy question whenever a force and a distance are known

Learn this definition · The machine rule

A lever, ramp or pulley multiplies the force but divides the distance by the same factor, so the work done is unchanged. Conservation of energy means no machine can give out more work than is put into it.

Calculating the work done in lifting something

  1. Find the force needed, which for lifting at a steady speed is the object's WEIGHT.
  2. Calculate the weight with W = m × g if only the mass is given.
  3. Multiply that force by the height raised: work = force × distance.
  4. State that this work equals the gravitational potential energy the object has gained.

When work is done, and when it is not

A. WORK IS DONE when a force moves an object through a distance in the direction of the force — pushing a trolley, lifting a box, stretching a spring.

B. NO WORK IS DONE if the object does not move, however large the force and however tiring it is. The distance is zero, so the work is zero.

Model answer [3 marks]

A force of 250 N pushes a box 6.0 m across a floor. Calculate the work done. [3]

Using W = F × d, the work done is 250 × 6.0 = 1500 J. This is also the energy transferred to the box and, through friction, to the thermal store of the floor.

Model answer [3 marks]

A student holds a 15 kg mass stationary at shoulder height for two minutes and says they have done a great deal of work on it. Explain why they have done no work on the mass. [3]

Work done is the force multiplied by the distance the object moves in the direction of that force. The mass does not move at all while it is being held, so the distance is zero and the work done on the mass is therefore also zero. The student's muscles are transferring energy, because they must contract repeatedly to hold the mass up, but that energy is transferred to the thermal store of the student's body rather than to the mass.

Not this: Holding something heavy is hard work, so a lot of work is being done on it.

This: Work in physics is force × distance moved. A stationary object has moved zero distance, so zero work has been done on it — however tiring it is. The energy your muscles use goes into your own thermal store, not into the object.

Mark-losing trap. No movement means NO WORK, whatever the force and however tiring it feels.

Mark-losing trap. To lift something, the force is its WEIGHT. Multiply the mass by g first.

Mark-losing trap. Work done and energy transferred are the same number in the same unit — say so, it is a mark.

Mark-losing trap. The distance is the one moved IN THE DIRECTION of the force.

3 · Prove it — the five questions

The five questions climb Grade 6 → Grade 7 → Grade 8 → Grade 9 → Grade 9 challenge, and are marked inside Incandio on your own device, by rule, with an authored diagnosis of the mistake you actually made. The mark schemes stay in the app so that the practice is worth doing; the questions themselves are here.

  1. Grade 6 · Calculate [2 marks] — A force of 30 N moves an object 4.0 m in the direction of the force. Calculate the work done.
  2. Grade 7 · Explain [2 marks] — A student holds a heavy box completely still for one minute. Explain why no work is done on the box.
  3. Grade 8 · Calculate [4 marks] — A 25 kg box is lifted through a height of 2.4 m at a steady speed. Take g as 10 N/kg. Calculate the work done.
  4. Grade 9 · Explain [5 marks] — A car brakes to a stop and the brake discs become hot. Select every statement that belongs in a full-mark explanation, using the idea of work done.
  5. 9+ · Analyse [6 marks] — A student uses a lever to lift a 400 N rock by 0.10 m, pushing down with a force of 50 N through a distance of 0.80 m. They conclude: 'The lever created extra energy, because 50 N lifted 400 N.' Select every statement that belongs in a full-mark analysis.

The people behind this science

Two ways into the same idea — the one who showed that work and heat are one account, and the one whose machines multiply force and never work. Inside Incandio each of them answers knowing exactly which lesson you have just finished.

James Prescott Joule — the one who showed that work and heat are one account

Statement 4.12 says work done equals energy transferred, and the unit on this page is Joule's name — both because of what he measured. His paddle-wheel experiment is precisely W = F × d turned into a temperature rise: falling weights did a calculable amount of work on the water, and he measured how much warmer the water became. Getting the same exchange rate from mechanical work, from electrical work and from compressing a gas is what established that work and heat are two descriptions of one quantity.

  • “How much work did the falling weights do on the water?”
  • “Why did you repeat the experiment in so many different ways?”
  • “What does it mean to say work and heat are the same quantity?”
  • “How did you measure a temperature rise that small?”
  • “Where does the work go when you push something against friction?”

Archimedes — the one whose machines multiply force and never work

A lever lets a small force lift a large weight, which looks very much like getting something for nothing — and this page explains why it is not. The small force acts through a long distance and the large weight moves only a short one, so the product, the work, comes out the same on both sides. Archimedes proved the law of the lever from first principles and understood exactly what it does and does not give you, which makes him the ideal figure for a page whose whole content is that force and distance trade against each other.

  • “Does a lever let you get more out than you put in?”
  • “If a small force lifts a great weight, what is the catch?”
  • “How did you prove the law of the lever from first principles?”
  • “Why does the small force have to move so much further?”
  • “Could any machine ever give more than it was given?”

Then defend it

On Incandio a lesson is not finished when the questions come out right. You teach the idea back to Ember, an AI apprentice who asks the awkward question, and then you argue it against James Prescott Joule in a structured debate marked against descriptors you can read before you enter. Learn it, teach it, then defend it — all three happen on this page once the app loads.

Carry on through the course