Chapter 3 of 8

All 8 chapters
  1. 1Calculating energy stores, readunderstood
  2. 2Springs and elastic energy, readunderstood
  3. 3Work done, readunderstood
  4. 4Power, readunderstood
  5. 5Efficiency, readunderstood
  6. 6Specific heat capacity, readunderstood
  7. 7Energy resources, readunderstood
  8. 8Energy at home, readunderstood

S4.9.3 Chapter 3

Work done

A force of 30 N moves a trolley 5 m in the direction of the force. How much work is done?

Your guess

Pick one before you read on. It is fine to be wrong.

Your guess

  • You picked A. Read on. At the end, the chapter comes back to your guess.

  • You picked B. Read on. At the end, the chapter comes back to your guess.

  • You picked C. Read on. At the end, the chapter comes back to your guess.

  • You picked D. Read on. At the end, the chapter comes back to your guess.

By the end you can

  • Calculate work done as force times distance moved
  • Explain that work done equals energy transferred

In everyday speech, work is anything tiring. In science, work done has one exact meaning. Work is done when a force moves something.

work done = force × distance moved in the direction of the force. In symbols, W = F × s. W is in joules (J). F is in newtons (N). s is in metres (m).

One joule is the work done when a force of 1 N moves something 1 m. So 1 J = 1 N × 1 m.

A box with a force arrow pointing at it from the left, labelled 50 N. A dashed box to the right shows where the box moves to. A line under both is labelled 4 m. The box is labelled box.box50 N4 m
A force of 50 N pushes a box 4 m. The dashed box is where it ends up.

Worked example

A force of 50 N pushes a box 4 m along the floor, in the direction of the force. How much work is done on the box?

  1. W = F × s.
  2. W = 50 × 4 = 200 J.

Answer: 200 J

Work done is the same as energy transferred. When a force does 200 J of work, 200 J of energy moves from one store to another. That is why both are measured in joules.

Two boxes joined by an arrow. The first box says chemical store of your body. The arrow says by a force. The second box says thermal store of the box and floor.chemical store ofyour bodythermal store of thebox and floorby a force
Pushing a box at a steady speed over a rough floor. The work you do ends up as thermal energy.

Where does the energy go? If you push a box at a steady speed, it is not speeding up, so its kinetic energy does not change. The work you do against friction warms the box and the floor a little.

Now lift something. To lift at a steady speed, your force must equal the weight. The weight in newtons is mass × g, with g = 9.8 N/kg. The distance is the height you lift it.

A bag in a box with an upward arrow labelled 39.2 N. A dashed bag above it shows where it is lifted to. A line beside them is labelled 2.5 m. The bag is labelled bag.bag39.2 N2.5 m
A 4 kg bag lifted 2.5 m. The lifting force is 39.2 N, the weight of the bag.

Worked example

A bag of 4 kg is lifted 2.5 m at a steady speed. How much work does the lifting force do? Use g = 9.8 N/kg.

  1. The lifting force equals the weight, and W = F × s.
  2. F = m × g = 4 × 9.8 = 39.2 N.
  3. W = 39.2 × 2.5 = 98 J.

Answer: 98 J

Compare with Chapter 1. The bag gains m × g × h = 4 × 9.8 × 2.5 = 98 J of gravitational potential energy. That is the same number. The work done by the lifting force is the energy transferred into the gravitational potential store.

Take care with direction. Only the distance moved in the direction of the force counts. Suppose you carry a bag along a level path. The force holding the bag up points up, and the bag moves sideways. Up and sideways are at right angles.

A bag with an upward arrow labelled 20 N. A dashed bag to the right shows where it moves to. A line under both is labelled 5 m. The bag is labelled bag.bag20 N5 m
The force is up. The bag moves sideways. The distance moved up is 0 m, so the work done by this force is 0 J.

The holding force does no work on the bag, because the bag does not move up or down. Your legs and arms still use energy. That energy goes into your own body and into the air, not into the bag.

A graph shows work too. Plot force against the distance moved. For a steady force the line is flat. The work done is the area under the line, a rectangle of height F and width s.

A graph of force in N against distance moved in m. The axes are labelled distance moved (m), from 0 to 5 in steps of 1, and force (N), from 0 to 12 in steps of 2. A flat line labelled steady force runs from 0 m to 4 m at 10 N. Dashed lines run from the dot at 4 m and 10 N to both axes.steady force12345246810120distance moved (m)force (N)
A steady 10 N over 4 m. The rectangle under the line is 10 × 4 = 40, so 40 J of work is done.

Three mistakes to avoid. Change cm to m before you multiply. A mass in kg is not a force, so turn it into a weight with m × g. And count only the distance moved in the direction of the force.

Worked example

A cart of mass 4 kg starts from rest on a smooth level floor. A force of 8 N pushes it 9 m. Ignore friction. How fast is it moving at the end?

  1. W = F × s = 8 × 9 = 72 J.
  2. All of it goes to the kinetic store, so Ek = 72 J.
  3. Ek = ½ × m × v², so v² = 2 × Ek ÷ m = 2 × 72 ÷ 4 = 36.
  4. v = √36 = 6 m/s.

Answer: 6 m/s

A cart with a force arrow pointing at it from the left, labelled 8 N. A dashed cart to the right shows where it moves to. A line under both is labelled 9 m. The cart is labelled cart.cart8 N9 m
The cart starts from rest. The 8 N force acts over all 9 m.

A wrong idea many people have

If you hold a heavy box still, you are doing work on it.

Why it feels right: Holding a heavy box makes your arms ache, and aching feels like work.

The test that breaks it: Work done = force × distance moved. A box held still moves 0 m. So W = F × 0 = 0 J.

What is true: You do no work on a box that does not move. Your muscles still use chemical energy to stay tense, and that is why you tire. The energy goes into your body, not into the box.

Try it

Work done lifting a bag of rice

You need: a bag of rice or flour with its mass printed in kg, a table or shelf, string, a ruler or tape measure.

Be safe: Lift only a bag you can carry comfortably. Bend your knees, keep your back straight and keep your feet clear. Use a steady table.

  1. Read the mass printed on the bag, in kg. Work out its weight: mass × 9.8.
  2. Hold a string from the floor to the top of the table. Measure the string in m. This is the height.
  3. Lift the bag from the floor to the table, slowly and at a steady speed.
  4. Work out the work done: weight × height.
  5. Now carry the bag across the room at the same height. How much work do you do on the bag in the up direction?

What you will see: Take a 2 kg bag and a table 0.75 m high. The weight is 19.6 N. The work is 19.6 × 0.75 = 14.7 J. Carrying the bag across the room adds 0 J, because it does not go up or down.

If you cannot try it, this is what happens.
A bag of rice with an upward arrow labelled 19.6 N. A dashed bag above it shows where it is lifted to. A line beside them is labelled 0.75 m. The bag is labelled rice.rice19.6 N0.75 m

Key words

work done
the energy transferred by a force, found as force × distance moved in the direction of the force.
joule
the unit of work and energy, written J. One joule is the work done by a force of 1 N moving something 1 m.

Back to your guess

The answer is C: 150 J

Work done is force × distance moved. 30 × 5 = 150 J. Adding or dividing the two numbers does not give an energy.

Check yourself

Try each one before you look. A wrong answer tells you where to go next.

  1. A force of 40 N moves a box 3 m along the floor, in the direction of the force. How much work is done?

    A box with a force arrow pointing at it from the left, labelled 40 N. A dashed box to the right shows where it moves to. A line under both is labelled 3 m. The box is labelled box.box40 N3 m
    Tap your answer.

    1. Yes, that is right. W = F × s = 40 × 3 = 120 J.

    2. Not this one. You added the force and the distance. Work done is force multiplied by distance. Try another.

    3. Not this one. You divided the force by the distance. Work done is force × distance, so multiply. Try another.

    4. Not this one. You took the distance from the force. Work done is force × distance, so multiply. Try another.

    See the answer

    120 J

    W = F × s = 40 × 3 = 120 J.

    • If you chose B: You added the force and the distance. Work done is force multiplied by distance.
    • If you chose C: You divided the force by the distance. Work done is force × distance, so multiply.
    • If you chose D: You took the distance from the force. Work done is force × distance, so multiply.

  2. A force of 8 N moves a crate 25 cm along the floor, in the direction of the force. How much work is done?

    Tap your answer.

    1. Not this one. You used 25 cm as if it were 25 m. Change cm to m first: 25 cm is 0.25 m. Go to M2.6.1. Try another.

    2. Not this one. You added 8 and 25. Work done is force × distance, with the distance in metres. Try another.

    3. Not this one. You divided 8 by 25. Work done is force multiplied by distance. Try another.

    4. Yes, that is right. 25 cm = 0.25 m. W = F × s = 8 × 0.25 = 2 J.

    See the answer

    2 J

    25 cm = 0.25 m. W = F × s = 8 × 0.25 = 2 J.

    • If you chose A: You used 25 cm as if it were 25 m. Change cm to m first: 25 cm is 0.25 m. Go to M2.6.1.
    • If you chose B: You added 8 and 25. Work done is force × distance, with the distance in metres.
    • If you chose C: You divided 8 by 25. Work done is force multiplied by distance.

  3. A girl carries a 10 kg bag at a steady speed along a level path. How much work does the force that holds the bag up do on the bag?

    A bag with an upward arrow. A dashed bag to the right shows where it moves to. A line under both is labelled 100 m. The force is labelled 98 N and the bag is labelled bag.bag98 N100 m
    Tap your answer.

    1. Not this one. Heavy and far both sound like work, but only the distance moved in the direction of the force counts. Try another.

    2. Yes, that is right. The bag moves along the path, not up. The distance moved in the direction of the force is 0 m, so W = F × 0 = 0 J.

    3. Not this one. Lifting uses a force along the movement. Here the force is up and the movement is sideways. Try another.

    4. Not this one. Feeling tired is not a measure of work done on the bag. Work is force × distance moved in the direction of the force. Try another.

    See the answer

    None, because the force is at right angles to the movement.

    The bag moves along the path, not up. The distance moved in the direction of the force is 0 m, so W = F × 0 = 0 J.

    • If you chose A: Heavy and far both sound like work, but only the distance moved in the direction of the force counts.
    • If you chose C: Lifting uses a force along the movement. Here the force is up and the movement is sideways.
    • If you chose D: Feeling tired is not a measure of work done on the bag. Work is force × distance moved in the direction of the force.

  4. A force does 90 J of work pushing a box at a steady speed over a rough floor. Where does the energy go?

    Tap your answer.

    1. Yes, that is right. Friction opposes the push. The work done against it warms the box and the floor, so the energy moves into the thermal store.

    2. Not this one. The box moves at a steady speed. It is not speeding up, so its kinetic energy does not change. Try another.

    3. Not this one. Work done is a way of transferring energy. The energy has to go somewhere. Try another.

    4. Not this one. Energy is never destroyed. Friction moves it into the thermal store as heat. Go to S3.8.3. Try another.

    See the answer

    Into the thermal store of the box and the floor.

    Friction opposes the push. The work done against it warms the box and the floor, so the energy moves into the thermal store.

    • If you chose B: The box moves at a steady speed. It is not speeding up, so its kinetic energy does not change.
    • If you chose C: Work done is a way of transferring energy. The energy has to go somewhere.
    • If you chose D: Energy is never destroyed. Friction moves it into the thermal store as heat. Go to S3.8.3.

  5. A crane lifts a load of 20 kg through 4 m at a steady speed. Use g = 9.8 N/kg. How much work does the crane do on the load?

    Tap your answer.

    1. Not this one. You multiplied 20 by 4 and left out g. A mass of 20 kg is not a force. Its weight is 20 × 9.8 N. Go to S3.7.4. Try another.

    2. Not this one. You found the weight, 20 × 9.8 = 196 N, but forgot to multiply by the height. Try another.

    3. Not this one. You multiplied by the height twice, 196 × 4 × 4. The height is used once: W = F × s. Try another.

    4. Yes, that is right. The lifting force equals the weight: 20 × 9.8 = 196 N. W = F × s = 196 × 4 = 784 J.

    See the answer

    784 J

    The lifting force equals the weight: 20 × 9.8 = 196 N. W = F × s = 196 × 4 = 784 J.

    • If you chose A: You multiplied 20 by 4 and left out g. A mass of 20 kg is not a force. Its weight is 20 × 9.8 N. Go to S3.7.4.
    • If you chose B: You found the weight, 20 × 9.8 = 196 N, but forgot to multiply by the height.
    • If you chose C: You multiplied by the height twice, 196 × 4 × 4. The height is used once: W = F × s.

  6. In which case is work done on the object, in the physics meaning of the words?

    Tap your answer.

    1. Not this one. The box does not move, so the distance moved is 0 m and the work done is 0 J. Try another.

    2. Not this one. The wall does not move, so no work is done on it, however hard the push. Try another.

    3. Yes, that is right. Work is done when a force moves something in the direction of the force. Only the pushed car moves the way it is pushed.

    4. Not this one. The holding force is up and the box moves sideways. At right angles, no work is done by that force. Try another.

    See the answer

    A person pushes a car and it moves along the road.

    Work is done when a force moves something in the direction of the force. Only the pushed car moves the way it is pushed.

    • If you chose A: The box does not move, so the distance moved is 0 m and the work done is 0 J.
    • If you chose B: The wall does not move, so no work is done on it, however hard the push.
    • If you chose D: The holding force is up and the box moves sideways. At right angles, no work is done by that force.

  7. From an earlier chapter

    A spring with k = 100 N/m is stretched by 0.1 m, within its limit. How much energy is stored in it?

    Tap your answer.

    1. Not this one. You left out the half. Ee = ½ × k × e². Go to S4.9.2. Try another.

    2. Yes, that is right. Ee = ½ × k × e² = ½ × 100 × 0.1 × 0.1 = ½ × 100 × 0.01 = 0.5 J.

    3. Not this one. You did not square the extension. The energy is ½ × k × e × e. Go to S4.9.2. Try another.

    4. Not this one. You multiplied k by e. That gives the force in newtons, not the energy. Go to S4.9.2. Try another.

    See the answer

    0.5 J

    Ee = ½ × k × e² = ½ × 100 × 0.1 × 0.1 = ½ × 100 × 0.01 = 0.5 J.

    • If you chose A: You left out the half. Ee = ½ × k × e². Go to S4.9.2.
    • If you chose C: You did not square the extension. The energy is ½ × k × e × e. Go to S4.9.2.
    • If you chose D: You multiplied k by e. That gives the force in newtons, not the energy. Go to S4.9.2.

  8. A force of 35 N moves a box 6 m in the direction of the force. How much work is done, in joules?

    See the answer

    210 J

    W = F × s = 35 × 6 = 210 J.

  9. A force of 12 N moves a trolley 40 cm in the direction of the force. How much work is done, in joules?

    See the answer

    4.8 J

    40 cm = 0.4 m. W = F × s = 12 × 0.4 = 4.8 J.

  10. A 2 kg cart starts from rest. A force of 5 N pushes it 5 m along a smooth floor. Ignore friction. How fast is it moving at the end, in m/s?

    See the answer

    5 m/s

    W = 5 × 5 = 25 J, all of it kinetic energy. v² = 2 × 25 ÷ 2 = 25, so v = 5 m/s.

Keep it

Copy this into your exercise book.

W = F × s, with s moved in the direction of the force. Work done = energy transferred, in J. Force at right angles, or no movement: no work. Lifting force = m × g.

Draw: A box, a force arrow and a dimension line for the distance moved, with W = F × s beside it.

Reading with a child? A short page for the adult: what this chapter teaches and three questions to ask.

No internet tomorrow? Save the whole book as one file (758 KB). It opens on any phone.