Work Done = Force × Distance (W = Fs)

✏️ Paper first! Work out every question on paper before you tap Show solution. Write down every step – the equation, the numbers with units, the rearranging and the answer with its unit. In the exam, if your final answer is wrong you can still get marks for correct working, but only if the examiner can see it.

Course: Combined Science + Separate Physics  |  Tier: Foundation + Higher  |  Equation sheet: given in the exam

The equation

work done = force × distance (along the line of action of the force)    W = F s

QuantitySymbolUnit
work doneWjoules (J)
forceFnewtons (N)
distancesmetres (m)

Rearranged: F = W ÷ s   |   s = W ÷ F

Use FIFA for every answer

  • F – Formula: write the equation as it appears on the sheet.
  • I – Insert: put in the numbers (convert to standard units first).
  • F – Fix: rearrange to make the unknown the subject.
  • A – Answer: calculate and always give the unit.

Foundation: aim for Q1–8.   Higher: aim for Q4–10. Most questions need rearranging.


Questions

Q1 (F) A shopper pushes a trolley with a force of 40 N for 25 m. Calculate the work done.

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F: W = F s
I: W = 40 × 25
F: W is already the subject – no rearranging needed
A: 1000 J

Q2 (F) A child does 600 J of work pulling a sledge 15 m across snow. Calculate the pulling force.

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F: W = F s
I: 600 = F × 15
F: F = 600 ÷ 15
A: 40 N

Q3 (F) A lift motor exerts a force of 800 N and does 12 000 J of work. How far does the lift move?

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F: W = F s
I: 12 000 = 800 × s
F: s = 12 000 ÷ 800
A: 15 m

Q4 (F) A cyclist pushes with a driving force of 150 N and does 4.5 kJ of work. How far does she travel?

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Convert first: 4.5 kJ = 4500 J
F: W = F s
I: 4500 = 150 × s
F: s = 4500 ÷ 150
A: 30 m

Q5 (F) A tractor does 1.2 MJ of work pulling a plough 480 m across a field. Calculate the pulling force in kN.

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Convert first: 1.2 MJ = 1 200 000 J
F: W = F s
I: 1 200 000 = F × 480
F: F = 1 200 000 ÷ 480 = 2500 N
A: 2500 ÷ 1000 = 2.5 kN

Q6 (F/H) A car’s brakes do 360 kJ of work to stop the car in 45 m. Calculate the braking force.

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Convert first: 360 kJ = 360 000 J
F: W = F s
I: 360 000 = F × 45
F: F = 360 000 ÷ 45
A: 8000 N

Q7 (F/H) A ferry’s engine provides a driving force of 24 kN and does 4.8 MJ of work. How far does the ferry travel? Give your answer in km.

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Convert first: 24 kN = 24 000 N; 4.8 MJ = 4 800 000 J
F: W = F s
I: 4 800 000 = 24 000 × s
F: s = 4 800 000 ÷ 24 000 = 200 m
A: 200 ÷ 1000 = 0.2 km

Q8 (F/H) A freight train does 3.0 × 109 J of work over a 15 km journey. Calculate the average driving force. Give your answer in standard form.

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Convert first: 15 km = 15 000 m = 1.5 × 104 m
F: W = F s
I: 3.0 × 109 = F × 1.5 × 104
F: F = 3.0 × 109 ÷ 1.5 × 104
A: 2.0 × 105 N

Q9 (H) A weightlifter does 2352 J of work lifting a barbell 2.0 m straight up at a steady speed. Calculate the mass of the barbell. (g = 9.8 N/kg)

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Step 1 – find the lifting force
F: W = F s
I: 2352 = F × 2.0
F: F = 2352 ÷ 2.0 = 1176 N
Step 2 – the lifting force equals the weight
F: W = m g
I: 1176 = m × 9.8
F: m = 1176 ÷ 9.8
A: 120 kg

Q10 (H) A car’s engine does 7.5 MJ of work during a 12.6 km journey. Calculate the average driving force. Give your answer to 2 significant figures.

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Convert first: 7.5 MJ = 7 500 000 J; 12.6 km = 12 600 m
F: W = F s
I: 7 500 000 = F × 12 600
F: F = 7 500 000 ÷ 12 600
A: 595.2… = 600 N (2 s.f.)