Work, Energy and Power
Work is energy transferred by a force; power is how fast that happens. Two equations, and one condition that catches people out — the force and the distance must be in the same direction.
1. Work done
Work done = Force × distance moved in the DIRECTION of the force W = F d
Unit: the joule (J). 1 J is the work done when a force of 1 N moves through 1 m.
Work done = energy transferred. They are the same quantity, measured in the same unit — which is why W = Fd sits alongside the energy equations.
Example: a 40 N force pushes a box 6 m.
- W = 40 × 6 = 240 J
The distance must be measured IN THE DIRECTION OF THE FORCE. If a force acts horizontally and the object moves vertically, that force does no work.
Two consequences worth knowing:
Carrying a heavy bag horizontally at constant height does NO work against gravity, because the weight acts downwards and the movement is horizontal. No movement means no work done. Pushing hard against a wall that doesn’t move transfers zero work, however tiring it feels.
2. Work against gravity and friction
Lifting an object — you work against its weight:
W = m g h — which is exactly the gain in gravitational potential energy.
Example: lifting a 20 kg box 1.5 m, with g = 9.8.
- W = 20 × 9.8 × 1.5 = 294 J
Dragging an object at constant speed — you work against friction:
The applied force equals the friction force, and the work done becomes thermal energy in the surfaces.
Example: dragging a crate 8 m against 50 N of friction.
- W = 50 × 8 = 400 J, all transferred to thermal energy
3. Power
Power is the RATE of doing work — the energy transferred per second.
P = W / t or P = E / t
Unit: the watt (W). 1 W = 1 J/s.
Example: 600 J of work done in 4 s.
- P = 600 ÷ 4 = 150 W
Power is energy DIVIDED by time. Multiplying instead was recorded across several topics. Check the unit: a watt is a joule per second.
Time must be in SECONDS. Convert minutes (× 60) and hours (× 3600) first.
In P = E/t, “t” is TIME — not energy transferred. Confusion about what the symbol stood for was recorded; write the equation out in words if you’re unsure.
Rearranged: W = P t and t = W / P.
A useful alternative form: since W = Fd, power can be written as
P = F v (force × velocity), for an object moving at a steady speed.
4. Efficiency
Efficiency = (useful energy output ÷ total energy input) × 100%
The same works with power: (useful power out ÷ total power in) × 100%.
Efficiency can never exceed 100%. If yours does, you have swapped input and output.
The “missing” energy has been dissipated, usually as thermal energy — not destroyed.
5. Putting it together
Many questions chain the ideas:
Example. A 500 W motor lifts a 30 kg load 4 m. How long does it take, if it is 100% efficient?
- Work needed = mgh = 30 × 9.8 × 4 = 1176 J
- t = W/P = 1176 ÷ 500 = 2.4 s
Example. A cyclist does 12 000 J of work in 40 s.
- P = 12 000 ÷ 40 = 300 W
Work out the energy first, then apply the power equation. Trying to do both at once is where slips happen.
6. Mistakes that cost marks
Using a distance not in the direction of the force.
Saying work is done when nothing moves.
Multiplying instead of dividing for power.
Not converting time to seconds.
Confusing the symbol t with energy.
Confusing work with power — one is joules, the other watts.
Efficiency over 100%.
Omitting units — J for work, W for power.
Frequently asked questions
What is work done? Force × distance moved in the direction of the force: W = Fd, in joules.
Is work the same as energy transferred? Yes — same quantity, same unit.
Do I do work carrying a bag horizontally? No work against gravity — the weight acts downwards, the motion is horizontal.
Do I do work pushing a wall that doesn’t move? No — no movement means no work done.
What is power? The rate of doing work: P = W/t, in watts.
What is 1 watt? 1 joule per second.
How do I find work done lifting something? W = mgh, equal to the gain in gravitational potential energy.
What happens to work done against friction? It becomes thermal energy.
What is efficiency? Useful output ÷ total input × 100% — never above 100%.
What is P = Fv? Power as force × velocity, for steady motion.
Quick revision checklist
- I know W = Fd and that distance is in the direction of the force
- I know work done = energy transferred, in joules
- I know no movement means no work
- I can calculate work against gravity (mgh) and against friction
- I know P = W/t and that a watt is a joule per second
- I convert time to seconds
- I divide, not multiply, for power
- I can rearrange to find work or time
- I know P = Fv
- I can calculate efficiency and check it’s under 100%
- I can chain energy and power calculations
- I give the right units
These notes cover work, energy and power in the Cambridge IGCSE Physics (0625) syllabus and are written for Grade 9–11 / Year 10–11 students. They are based on teaching patterns observed across a large set of one-to-one IGCSE Physics lessons, with particular attention to the errors students make most often and the wording examiners reward. Always check the current syllabus and formula list for your own exam series.
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