What you'll learn
This revision guide covers the fundamental concept of work done by forces and how energy is transferred when forces move objects. You'll learn to calculate work done, understand the relationship between work and energy transfers, and apply these principles to real-world scenarios. This topic is essential for understanding energy conservation and forms a key part of the Edexcel GCSE Physics specification.
Key terms and definitions
Work done — the energy transferred when a force moves an object through a distance; measured in joules (J)
Force — a push or pull acting on an object, measured in newtons (N)
Displacement — the distance moved by an object in a particular direction, measured in metres (m)
Energy transfer — the process by which energy changes from one store to another or moves from one object to another
Power — the rate at which energy is transferred or work is done, measured in watts (W)
Joule — the unit of energy and work; one joule equals the work done when a force of one newton moves an object one metre in the direction of the force
Gravitational potential energy — the energy stored in an object due to its position in a gravitational field
Kinetic energy — the energy an object possesses due to its motion
Core concepts
The work done equation
When a force causes an object to move, work is done and energy is transferred. The amount of work done depends on both the size of the force and the distance moved in the direction of that force.
The equation for work done is:
W = F × s
Where:
- W = work done (J)
- F = force applied (N)
- s = distance moved in the direction of the force (m)
Key points about this equation:
- Work is only done when the force causes movement
- If there is no movement, no work is done (even if a force is applied)
- The distance must be measured in the direction of the force
- One joule of work is done when a force of 1 N moves an object 1 m
For example, if you push a shopping trolley with a force of 50 N and it moves 10 m in the direction you're pushing, the work done is:
W = 50 × 10 = 500 J
Work done against friction
When objects move, they often experience friction — a force that opposes motion. Work must be done against friction to keep an object moving at constant speed.
When work is done against friction:
- Energy is transferred from the kinetic energy store of the moving object
- Energy is transferred to the thermal energy stores of the object and its surroundings
- The object and surroundings heat up
- This is why your hands warm up when you rub them together
The work done against friction can be calculated using the same equation (W = F × s), where F is now the frictional force.
For a car travelling at constant speed on a level road:
- The driving force from the engine equals the frictional forces (air resistance and friction between tyres and road)
- Work done by the engine transfers energy from the chemical energy store of the fuel
- This energy is transferred to thermal energy stores by friction
- The temperature of the brakes, tyres, road, and surrounding air increases
Work done and gravitational potential energy
When an object is lifted vertically, work is done against the gravitational force. This work increases the object's gravitational potential energy (GPE).
The work done lifting an object equals the increase in its gravitational potential energy:
W = m × g × h
Where:
- W = work done (J)
- m = mass (kg)
- g = gravitational field strength (N/kg) — on Earth, g = 9.8 N/kg (often approximated to 10 N/kg in calculations)
- h = vertical height gained (m)
This equation shows that:
- More work is required to lift heavier objects
- More work is required to lift objects higher
- The work done is independent of the path taken — only the vertical height change matters
Example: Lifting a 2 kg book onto a shelf 1.5 m high requires: W = 2 × 10 × 1.5 = 30 J
Work done and kinetic energy
When a force causes an object to accelerate, work is done and the object's kinetic energy increases. The work done on the object equals the change in kinetic energy.
The kinetic energy equation is:
KE = ½ × m × v²
Where:
- KE = kinetic energy (J)
- m = mass (kg)
- v = speed (m/s)
When a resultant force acts on an object and causes it to accelerate from rest:
- Work done by the force = final kinetic energy of the object
- W = ½mv²
When an object slows down:
- Work is done against the motion (often by friction or air resistance)
- Kinetic energy decreases
- Energy is transferred to other stores (usually thermal)
Power and work done
Power is the rate at which work is done or the rate at which energy is transferred. A more powerful machine does the same amount of work in less time.
The power equation is:
P = W ÷ t
or
P = E ÷ t
Where:
- P = power (W)
- W = work done (J)
- E = energy transferred (J)
- t = time (s)
One watt (1 W) equals one joule of energy transferred per second (1 J/s).
Key points:
- A 100 W light bulb transfers 100 J of energy every second
- A more powerful car engine can do the same work in less time, allowing faster acceleration
- Power can also be calculated from force and speed for objects moving at constant velocity
For constant speed:
P = F × v
Where:
- P = power (W)
- F = force (N)
- v = speed (m/s)
This is useful for calculating the power required to maintain constant speed against friction.
Energy transfers in everyday situations
Understanding work done helps explain many everyday situations:
Climbing stairs:
- Work is done against gravitational force
- Chemical energy from food → gravitational potential energy
- Some energy also transferred to thermal energy stores (you get warm)
Cycling:
- Work done by leg muscles transfers chemical energy from food
- Some energy → kinetic energy of cyclist and bicycle
- Much energy → thermal energy due to friction and air resistance
Braking:
- Work done by friction force between brake pads and wheel
- Kinetic energy → thermal energy
- Brakes and wheels heat up significantly
Using a lift (elevator):
- Electric motor does work against gravitational force
- Electrical energy → gravitational potential energy (and thermal energy due to friction)
Worked examples
Example 1: Calculating work done moving a box
Question: A warehouse worker pushes a box with a force of 80 N. The box moves 5.0 m across the floor in the direction of the push. Calculate the work done by the worker. (2 marks)
Solution:
State the equation: W = F × s (1 mark)
Substitute values and calculate: W = 80 × 5.0 W = 400 J (1 mark)
Examiner tip: Always include the unit (J) in your final answer for full marks.
Example 2: Work done lifting an object
Question: A student lifts a 0.50 kg textbook from the floor onto a desk 0.80 m high. (a) Calculate the work done by the student. Use g = 10 N/kg. (3 marks) (b) State what happens to the energy transferred. (1 mark)
Solution:
(a) State the equation: W = m × g × h (1 mark)
Substitute values: W = 0.50 × 10 × 0.80 (1 mark)
Calculate: W = 4.0 J (1 mark)
(b) The energy is transferred to the gravitational potential energy store of the book (1 mark)
Examiner tip: Part (b) requires you to identify the energy store — be specific rather than just saying "potential energy."
Example 3: Power calculation
Question: A crane lifts a 500 kg load through a vertical height of 12 m in 20 s. (a) Calculate the work done by the crane. Use g = 10 N/kg. (3 marks) (b) Calculate the power of the crane motor. (2 marks)
Solution:
(a) State the equation: W = m × g × h (1 mark)
Substitute and calculate: W = 500 × 10 × 12 W = 60 000 J (or 60 kJ) (2 marks)
(b) State the equation: P = W ÷ t (1 mark)
Substitute and calculate: P = 60 000 ÷ 20 P = 3000 W (or 3.0 kW) (1 mark)
Examiner tip: Large numbers can be expressed in kJ or kW — both are acceptable if correctly converted.
Common mistakes and how to avoid them
Confusing force and work — Force is measured in newtons (N); work is measured in joules (J). Work is only done when a force causes movement. A force can exist without work being done.
Using the wrong distance — Work done equals force multiplied by distance moved in the direction of the force. If you push horizontally but the object moves at an angle, only the horizontal component counts.
Forgetting to square the velocity — In the kinetic energy equation KE = ½mv², the velocity must be squared. Doubling the speed quadruples the kinetic energy, not doubles it.
Mixing up power and energy — Power is the rate of energy transfer, not the amount of energy. A 100 W bulb uses 100 J per second, so in 10 seconds it uses 1000 J.
Incorrectly handling units — Ensure all quantities are in standard units: force in N, distance in m, mass in kg, time in s. Convert before calculating (e.g., 2 km = 2000 m, 50 cm = 0.5 m).
Stating "energy is lost" — Energy is always conserved; it cannot be lost. Instead, say energy is "transferred to less useful stores" or "dissipated to the surroundings."
Exam technique for "Energy — forces doing work"
Show your working clearly — Calculation questions typically award one mark for the correct equation, one for correct substitution, and one for the answer with unit. You can gain partial marks even if your final answer is wrong.
Learn the equations — The equations W = Fs, KE = ½mv², P = W/t, and W = mgh must be recalled from memory. They appear on all tiers of the Edexcel specification and are not provided in the exam.
Command word "calculate" — This requires you to use numbers from the question to work out an answer. You must show your working and include the correct unit for full marks.
Command word "explain" — You must use scientific reasoning to make clear how or why something happens. For work done questions, link the force, movement, and energy transfer explicitly.
Quick revision summary
Work is done when a force moves an object, transferring energy. Calculate work using W = Fs (force × distance). When lifting objects, work done equals the increase in gravitational potential energy (W = mgh). When accelerating objects, work increases kinetic energy. Power measures the rate of doing work (P = W/t). Energy is always conserved but transferred between stores when work is done, often with some energy dissipated as thermal energy due to friction.