What you'll learn
This revision guide covers the fundamental concepts of work, energy and power as specified in the CIE IGCSE Co-ordinated Science (Double Award) syllabus. You'll learn how to calculate work done by forces, understand energy transfers and transformations, and apply the relationship between power, work and time. These concepts are essential for understanding mechanics and energy systems in physics.
Key terms and definitions
Work done — the energy transferred when a force moves an object through a distance; measured in joules (J)
Energy — the capacity to do work; exists in various forms including kinetic, gravitational potential, elastic potential, chemical, thermal, light, sound, electrical and nuclear
Power — the rate of doing work or transferring energy; measured in watts (W) where 1 W = 1 J/s
Kinetic energy — the energy possessed by a moving object, depending on its mass and velocity
Gravitational potential energy — the energy stored in an object due to its position in a gravitational field
Joule (J) — the SI unit of energy and work; one joule is the work done when a force of 1 newton moves an object through 1 metre in the direction of the force
Watt (W) — the SI unit of power; one watt equals one joule per second
Conservation of energy — the principle that energy cannot be created or destroyed, only transferred from one form to another
Core concepts
Work done by forces
Work is done when a force causes an object to move. The amount of work done depends on both the magnitude of the force and the distance moved in the direction of the force.
The equation for work done is:
Work done (J) = Force (N) × Distance moved in direction of force (m)
W = F × d
Key points about work done:
- Work is only done when the object actually moves
- The distance must be measured in the direction of the force
- If the force and movement are in opposite directions, negative work is done
- No work is done if the force is perpendicular to the direction of movement
- 1 joule of work is done when a force of 1 newton moves an object 1 metre
For example, when you lift a 2 kg bag of sugar (weight ≈ 20 N) vertically through 1.5 m, the work done against gravity is:
W = 20 N × 1.5 m = 30 J
Energy and its forms
Energy exists in multiple forms, all measured in joules. The main forms you need to know are:
Kinetic energy (KE) — possessed by moving objects
- Depends on mass and velocity
- Formula: KE = ½ × m × v²
- Where m is mass in kg and v is velocity in m/s
Gravitational potential energy (GPE) — stored energy due to position above ground
- Depends on mass, gravitational field strength, and height
- Formula: GPE = m × g × h
- Where m is mass (kg), g is gravitational field strength (N/kg), and h is height (m)
- On Earth, g ≈ 10 N/kg (or 10 m/s²)
Elastic potential energy — stored in stretched or compressed elastic objects like springs
Chemical energy — stored in fuels, food, and batteries
Thermal (heat) energy — energy due to the temperature of an object
Electrical energy — energy transferred by electric currents
Light energy — electromagnetic radiation that can be detected by the eye
Sound energy — energy transmitted by vibrations through a medium
Nuclear energy — stored in atomic nuclei
Energy transfers and transformations
Energy can be transferred from one form to another, but the total amount of energy remains constant (law of conservation of energy).
Common energy transformations:
Falling object:
- GPE → KE (as height decreases, speed increases)
- Some energy transferred to thermal energy due to air resistance
Electric motor:
- Electrical energy → Kinetic energy + thermal energy + sound energy
Light bulb:
- Electrical energy → Light energy + thermal energy
Photosynthesis:
- Light energy → Chemical energy (stored in glucose)
Car braking:
- Kinetic energy → Thermal energy (in brakes and surroundings)
Energy transfer diagrams (Sankey diagrams) show how energy is distributed in a system. The width of arrows represents the amount of energy. Useful energy goes straight ahead, while wasted energy branches off (usually as thermal or sound energy).
Efficiency
Not all input energy becomes useful output energy. Some energy is always transferred to less useful forms (often thermal energy).
Efficiency is the fraction of input energy that is usefully transferred:
Efficiency = (Useful energy output ÷ Total energy input) × 100%
Or equivalently:
Efficiency = (Useful power output ÷ Total power input) × 100%
Key points:
- Efficiency is expressed as a percentage or decimal (between 0 and 1)
- No real machine is 100% efficient
- The "missing" energy isn't destroyed — it's transferred to the surroundings
- Reducing friction, air resistance, and electrical resistance improves efficiency
For example, if a motor receives 500 J of electrical energy and transfers 400 J as useful kinetic energy:
Efficiency = (400 J ÷ 500 J) × 100% = 80%
The remaining 100 J (20%) is wasted as thermal and sound energy.
Power calculations
Power measures how quickly work is done or energy is transferred. A more powerful device transfers energy at a faster rate.
Power (W) = Work done (J) ÷ Time taken (s)
P = W ÷ t
Or equivalently:
Power (W) = Energy transferred (J) ÷ Time taken (s)
P = E ÷ t
Rearranging these equations:
- Work done (or energy transferred) = Power × Time
- Time = Work done (or energy transferred) ÷ Power
Common power values:
- Human walking: 50–100 W
- Cyclist: 200–400 W
- Hairdryer: 1000–2000 W (1–2 kW)
- Kettle: 2000–3000 W (2–3 kW)
- Car engine: 50,000–150,000 W (50–150 kW)
The kilowatt (kW) is often used for larger powers: 1 kW = 1000 W
Gravitational potential and kinetic energy calculations
Calculating gravitational potential energy:
GPE = m × g × h
Where:
- m = mass in kg
- g = gravitational field strength (10 N/kg on Earth)
- h = height in m
Example: A 50 kg student climbs stairs, increasing their height by 3 m.
GPE gained = 50 kg × 10 N/kg × 3 m = 1500 J
Calculating kinetic energy:
KE = ½ × m × v²
Where:
- m = mass in kg
- v = velocity in m/s
Example: A 1200 kg car travels at 20 m/s.
KE = ½ × 1200 kg × (20 m/s)² = ½ × 1200 × 400 = 240,000 J = 240 kJ
Energy conservation in falling objects:
When an object falls freely (ignoring air resistance):
- GPE lost = KE gained
- m × g × Δh = ½ × m × v²
This allows you to calculate final velocity from height fallen, or vice versa.
Worked examples
Example 1: Work done and power
Question: A builder lifts 20 bricks, each of mass 2.5 kg, from the ground onto a wall 1.8 m high. Calculate: (a) the work done in lifting one brick [2 marks] (b) the total work done lifting all 20 bricks [1 mark] (c) the power developed if this takes 2 minutes [2 marks]
Solution:
(a) Weight of one brick = mass × g = 2.5 kg × 10 N/kg = 25 N [1 mark] Work done = force × distance = 25 N × 1.8 m = 45 J [1 mark]
(b) Total work = 45 J × 20 = 900 J [1 mark]
(c) Time = 2 minutes = 120 s Power = work done ÷ time = 900 J ÷ 120 s = 7.5 W [2 marks: 1 for converting time, 1 for calculation]
Example 2: Energy transformations
Question: A 0.2 kg ball is dropped from a height of 5 m. (a) Calculate its gravitational potential energy before release [2 marks] (b) Calculate its kinetic energy just before hitting the ground (assume no energy loss) [1 mark] (c) Calculate its velocity just before impact [2 marks]
Solution:
(a) GPE = m × g × h = 0.2 kg × 10 N/kg × 5 m = 10 J [2 marks]
(b) By conservation of energy, GPE lost = KE gained Therefore KE = 10 J [1 mark]
(c) KE = ½ × m × v² 10 = ½ × 0.2 × v² 10 = 0.1 × v² v² = 100 v = 10 m/s [2 marks]
Example 3: Efficiency calculation
Question: An electric motor uses 1500 J of electrical energy to lift a 20 kg load through a vertical height of 6 m. (a) Calculate the useful work done by the motor [2 marks] (b) Calculate the efficiency of the motor [2 marks]
Solution:
(a) Useful work done = force × distance = weight × height Weight = 20 kg × 10 N/kg = 200 N [1 mark] Work done = 200 N × 6 m = 1200 J [1 mark]
(b) Efficiency = (useful energy output ÷ total energy input) × 100% Efficiency = (1200 J ÷ 1500 J) × 100% = 80% [2 marks]
Common mistakes and how to avoid them
Confusing mass and weight — Remember that weight (in newtons) = mass (in kg) × g. Weight is a force; mass is not. When lifting objects, you work against the weight force, not just the mass.
Forgetting to square velocity in KE calculations — The kinetic energy formula is ½mv², not ½mv. Always square the velocity value before multiplying.
Using incorrect units — Energy and work must be in joules, power in watts, time in seconds, force in newtons, distance in metres. Convert minutes to seconds and kilometres to metres before calculating.
Not converting between kW and W — Remember 1 kW = 1000 W. When calculating energy from power and time, ensure power is in watts, not kilowatts (unless you want energy in kJ).
Assuming 100% efficiency — Real systems always waste some energy. Don't assume all input energy becomes useful output unless specifically told to ignore energy losses.
Incorrectly applying energy conservation — When an object falls, GPE decreases and KE increases by the same amount (if air resistance is negligible). The total energy stays constant, but individual forms change.
Exam technique for "Work, energy and power"
Show all working clearly — Questions worth 2+ marks require you to show the steps in calculations. Write the formula, substitute values with units, then calculate the answer.
Check command words carefully — "Calculate" requires numerical working and an answer with units. "State" needs a short factual answer. "Explain" requires reasoning showing cause and effect.
Include units in final answers — Marks are frequently lost for missing units. Learn the standard units: J for energy and work, W for power, m for distance, s for time, N for force.
Use g = 10 N/kg unless told otherwise — This simplifies calculations and is standard for IGCSE. Some questions may give a different value (9.8 N/kg) — always use the value provided in the question.
Quick revision summary
Work is done when a force moves an object (W = F × d). Energy exists in multiple forms and is measured in joules; it can be transferred but never created or destroyed. Kinetic energy depends on mass and velocity squared (½mv²), while gravitational potential energy depends on mass, gravitational field strength and height (mgh). Power is the rate of energy transfer or work done (P = E/t or P = W/t), measured in watts. Efficiency compares useful energy output to total energy input as a percentage. Always show working, include correct units, and remember that real systems waste energy.