IGCSE Physics · Unit 1: Motion, Forces and Energy · Core + Extended

Energy, Work and Power CoreExtended adds KE/GPE equations, Sankey diagrams & efficiency formulas

Energy is one of the “connecting threads” of the whole syllabus — it reappears in thermal physics, waves, electricity, and even nuclear and space physics. This note covers where energy is stored, how it moves between those stores, how work and energy relate to each other, where our electricity actually comes from, and how to calculate power and efficiency.

Why this matters Energy questions show up everywhere in the exam — from a falling ball to a power station to a light bulb. The single most important idea in this whole topic is conservation of energy: energy is never created or destroyed, only transferred from one store to another (and some is usually “wasted,” typically as heat). Master that one sentence and most of this topic falls into place.

1. Energy Stores and Energy Transfers

Energy can be stored in a number of different ways: kinetic (movement), gravitational potential (height above the ground), chemical (in fuels, food, batteries), elastic (strain) (in stretched or squashed objects), nuclear (in the nucleus of an atom), electrostatic (in charged objects), and internal (thermal) (the kinetic and potential energy of the particles making up an object).

Energy moves between these stores through transfers. The syllabus recognises several transfer pathways:

  • By forces (mechanical work done) — e.g. lifting a box, pushing a trolley
  • By electric currents (electrical work done) — e.g. current flowing through a heater or motor
  • By heating — e.g. a flame heating a pan directly (not via a current)
  • By electromagnetic, sound, or other waves — e.g. light from the Sun, sound from a speaker
Worked example — identifying stores and transfers A ball is thrown straight up into the air.
On the way up: kinetic energy store is transferred (by the force of gravity acting against the motion) into the gravitational potential energy store, as the ball slows down and rises.
On the way down: the reverse happens — gravitational potential energy is transferred back into kinetic energy as the ball speeds up and falls.

2. The Principle of Conservation of Energy

The principle of conservation of energy states that energy cannot be created or destroyed — it can only be transferred from one store to another. The total amount of energy in a closed system stays exactly the same.

Simple energy transfers can be shown using a flow diagram: a straight arrow chain showing energy moving from one store, into the useful output store(s), with any wasted energy (almost always ending up as thermal energy in the surroundings) shown branching off.

Worked example — a simple flow diagram in words A hand-cranked torch:
chemical energy (in the user’s muscles) → [mechanical work done, by turning the crank] → kinetic energy (of the generator) → [electrical work done] → electrical energy → [transfer by the bulb] → light energy (useful output) + thermal energy (wasted, the bulb also gets warm)
Sankey diagrams Extended A Sankey diagram is a more detailed way of showing energy conservation across multiple stages: it uses arrows whose width is proportional to the amount of energy each pathway carries. A single input arrow splits into a “useful” branch and a “wasted” branch (often more than one wasted branch), and the combined width of all the output arrows always equals the width of the input arrow — this is exactly the conservation of energy principle, drawn to scale.
Try it — Stores, Transfers and Conservation
  1. Describe, using energy stores and transfers, what happens to the energy of a battery-powered toy car as it moves across the floor and gradually slows down due to friction.
  2. A skier at the top of a snowy slope skis down to the bottom. Describe the main energy transfer taking place.
  3. Explain what the principle of conservation of energy tells us about the “wasted” energy in a process — does it disappear?
Show answers
  1. Chemical energy (stored in the battery) is transferred, by electrical work done, into kinetic energy (of the moving car). As friction acts between the wheels/floor and within the motor, some of this kinetic energy is continually transferred into thermal energy (heating the car and its surroundings), which is why the car eventually slows down and stops.
  2. Gravitational potential energy (due to height) is transferred into kinetic energy (of motion) as the skier descends — though in reality some is also transferred to thermal energy due to friction/air resistance.
  3. No — energy cannot be destroyed. “Wasted” energy has simply been transferred into a store (almost always thermal energy dispersed into the surroundings) that is no longer useful for the intended purpose, rather than ceasing to exist.

3. Kinetic and Gravitational Potential Energy Extended only

Eₖ = ½mv²
ΔEₚ = mgΔh
Worked example — kinetic energy Find the kinetic energy of a 1200 kg car travelling at 20 m/s.
Eₖ = ½mv² = ½ × 1200 × 20² = ½ × 1200 × 400 = 240000 J (240 kJ)
Worked example — gravitational potential energy Find the change in gravitational potential energy of a 5 kg box lifted 3 m upward (g = 9.8 N/kg).
ΔEₚ = mgΔh = 5 × 9.8 × 3 = 147 J
Worked example — combining KE, GPE and conservation of energy A 2 kg ball is dropped from rest from a height of 5 m. Assuming no air resistance, find its speed just before it hits the ground (g = 9.8 N/kg).
By conservation of energy, GPE lost = KE gained:
mgΔh = ½mv²
Notice the mass m cancels from both sides:
gΔh = ½v² → 9.8 × 5 = ½v² → 49 = ½v² → v² = 98
v = √98 ≈ 9.9 m/s
Try it — Eₖ, Eₚ and Conservation
  1. Calculate the kinetic energy of a 0.5 kg ball travelling at 12 m/s.
  2. Calculate the change in gravitational potential energy of a 2 kg book lifted 1.5 m onto a shelf (g = 9.8 N/kg).
  3. A 0.2 kg stone is dropped from rest from a height of 20 m. Ignoring air resistance, find its speed just before it lands (g = 9.8 N/kg).
Show answers
  1. Eₖ = ½ × 0.5 × 12² = ½ × 0.5 × 144 = 36 J
  2. ΔEₚ = 2 × 9.8 × 1.5 = 29.4 J
  3. mgΔh = ½mv² → gΔh = ½v² → 9.8 × 20 = ½v² → 196 = ½v² → v² = 392 → v = √392 ≈ 19.8 m/s

4. Work Done

Mechanical or electrical work done is equal to the energy transferred. For a force moving an object through a distance:

W = Fd = ΔE
Worked example — calculating work done A person pushes a crate with a force of 150 N, moving it 4 m across a warehouse floor. Find the work done.
W = Fd = 150 × 4 = 600 J
This means 600 J of energy has been transferred (mostly into kinetic energy and, due to friction, thermal energy).
Try it — Work Done
  1. A force of 80 N moves an object 6 m in the direction of the force. Calculate the work done.
  2. A crane does 12000 J of work lifting a load a distance of 5 m. Calculate the force the crane exerts.
Show answers
  1. W = Fd = 80 × 6 = 480 J
  2. F = W/d = 12000/5 = 2400 N

5. Energy Resources

Electricity is generated on a large scale from a range of resources. Several of these work by producing high-pressure steam or moving fluid that spins a turbine, which turns a generator to produce electricity — often heated first using a boiler.

ResourceHow useful energy/electrical power is obtained
Fossil fuelschemical energy released by burning, heats water in a boiler to make steam, which drives a turbine and generator
Biofuelschemical energy released by burning plant/organic material, used similarly to fossil fuels
Water (hydroelectric, waves, tides)moving/falling water directly drives a turbine connected to a generator
Geothermalheat from hot rocks underground heats water into steam, which drives a turbine and generator
Nuclear fuelnuclear fission releases energy as heat, used to boil water into steam, driving a turbine and generator
Solar cellslight from the Sun is converted directly into electrical power (no turbine involved)
Solar panelsinfrared and other electromagnetic waves from the Sun heat water directly (for hot water, not electricity)
Windultimately powered by the Sun (uneven heating of the atmosphere); moving air directly drives a turbine and generator
Advantages and disadvantages — the four factors to weigh up When comparing energy resources, always consider: renewability (will it run out?), availability (is it there when needed — e.g. does the wind always blow, does the sun always shine?), reliability (can it be turned on and off on demand?), scale (how much power can it realistically supply?), and environmental impact (pollution, habitat disruption, greenhouse gas emissions, waste produced).
Worked example — comparing two resources Compare wind power and a coal-fired power station using the five factors above.
Renewability: wind is renewable (won’t run out); coal is non-renewable (finite reserves).
Availability: wind is not always available (depends on weather); coal can be burned whenever supplies are on hand.
Reliability: a coal station can generate a steady, controllable output on demand; wind output varies and cannot be guaranteed at a given moment.
Scale: a single coal station can supply a very large, concentrated amount of power; wind farms typically need many turbines spread over a large area for a comparable output.
Environmental impact: coal produces greenhouse gases and air pollution when burned; wind produces no emissions during operation, though turbines have some visual/noise impact and use land or sea space.

Efficiency describes what fraction of the total energy put into a process ends up as useful output, rather than being wasted. Qualitatively, a more efficient device wastes less energy (usually as heat) for the same useful output.

Efficiency equations Extended % efficiency = (useful energy output / total energy input) × 100%
% efficiency = (useful power output / total power input) × 100%
Worked example — calculating efficiency A motor is supplied with 500 J of electrical energy, and produces 350 J of useful kinetic energy output (the rest is wasted as heat and sound). Find its efficiency.
% efficiency = (350 / 500) × 100 = 70%
Worked example — Sun as the source of energy resources Extended Radiation from the Sun is the ultimate source of energy for almost all our energy resources — including fossil fuels (formed from ancient plant/animal matter that originally captured sunlight), biofuels, wind (caused by the Sun unevenly heating the atmosphere), and water/wave power (driven by weather patterns caused by the Sun). The exceptions are geothermal (heat from the Earth’s interior), nuclear (energy stored in atomic nuclei), and tidal (caused mainly by the gravitational pull of the Moon).
The Sun itself is powered by nuclear fusion, and research is ongoing into whether fusion reactions could be used to generate electricity on a large scale here on Earth.
Try it — Energy Resources and Efficiency
  1. Explain why solar power is not considered a fully “reliable” energy resource, even though sunlight is free and renewable.
  2. A light bulb is supplied with 60 J of electrical energy and produces 12 J of useful light energy. Calculate its efficiency.
  3. Name the three energy resources that do NOT ultimately originate from the Sun’s radiation.
Show answers
  1. Solar power output depends on how much sunlight is currently available — it drops at night, on cloudy days, and varies by season, meaning it cannot reliably supply power on demand at every moment, unlike a resource such as a fossil-fuel power station that can be switched on whenever needed.
  2. % efficiency = (12/60) × 100 = 20%
  3. Geothermal, nuclear, and tidal.

6. Power

Power is defined as work done per unit time, and equivalently as energy transferred per unit time.

P = W / t
P = ΔE / t

Power is measured in watts (W), where 1 watt = 1 joule of energy transferred (or work done) per second.

Worked example — calculating power A motor does 3000 J of work in 12 s. Find its power.
P = W / t = 3000 / 12 = 250 W
Worked example — combining power with energy transfer A 60 W light bulb is left on for 5 minutes. Calculate the total energy transferred.
First convert time to seconds: 5 minutes = 300 s
Rearranging P = ΔE/t: ΔE = P × t = 60 × 300 = 18000 J (18 kJ)
Try it — Power
  1. A crane does 24000 J of work in 8 s. Calculate its power.
  2. A 100 W lamp is switched on for 2 minutes. Calculate the total energy transferred.
  3. A pump has a power output of 400 W. Calculate how long it takes to transfer 20000 J of energy.
Show answers
  1. P = W/t = 24000/8 = 3000 W
  2. t = 2 minutes = 120 s. ΔE = P × t = 100 × 120 = 12000 J
  3. t = ΔE/P = 20000/400 = 50 s
Common mistakes to watch for
  • Forgetting to convert time into seconds before using P = W/t or P = ΔE/t.
  • Forgetting to square the velocity in Eₖ = ½mv² (a very common slip — students often calculate ½mv instead).
  • Using the height change (Δh) incorrectly in ΔEₚ = mgΔh — this must be the change in vertical height, not distance travelled along a slope.
  • Thinking “wasted” energy disappears rather than being transferred into a less useful store (almost always thermal energy).
  • Confusing renewability (will it run out?) with reliability (can it supply power on demand?) — these are two separate factors, and a resource can be renewable but unreliable (e.g. solar, wind).
  • Forgetting the ×100 when calculating a percentage efficiency, or writing an efficiency value greater than 100% (which would break conservation of energy).

7. Quick-Fire Challenge Round

True or False?
  1. Energy can be destroyed if a process is inefficient enough.
  2. In a Sankey diagram, the width of each arrow represents the amount of energy carried by that pathway.
  3. Wind power and solar power are both ultimately powered by the Sun.
  4. Power is defined as energy transferred per unit time.
Show answers
  1. False — energy cannot be created or destroyed, only transferred between stores; an inefficient process wastes more energy (usually as heat) rather than destroying it.
  2. True — this is what makes a Sankey diagram useful for visualising exactly how much energy goes where.
  3. True — wind is caused by the Sun’s uneven heating of the atmosphere, and solar power obviously comes directly from the Sun’s radiation.
  4. True — P = ΔE/t (equivalently, work done per unit time, since work done equals energy transferred).
Spot the Error
  1. “A 4 kg object moving at 3 m/s has kinetic energy Eₖ = ½ × 4 × 3 = 6 J.”
  2. “A device is supplied with 200 J and produces 250 J of useful output, giving an efficiency of 125%.”
  3. “A motor does 500 J of work in 2 minutes, so its power is 500/2 = 250 W.”
Show answers
  1. The velocity should be squared: Eₖ = ½mv² = ½ × 4 × 3² = ½ × 4 × 9 = 18 J, not 6 J.
  2. An efficiency over 100% is impossible, since it would mean more useful energy came out than total energy went in — this breaks the conservation of energy. The numbers given must be checked; a device can never output more useful energy than it was supplied with.
  3. Time must be in seconds before using P = W/t. 2 minutes = 120 s, so P = 500/120 ≈ 4.17 W, not 250 W.

8. Mixed Practice — Bringing It All Together

  1. Calculate the kinetic energy of a 1500 kg car travelling at 10 m/s.
  2. Calculate the change in gravitational potential energy of a 3 kg object lifted 4 m (g = 9.8 N/kg).
  3. A force of 60 N moves an object 5 m. Calculate the work done.
  4. A device is supplied with 800 J and usefully outputs 600 J. Calculate its efficiency.
  5. A pump transfers 15000 J of energy in 30 s. Calculate its power.
Show answers
  1. Eₖ = ½ × 1500 × 10² = ½ × 1500 × 100 = 75000 J
  2. ΔEₚ = 3 × 9.8 × 4 = 117.6 J
  3. W = Fd = 60 × 5 = 300 J
  4. % efficiency = (600/800) × 100 = 75%
  5. P = ΔE/t = 15000/30 = 500 W

Practice at Home

A large topic, so take this set across a couple of sittings. Parts C and D include Extended-only content.

Part A — Energy stores, transfers and conservation
  1. List the seven energy stores named in the syllabus.
  2. Describe the main energy transfer taking place when a battery-powered fan spins.
  3. State the principle of conservation of energy in your own words.
Part B — Work done
  1. A force of 120 N moves a box 3 m. Calculate the work done.
  2. A lift motor does 45000 J of work lifting a lift car 10 m. Calculate the force exerted by the motor.
Part C — Kinetic/gravitational potential energy and efficiency (Extended)
  1. Calculate the kinetic energy of a 0.8 kg ball travelling at 15 m/s.
  2. Calculate the change in gravitational potential energy of a 10 kg object raised 2.5 m (g = 9.8 N/kg).
  3. A generator is supplied with 2000 W of power and usefully outputs 1500 W. Calculate its efficiency.
Part D — Energy resources and power
  1. Describe how electricity is generated from a hydroelectric dam, referring to a turbine and generator.
  2. Compare a nuclear power station and a solar farm using the five factors: renewability, availability, reliability, scale, and environmental impact.
  3. A washing machine has a power rating of 2000 W and runs for 45 minutes. Calculate the total energy transferred, in joules.

Key Vocabulary Recap

Conservation of energy — energy cannot be created or destroyed, only transferred between stores
Sankey diagram — a diagram where arrow width shows the amount of energy carried by each pathway
Work done — energy transferred by a force moving through a distance (W = Fd)
Efficiency — the fraction (or percentage) of total energy input that ends up as useful output
Renewable — an energy resource that will not run out (e.g. wind, solar, hydro)
Power — the rate of doing work or transferring energy (P = ΔE/t), measured in watts

Syllabus Reference

This note covers Cambridge IGCSE Physics (0625) section 1.7, Energy, work and power — 1.7.1 Energy (Core: energy stores, transfer pathways, conservation of energy with simple flow diagrams; Supplement: Eₖ = ½mv², ΔEₚ = mgΔh, conservation of energy with Sankey diagrams), 1.7.2 Work (Core: W = Fd = ΔE), 1.7.3 Energy resources (Core: how electrical power is obtained from each resource including boiler/turbine/generator references, advantages/disadvantages by renewability/availability/reliability/scale/environmental impact, qualitative efficiency; Supplement: the Sun as the source of most resources, nuclear fusion in the Sun and fusion research, the percentage efficiency equations), and 1.7.4 Power (Core: P = W/t = ΔE/t).

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