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Topic 1 · 1.7

Energy, work, power and energy resources

Core and Extended · Papers 1–6

🎯What you need to be able to do

  • Name the energy stores and describe transfers between them; apply conservation of energy with flow diagrams, and Sankey diagrams EXTENDED.
  • Use \( E_k = \tfrac12 mv^2 \) and \( \Delta E_p = mg\Delta h \) EXTENDED.
  • Use \( W = Fd = \Delta E \) for work done and \( P = \dfrac{W}{t} = \dfrac{\Delta E}{t} \) for power.
  • Describe how electricity is generated from each energy resource, with advantages and disadvantages; use efficiency EXTENDED.

📚The physics

Energy stores and transfers

Energy may be stored as kinetic, gravitational potential, chemical, elastic (strain), nuclear, electrostatic and internal (thermal) energy. It is transferred between stores by forces (mechanical work done), electrical currents (electrical work done), heating, and by electromagnetic, sound and other waves.

A flow diagram for a car driving up a hill: energy from the chemical store in the fuel is transferred by mechanical work to the kinetic store and the gravitational store of the car, and by heating and sound to the internal (thermal) store of the surroundings. A box states the principle of conservation of energy.
The principle of conservation of energy: energy cannot be created or destroyed, only transferred.

Kinetic and gravitational potential energy EXTENDED

\[ E_k = \tfrac12 mv^2 \qquad \Delta E_p = mg\Delta h \]
A 0.50 kg ball falls 2.0 m. At the top it has 9.8 J of gravitational potential energy and no kinetic energy; halfway down it has 4.9 J of each; just before landing it has 9.8 J of kinetic energy and none of gravitational potential energy.
EXTENDED Without air resistance, the gravitational energy lost equals the kinetic energy gained: \( mgh = \tfrac12 mv^2 \), so \( v = \sqrt{2gh} = 6.3 \) m/s.

Work and power

Mechanical or electrical work done equals the energy transferred. Power is work done (energy transferred) per unit time:

\[ W = Fd = \Delta E \qquad P = \frac{W}{t} = \frac{\Delta E}{t} \]

Work is in joules (J); power in watts (W), where 1 W = 1 J/s.

Efficiency EXTENDED

\[ \text{efficiency} = \frac{\text{useful energy output}}{\text{total energy input}} \times 100\% = \frac{\text{useful power output}}{\text{total power input}} \times 100\% \]

No device is 100% efficient: some energy is always wasted, usually by heating the surroundings. A Sankey diagram shows this with arrows whose widths are proportional to the energy.

Energy resources

  • Fossil fuels (coal, oil, gas) and biofuels: burned to heat water to steam, which turns turbines and generators. Reliable and available on demand; fossil fuels are non-renewable and release carbon dioxide; biofuels are renewable but need farmland.
  • Nuclear fuel: fission heats water to steam. Large scale, reliable, no carbon dioxide; radioactive waste, costly to build and decommission.
  • Water: waves, tides and hydroelectric dams drive turbines directly. Renewable and no fuel cost; waves are unreliable, tidal and hydroelectric schemes flood or change habitats and suit only some places.
  • Geothermal: hot rocks heat water to steam. Renewable and reliable, but only in volcanic areas (Indonesia uses it).
  • Solar: solar cells turn light into electricity; solar panels heat water. The Sun also drives the wind. Renewable, but only available when the Sun shines or the wind blows, and large areas are needed.
A thermal power station as a chain of boxes: fuel or reactor, boiler turning water to steam, turbine turned by steam, generator changing kinetic energy to electrical, then transformer and grid. Steam is condensed and the water returns to the boiler.
Fuel, nuclear and geothermal stations all boil water to turn a turbine connected to a generator.
Arrows from the Sun to fossil fuels, biofuels, wind, waves, hydroelectric power and solar cells and panels. A separate box lists the resources not from the Sun: geothermal, nuclear fuel and tidal energy, and notes that the Sun itself is powered by nuclear fusion.
EXTENDED Research is under way to use nuclear fusion to generate electricity on a large scale.

✏️Worked example

An electric motor with an input power of 200 W lifts a 25 kg load through 3.0 m in 5.0 s. (a) Calculate the weight of the load and the work done on it. [2] (b) Calculate the useful power output. [1] (c) EXTENDED Calculate the efficiency of the motor and sketch a Sankey diagram. [3]

(a) W = mg = 25 × 9.8 = 245 N; work done = Fd = 245 × 3.0 = 735 J.

(b) P = W/t = 735 / 5.0 = 147 W.

(c) Energy input = 200 × 5.0 = 1000 J; efficiency = 735 / 1000 × 100% = 74% (73.5%).

A Sankey diagram: an input arrow of 1000 J of electrical energy splits into a wide arrow of 735 J of useful energy in the gravitational store of the load and a narrower arrow of 265 J wasted, bending down, as heating and sound.
Check it. Useful + wasted = 735 + 265 = 1000 J, the input. An efficiency over 100% means the fraction is upside down.
Using the mass as the force. Work = force × distance: lift against the weight (245 N), not 25.

📝Practise

In the style of the multiple-choice and theory papers. EXTENDED marks Supplement content.

1. (Multiple choice.) Which energy resource does not have the Sun as its main source of energy? A: biofuel. B: tidal. C: wind. D: waves.
B. Tides are caused mainly by the Moon’s gravity. (Geothermal and nuclear are the other two.)
2. (Theory.) A forklift lifts a crate of weight 820 N through a vertical height of 1.5 m. Calculate the work done on the crate, with its unit, and the crate’s mass. [4] (Modelled on 0625/32 June 2026 Q2(a).)
Work = Fd = 820 × 1.5 = 1230 J. Mass = W/g = 820 / 9.8 = 84 kg.
3. (Multiple choice.) EXTENDED A skier of mass 70 kg starts from rest and descends a vertical height of 40 m, reaching 18 m/s at the bottom. How much energy is transferred to the surroundings? A: less than 10 kJ. B: 10–20 kJ. C: 20–30 kJ. D: more than 30 kJ. (Modelled on 0625/22 June 2026 Q7.)
B. Ep lost = 70 × 9.8 × 40 = 27 440 J; Ek gained = ½ × 70 × 182 = 11 340 J; wasted = 16 100 J = 16 kJ.
4. (Theory.) A 2.0 kW kettle is switched on for 3.0 minutes. Calculate the energy transferred. [2]
E = Pt = 2000 × 180 = 360 000 J (360 kJ).
5. (Theory.) EXTENDED A 1500 kg car travels at 20 m/s. Calculate its kinetic energy. The brakes stop it in 40 m: calculate the average braking force. [4]
Ek = ½ × 1500 × 202 = 300 000 J. Work done by brakes = Ek, so F = 300 000 / 40 = 7500 N.
6. (Theory.) Give one advantage and one disadvantage of generating electricity from nuclear fuel rather than from solar cells. [2] (Modelled on 0625/42 June 2026 Q10(a)(iii).)
Advantage: available 24 hours a day, whatever the weather (reliable, large scale). Disadvantage: produces radioactive waste that must be stored safely for a very long time (or: non-renewable; expensive to decommission; risk of radiation leaks).
7. (Theory.) EXTENDED A lamp is supplied with 60 J each second and emits 9.0 J of light each second. Calculate its efficiency and state what happens to the rest of the energy. [3]
Efficiency = 9.0 / 60 × 100% = 15%. The other 51 J each second is transferred to the internal (thermal) store of the surroundings by heating.
8. (Theory.) An electric car travels at constant velocity along a level road. Describe the energy transfers. [2]
Energy from the chemical store of the battery is transferred by electrical work to the motor, then by mechanical work against friction and air resistance to the internal (thermal) store of the surroundings. The kinetic store stays constant.

🔗Go deeper — other people’s work

These are external resources, not mine. If one stops working, tell me and everything above it on this page still stands.

  • PhET “Energy Skate Park: Basics” — kinetic and potential energy with friction
  • PhET “Energy Forms and Changes” — energy stores and transfers