Work, power and efficiency equations
Work done = energy transferred: W = Fd, where d is the distance moved in the direction of the force. Work and energy are in joules (J); there is no time term. Power is the rate of doing work: P = W/t, in watts (W); 1 W = 1 J/s. Efficiency is the fraction of the input transferred usefully rather than wasted. (Extended) Ek = ½mv² (m in kg, v in m/s), ΔEp = mgΔh (g = 10 N/kg), and efficiency = useful output ÷ total input × 100%, in energy or power form.
The main energy resources
Advantage / disadvantage of each. Fossil fuels: reliable, high output, but non-renewable, releasing CO2 and pollutants. Biofuels: renewable, near carbon-neutral, but need land. Water (hydro, tidal, wave): renewable, no fuel cost, but needs the right geography; dams flood land. Geothermal: renewable, reliable, but needs hot rocks near the surface. Nuclear fission: no CO2, reliable, but radioactive waste. Solar: no fuel, none at night. Wind: no CO2, but stops when wind drops.
Energy stores, pathways and conservation
Energy stores: kinetic, gravitational potential, chemical, elastic (strain), nuclear, electrostatic, internal (thermal). Transfer pathways move energy between them: mechanically (a force does work), electrically, by heating, by radiation (light, sound, other waves). Conservation of energy: energy cannot be created or destroyed, only transferred or stored, so the total for a closed system stays constant. Energy flow diagrams track this; Sankey diagrams are not required.
Drawn from real examiner reports.
Work ≠ power — no time in W = Fd
The mark-scheme wording is force × distance moved in the direction of the force, and this equals the energy transferred. "Energy used" alone is too vague. W = Fd carries no time term, so if a question supplies a time that belongs to a power calculation instead. Convert cm to m first — a distance left in centimetres gives an answer 100 times too large.
Digest P1 (Energy/work/power): work = force × distance = energy transferred, no time term (that is power), convert cm→m (Jun 2022 P31 Q3c; Nov 2023 P31 Q9bii).
(Extended) Ek — square v, then halve
Ek = ½mv² is the most error-prone calculation in P1: the speed is squared and then halved, and candidates routinely drop one step or the other. Because of the square, doubling the speed gives four times the kinetic energy, not twice. Mass must be in kilograms, so 500 g becomes 0.5 kg; substituting grams gives an answer 1000 times too big.
Digest P1 (Energy/work/power): KE = ½mv² depends on the square of speed — candidates forget to halve or to square v — and convert g→kg (Jun 2022 P21 Q30; Nov 2023 P41 Q6aii).
(Extended) GPE — never drop the × g
In ΔEp = mgΔh, omitting the × g leaves an answer wrong by a factor of 10 (Cambridge uses g = 10 N/kg). Δh is the vertical height change, not the distance along a slope or a staircase, and the mass must be in kilograms. The answer is an energy, so the unit is the joule — do not quote newtons just because g appeared in the working.
(Extended) Efficiency — divide, not multiply
Efficiency = useful output ÷ total input. Divide useful by total: do not multiply the two, and do not invert the fraction — an efficiency above 1 (or above 100%) is impossible. To express it as a percentage multiply the fraction by 100, so a fraction of 0.9 is 90%; write × 100, never × 90. The same equation works with power in place of energy.
Digest P1 (Energy/work/power): efficiency = useful ÷ total × 100 (÷ not ×, and ×0.9 not ×90) (Jun 2023 P42 Q6b).
Three energy-resource myths
Geothermal is renewable — its energy comes from continuous radioactive decay in hot rocks — yet many call it non-renewable. Hydroelectric energy is transferred from the gravitational potential store of stored water, not from a chemical, nuclear or elastic store. A nuclear-fission station does use a turbine and generator; only the heat source differs from a coal station.
Digest P1 (Energy resources): geothermal is renewable; hydroelectric energy comes from the GPE of water; fission stations DO use a turbine and generator — one bundle covering all three (Jun 2022 P12 Q31; Nov 2022 P11 Q32; Nov 2023 P11 Q31).
Fuels store chemical, not kinetic, energy
The energy in petrol, diesel, coal and food sits in a chemical (potential) store, not a kinetic store — nothing is moving until the fuel is burned and energy is transferred onward to the kinetic and thermal stores. Name the store precisely: "movement energy" and "fuel energy" are not store names, and they are not credited.
Digest P1 (Energy/work/power): chemical (potential) energy is stored in fuels/petroleum/diesel, not kinetic (Jun 2022 P31 Q6e).
(Extended) The Sun fuses; reactors fission
Energy is released in the Sun by nuclear fusion, hydrogen fusing into helium; nuclear reactors on Earth release it by nuclear fission. Do not swap the two, and do not write combustion or radiation for the Sun. The Sun is also the ultimate source of most resources — wind, waves, biofuels, fossil fuels, solar — but not geothermal, nuclear or tidal, which comes from the Moon.
Digest P6 (Space physics), cross-strand: energy is released in the Sun by nuclear fusion of hydrogen into helium, not fission/combustion/radiation (Jun 2022 P23 Q31; Nov 2022 P41 Q6c).
Write the formula first
Put the equation down before any numbers: W = Fd, P = W/t, Ek = ½mv², ΔEp = mgΔh, or efficiency = useful ÷ total × 100%. The correct formula usually earns the first mark even when the arithmetic then slips, and writing it out is what stops you inverting the rearrangement.
Convert units before substituting
Convert first, not after: cm → m (÷100), g → kg (÷1000), kW → W (×1000). Then state the unit on every answer — J for work and energy, W for power, % for efficiency. A bare number loses the final mark even when the working is right.
Match resource points to the tariff
Give as many distinct points as there are marks, and change axis each time: renewable or not, CO2 and pollution, reliability, land or geography needed. "Clean" and "no pollution" count as one point, not two. Answer about the resource the question actually names.
Command words for this topic
Define power = work done (energy transferred) per unit time. State the principle of conservation of energy = energy cannot be created or destroyed, only transferred or stored, total constant. Calculate or Determine = formula, substitution, answer with its unit.
Cambridge 0654 spec reference: Section P1 "Motion, forces and energy", sub-topic P1.6. This leaf covers energy stores and transfers, the principle of conservation of energy (simple examples and flow diagrams; Sankey not required), work done (), power (), the main energy resources with their advantages and disadvantages, and efficiency (qualitative at Core). Extended (Supplement) statements, flagged (E), add , , the Sun as the source of most resources, fusion/fission as the release processes, and the efficiency equation.
Gravitational field strength throughout (Cambridge standard).
| Quantity | Formula | Symbols and units |
|---|---|---|
| Work done = energy transferred | (J), force (N), distance in the direction of the force (m) | |
| Power | power (W), time (s); | |
| (E) Kinetic energy | mass (kg), speed (m/s), (J) | |
| (E) Gravitational PE change | , height change (m) | |
| (E) Efficiency | energy form or power form; answer as a percentage |
Definitions (mark-scheme form): work done = force distance moved in the direction of the force ( energy transferred), unit J. Power = work done (energy transferred) per unit time, unit W. Conservation of energy = energy cannot be created or destroyed, only transferred or stored; the total stays constant.
(Core) Name four energy stores and the four ways energy can be transferred between them.
(Core) A person pushes a trolley with a horizontal force of 200 N and moves it 3.0 m in the direction of the force.
Calculate the work done on the trolley. Show your working. (2 marks)
