Energy: revision notes and practice

What you will learn

• Describe energy stores and the pathways between them.
• Calculate work done, kinetic energy, gravitational energy and power with matching units.
• Explain conservation, dissipation and efficiency without saying that energy disappears.

Key rules

Work done

W = F × s for a constant force in the direction of movement. Use force in N and distance in m.

Kinetic energy

Eₖ = ½mv². Use mass in kg and speed in m/s. Square the speed before multiplying.

Gravitational potential energy

Gain in energy = mgh. Use mass in kg, vertical height gain in m and the value of g given in the question, in N/kg.

Worked examples

Example 1: A constant force of 18 N moves an object 4 m in the direction of the force. Find the work done.

1. Use W = F × s.
2. W = 18 × 4 = 72 J.

72 J

Example 2: A 2.5 kg object moves at 4 m/s. Calculate its kinetic energy.

1. Square the speed: 4² = 16.
2. Eₖ = ½ × 2.5 × 16 = 20 J.

20 J

A practice question

A constant force of 47 N moves an object 6 m in the direction of the force. Calculate the work done.

1. Describe the system before choosing an equation

A system is the object or group of objects you are studying. First describe what changes: does something move faster, rise, warm up or stretch? Kinetic, gravitational potential, elastic potential, chemical and thermal stores help explain these situations. Energy is measured in joules, J; a store describes where energy is held, rather than a new kind of substance.

An electric motor lifting a load transfers energy electrically, then mechanically. The load gains gravitational potential energy while the motor and surroundings also warm. Name the starting store, transfer pathway and final stores instead of writing only 'energy is used'.

2. Work done is an energy transfer

For a constant force acting along the movement, multiply force by distance. A 15 N force moving a box 6 m transfers 90 J. Rearrange to F = W/s or s = W/F when another quantity is missing. A force in newtons multiplied by a distance in metres gives joules.

Use the distance along the force's direction. The simple equation cannot be applied unchanged to an angled force or a varying force. Holding a bag still involves no mechanical work on the bag because it does not move, although your body still transfers energy internally.

W = Fs; W in J, F in N, s in m

3. Kinetic energy depends strongly on speed

Kinetic energy is associated with motion. Convert mass to kilograms and speed to metres per second before squaring the speed. For a 4 kg trolley at 3 m/s, Eₖ = 0.5 × 4 × 9 = 18 J. Doubling the mass doubles this energy; doubling the speed makes it four times as large.

To find speed, rearrange to v² = 2Eₖ/m, then take the positive square root. For 50 J and 4 kg, v = √25 = 5 m/s. Do not forget the square root or square the mass by mistake.

Eₖ = ½mv²; m in kg, v in m/s, Eₖ in J

4. Height changes gravitational potential energy

Near Earth's surface, a raised object gains energy according to its mass, the gravitational field strength and its vertical height change. A 2 kg object lifted 3 m gains 58.8 J when g = 9.8 N/kg. The route may be a ramp, but use the vertical rise rather than the ramp length.

Rearrange to h = ΔEₚ/(mg). When an object falls, its gravitational store decreases. If air resistance is negligible, that decrease becomes kinetic energy; with air resistance, some energy also reaches thermal stores. Use the value of g supplied and keep it consistent throughout your calculation.

ΔEₚ = mgΔh; Δh in m, g in N/kg, ΔEₚ in J

5. Springs and warming materials

A spring stores elastic potential energy when stretched or compressed. Eₑ = ½ke² applies while force is proportional to extension. Here k is the spring constant in N/m and e is extension in metres, measured from the natural length. A 200 N/m spring extended 0.10 m stores 1 J.

For a temperature change without a change of state, ΔE = mcΔθ. Specific heat capacity c describes the energy needed per kilogram per degree Celsius. Heating 0.5 kg of a material with c = 400 J/(kg °C) through 10 °C requires 2000 J. A larger specific heat capacity means more energy for the same mass and temperature rise.

Eₑ = ½ke²; ΔE = mcΔθ

6. Power tells you how quickly energy moves

Power is the rate of energy transfer, measured in watts. One watt means one joule per second. Two motors might lift the same load through the same height, transferring the same useful energy; the faster motor has the greater useful power. Power is not an amount of energy.

A device transferring 2400 J in 30 s has an average power of 80 W. Use E = Pt to find energy or t = E/P to find time. Convert minutes to seconds and kilowatts to watts before substituting. These calculations assume the stated power is constant or an appropriate average.

P = E/t = W/t; P in W, t in s

7. Follow useful and unwanted transfers

Energy is conserved: it cannot be created or destroyed. In a closed system the total stays constant, even when it becomes spread through thermal stores that are less useful for the intended job. Friction heating brakes is an example of dissipation. 'Wasted' energy still exists.

Efficiency = useful output/input, using energy or power consistently. A lamp transferring 25 J usefully from 100 J input has efficiency 0.25, or 25%. It cannot exceed 100%. Higher extension: explain how insulation or lubrication reduces unwanted transfers and can improve the intended transfer's efficiency.

Efficiency = useful output energy ÷ total input energy; multiply by 100 for %

8. Connect the equations to a practical

In a supervised heating experiment, measure the material's mass and starting temperature, then record the electrical energy supplied and temperature rise. Calculate c = E/(mΔθ). Insulation reduces heating of the surroundings, and good contact between heater, thermometer and material improves measurement. Do not handle hot equipment without your teacher's procedure.

If you assume every supplied joule warms the material, energy losses usually make the calculated specific heat capacity too large. Repeat measurements, identify unusual results and explain the specific effect of a limitation. 'Human error' alone does not explain which measurement changed or why.

Check your understanding

How to earn the marks

• List known quantities and convert units before selecting the equation.
• Use a temperature difference or vertical height change when the equation needs a change.
• Show substitution, retain calculator precision and include J, W or the relevant final unit.
• In explanations, name the stores and transfer pathways; account for unwanted energy too.

A common mistake

Doubling speed makes kinetic energy four times as large if mass stays constant, because speed is squared.

Course context and official specifications

This guide covers selected skills. Some extensions are Higher content; choose your official tier separately from practice difficulty in the app. These are original questions and explanations.

• AQA GCSE Physics — 4.1.1.2, 4.1.1.4; 4.5.2

  The core calculations in this bank are selected separate Physics skills. Foundation and Higher content differ within these larger sections; this is not complete topic coverage.

• Edexcel GCSE Physics — 3.1–3.2; 8.5–8.9

  The core calculations in this bank are selected separate Physics skills. Foundation and Higher content differ within these larger sections; this is not complete topic coverage.

• OCR Gateway GCSE Physics A — P7.1, P7.2; P2.2m–P2.2o; P2.3

  The core calculations in this bank are selected separate Physics skills. Foundation and Higher content differ within these larger sections; this is not complete topic coverage.

• OCR Twenty First Century GCSE Physics B — P2.1; P4.4

  The core calculations in this bank are selected separate Physics skills. Foundation and Higher content differ within these larger sections; this is not complete topic coverage.

Keep your next step small

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