Energy transferred when a force moves an object in the direction of the force.
W = FdW = work done (J) · F = force (N) · d = distance moved in direction of force (m)
If the force and the displacement are not in the same direction, only the component of force in the direction of motion does work. 1 joule = 1 newton-metre.
Worked example
A person pushes a box with a force of 80 N for a distance of 5 m. Find the work done.
W = Fd = 80 × 5 = 400 J
2. Kinetic Energy
Kinetic energy
Energy an object has due to its motion.
KE = ½mv²KE = kinetic energy (J) · m = mass (kg) · v = speed (m/s)
Worked example
A 1200 kg car moves at 20 m/s. Find its kinetic energy.
KE = ½ × 1200 × 20² = ½ × 1200 × 400 = 240 000 J = 240 kJ
Speed is squared
Doubling the speed quadruples the kinetic energy. A car at 60 km/h has four times the KE of a car at 30 km/h — this is why braking distance increases rapidly with speed.
3. Gravitational Potential Energy
Gravitational potential energy (GPE)
Energy an object has due to its position in a gravitational field.
GPE = mghGPE in J · m = mass (kg) · g = 10 N/kg · h = height above reference point (m)
Worked example
A 2 kg ball is raised 3 m. Find the gain in GPE.
GPE = mgh = 2 × 10 × 3 = 60 J
4. Conservation of Energy
Principle of conservation of energy
Energy cannot be created or destroyed — it can only be transferred from one form to another. The total energy in a closed system remains constant.
In a frictionless pendulum: GPE → KE → GPE → KE… continuously. At the lowest point, all energy is KE. At the highest point, all energy is GPE.
In a real system, some energy is always lost to the surroundings as heat (due to friction or air resistance). Total energy is still conserved — it just transfers to thermal energy of the surroundings.
Useful energy transfer chains
Solar cell: light → electrical. Generator: kinetic → electrical. Electric motor: electrical → kinetic. Loudspeaker: electrical → sound.
5. Power
Power
The rate of energy transfer (or the rate of doing work).
P = E ÷ t = W ÷ tP = power (W) · E = energy (J) · t = time (s) · 1 W = 1 J/s
Worked example
A motor transfers 12 000 J in 2 minutes. Find the power output.
t = 2 × 60 = 120 s. P = 12 000 ÷ 120 = 100 W
6. Efficiency
efficiency = (useful energy output ÷ total energy input) × 100%Efficiency has no unit. It is always less than 100% in a real machine.
Worked example
A motor takes in 500 J and produces 350 J of useful kinetic energy. Find the efficiency.
Efficiency = (350 ÷ 500) × 100% = 70%
The remaining 30% (150 J) is wasted as heat due to friction.
Common mistake
Efficiency cannot exceed 100%. If your calculation gives >100%, check whether you have divided by the input or output — always divide useful output by total input.
Key Energy Equations
KE = ½mv² | GPE = mgh | W = Fd | P = W/t
All energies in joules (J). Power in watts (W). Remember: KE doubles when v increases by root 2.
Must-Know for Exam
Work = Force x distance (in direction of force). No movement = no work done.
KE = 0.5mv2. Doubling speed -> 4x KE. Doubling mass -> 2x KE.
GPE = mgh. Only depends on vertical height change h.
Conservation of energy: KE lost = GPE gained + heat lost to friction (in realistic situations)
Efficiency = useful output / total input x 100. Always < 100% (some energy lost as heat/sound).
Power = energy transferred / time = Force x velocity (P = Fv for constant speed)
7. Common Exam Traps
Trap 1 — Work only done when object moves
Holding a heavy bag stationary does no work on the bag (no displacement in the direction of force). You may feel tired but no energy is transferred to the bag.
Trap 2 — v² not v in KE formula
KE = ½mv² — the velocity is squared. Forgetting to square the velocity is the most common calculation error on this topic.
Trap 3 — Convert time to seconds for power
If time is given in minutes, multiply by 60 before using P = E ÷ t. Power units require time in seconds.
Key Terms — Flashcard Review
Tap each card to reveal the definition.
Work done
W = Fd. Work is done only when force causes movement in its direction. Unit: joule (J).
Kinetic energy
KE = 0.5 mv2. Depends on MASS and SQUARE of speed. Doubling speed quadruples KE.
Gravitational PE
GPE = mgh. Energy stored due to position in a gravitational field. Unit: joule (J).
Conservation of energy
Energy cannot be created or destroyed, only transferred between forms. Total energy is constant.
Power
Rate of doing work (energy transfer). P = W/t = Fv. Unit: watt (W) = J/s.
Efficiency
Efficiency = useful energy output / total energy input x 100%. Always less than 100% due to heat losses.
🎯 Practice Quiz — Test Yourself
8 O Level-style questions on this topic. Select an answer to see instant feedback.
Question 1 of 8
In a battery-powered torch, the energy conversion chain is:
Explanation: Battery: chemical → electrical. Bulb: electrical → light (+ heat). Full chain: chemical → electrical → light.
Question 2 of 8
GPE gained by 2 kg raised 5 m: (g = 10 N/kg)
Explanation: GPE = mgh = 2 × 10 × 5 = 100 J.
Question 3 of 8
A machine does 500 J useful work from 800 J input. Efficiency is:
Explanation: Total energy is always conserved — it can only be converted from one form to another, never created or destroyed.
Question 5 of 8
Power is defined as:
Explanation: Power = Work done / time = Energy transferred / time. Unit: Watt (W) = J/s.
Question 6 of 8
A 2 kg object moving at 6 m/s has a kinetic energy of:
Explanation: KE = 0.5 x m x v2 = 0.5 x 2 x 36 = 36 J. The v is squared first: 6 x 6 = 36, then multiply by 0.5 x 2. A common error is forgetting to square the velocity.
Question 7 of 8
A machine does 6000 J of useful work from 10 000 J of input energy. Its efficiency is:
Explanation: Efficiency = useful output / total input x 100 = 6000/10000 x 100 = 60%. Efficiency is always less than 100%. The remaining 40% (4000 J) is wasted, usually as heat.
Question 8 of 8
A 500 W motor lifts a 20 kg load 5 m in a certain time. The time taken is (g = 10 N/kg):
Explanation: GPE gained = mgh = 20 x 10 x 5 = 1000 J. Power = work/time, so time = work/power = 1000/500 = 2 s. (Assuming 100% efficiency for simplicity.)