Physics • Year 11 • Module 2 • Lesson 8
Power
Lock in the definition of power, the three power formulae, and the critical distinction between work and power before tackling harder questions.
1. Term–definition match
The definitions below are shuffled. In the right-hand column write the matching term from this list: power, watt, work, average power, instantaneous power, kilowatt, rate of energy transfer, driving force, resistance force, constant velocity. 10 marks (1 each)
| # | Definition | Matching term |
|---|---|---|
| 1.1 | The rate at which energy is transferred or work is done; measured in watts. | |
| 1.2 | The SI unit of power; equal to one joule per second (1 J/s). | |
| 1.3 | The total energy transferred by a force through a displacement; measured in joules, not a rate. | |
| 1.4 | Total energy transferred divided by total time over a measured interval; P = ΔE/Δt. | |
| 1.5 | Power at a specific moment in time; P = Fv cosθ when force and velocity are known at that instant. | |
| 1.6 | A unit of power equal to 1000 watts; often used for engines and motors. | |
| 1.7 | Another name for power that emphasises what it measures — energy moving per unit time. | |
| 1.8 | The forward force an engine or motor provides to move a vehicle; symbol Fdrive. | |
| 1.9 | The total backward force (friction, air resistance) opposing motion; symbol Fresist. | |
| 1.10 | The condition where acceleration equals zero; Newton’s First Law gives Fdrive = Fresist in this state. |
2. True or false — with correction
Circle T or F for each statement. If the statement is false, write the corrected version on the line below it. 12 marks (1 T/F + 1 correction each)
2.1 An athlete and a walker who climb the same staircase do the same amount of work if they have the same mass. T / F
2.2 Power depends on how much work is done but not on how long it takes. T / F
2.3 At constant velocity, the driving force of an engine equals the car’s weight. T / F
2.4 If a constant force is applied during acceleration and speed increases, the instantaneous power P = Fv increases over time. T / F
2.5 The formula P = mgh/Δt applies to any motion involving gravity, including a car driving up a slope at an angle. T / F
2.6 Doubling the speed of a vehicle while maintaining the same driving force doubles the power output. T / F
3. Fill-in-the-blank paragraph
Use the word bank to complete the passage. Each word is used once. 8 marks (1 per blank)
Word bank:
constant · energy · force · joules · rate · resistance · time · watts
Power is defined as the ___________ of energy transfer — the amount of ___________ transferred per unit of ___________. Its SI unit is the ___________ (W), where 1 W equals 1 ___________ per second. When an object moves at ___________ velocity, Newton’s First Law tells us that the driving ___________ exactly equals the total ___________ force. In this case, power can be calculated as P = Fdrive × v.
4. Short recall questions
Answer each question in 1–2 sentences using precise physics terms. 8 marks (2 each)
4.1 State the difference between work and power. Why can two people do the same work but have very different power outputs?
4.2 When is it correct to use P = mgh/Δt? State one situation where this formula gives an incomplete answer and explain why.
4.3 Explain the key reasoning step needed before applying P = Fv to a vehicle travelling at constant speed.
4.4 Why does the same letter ‘W’ appear in both ‘P = 500 W’ and ‘W = 500 J’, yet mean something completely different in each case?
5. Build a concept map
Draw labelled arrows between the six terms below to show how they connect. Each arrow must carry a linking phrase (e.g. “is measured in”, “equals when v is constant”, “divided by time gives”). Aim for at least 6 labelled arrows. 6 marks (1 per valid labelled arrow)
Supplied terms: power · work · watt · force × velocity · driving force · resistance force.
6. Formula identification table
For each scenario below, identify which power formula applies and write it in the ‘Formula’ column. Then state one key condition that must be true for that formula to be valid. 6 marks (1 per row)
| Scenario | Formula to use | Key condition |
|---|---|---|
| A crane lifts a 400 kg crate 12 m vertically in 30 s. | ||
| A motor transfers 18 000 J of energy in 60 s. | ||
| A car travels at constant 20 m/s against 700 N of air resistance. | ||
| A cyclist applies 150 N of force at 6 m/s along the direction of motion. | ||
| A pump lifts 300 kg of water 5 m per minute. | ||
| A train accelerates; its engine provides 40 000 N at the instant its speed reaches 15 m/s. |
Q1 — Term–definition match
1.1 power • 1.2 watt • 1.3 work • 1.4 average power • 1.5 instantaneous power • 1.6 kilowatt • 1.7 rate of energy transfer • 1.8 driving force • 1.9 resistance force • 1.10 constant velocity.
Q2 — True / false with correction
2.1 True. Work = mgh; if mass and height are the same, both persons do identical work regardless of time taken.
2.2 False. Power depends on both how much work is done AND how long it takes: P = W/Δt. The same work done in a shorter time gives greater power.
2.3 False. At constant velocity, the driving force equals the resistance force (Newton 1: net force = 0). The car’s weight acts downward and is balanced by the normal force; it is irrelevant to horizontal power calculations on a flat road.
2.4 True. P = Fv; if F is constant and v increases during acceleration, then P increases proportionally.
2.5 False. P = mgh/Δt is valid only for purely vertical lifting. For a car on a slope, it underestimates total power because it ignores horizontal kinetic energy changes and friction along the slope.
2.6 True. P = Fv; with constant force F, doubling v doubles P.
Q3 — Cloze paragraph
In order: rate / energy / time / watts / joules / constant / force / resistance.
Q4.1 — Work vs power
Work is the total energy transferred by a force through a displacement (measured in joules); it does not depend on time. Power is the rate of doing work — energy transferred per second (measured in watts). Two people can do the same work but at different power outputs if one completes the task in a shorter time; e.g. the athlete (4 s) and the walker (40 s) both do W = 3430 J on the same staircase, but the athlete’s power is 10× greater.
Q4.2 — When to use P = mgh/Δt
P = mgh/Δt is correct for purely vertical lifting at constant speed, where all work goes against gravity. It gives an incomplete (underestimate) answer for a person running upstairs, because it ignores the kinetic energy of limb movement, heat generated in muscles, and any horizontal displacement — the actual total power expenditure is higher.
Q4.3 — Key step before P = Fv
First check whether velocity is constant. If it is, apply Newton’s First Law: net force = 0, so Fdrive = Fresist. Use this driving force (not the weight, not an arbitrary force) in P = Fdrive × v.
Q4.4 — The ‘W’ symbol ambiguity
‘W’ in ‘P = 500 W’ is the abbreviation for the unit “watts” (the SI unit of power). ‘W’ in ‘W = 500 J’ is a variable symbol for work, measured in joules. They are entirely different quantities — context and the units stated distinguish them.
Q5 — Sample concept map
Accept any map with valid labelled arrows including:
- power — is measured in → watt
- work — divided by time equals → power
- force × velocity — gives → power
- driving force — equals at constant velocity → resistance force
- driving force — multiplied by v gives → power
- watt — equals 1 J/s which is 1 unit of → power
Award 1 mark per valid labelled arrow (minimum 6 required).
Q6 — Formula identification table
Row 1 (crane lifting): P = mgh/Δt — condition: purely vertical lifting. Row 2 (motor, energy given): P = ΔE/Δt — condition: total energy transferred is known. Row 3 (car at constant v): P = Fv (using Fdrive = Fresist = 700 N from Newton 1) — condition: constant velocity. Row 4 (cyclist, F and v given): P = Fv (or P = Fv cos0° = Fv since motion is along force direction) — condition: force is parallel to velocity (θ = 0°). Row 5 (pump, vertical lift): P = mgh/Δt — condition: purely vertical lifting, Δt = 60 s. Row 6 (train instantaneous): P = Fv — condition: instantaneous power at a specific moment; force and velocity both known at that instant.