Physics • Year 11 • Module 2 • Lesson 10
Phase 2 Consolidation
Lock in all six Phase 2 formulae, recognise the conditions each requires, and practise the core vocabulary before attempting harder questions.
1. Term–definition match
The definitions below are shuffled. In the right-hand column write the matching term from this list: work, kinetic energy, work-energy theorem, gravitational potential energy, mechanical energy, power, joule, watt, conservative force, non-conservative force. 10 marks (1 each)
| # | Definition | Matching term |
|---|---|---|
| 1.1 | Energy stored in an object due to its position in a gravitational field; equals mgh. | |
| 1.2 | Energy an object possesses due to its motion; equals ½mv². | |
| 1.3 | Energy transferred when a force acts through a displacement; W = Fs cosθ. | |
| 1.4 | The principle that the net work done on an object equals its change in kinetic energy. | |
| 1.5 | The sum of kinetic energy and gravitational potential energy at any point; conserved when only gravity acts. | |
| 1.6 | The rate at which energy is transferred or converted; P = ΔE/Δt. | |
| 1.7 | The SI unit of energy and work; 1 J = 1 N·m = 1 kg·m²/s². | |
| 1.8 | The SI unit of power; 1 W = 1 J/s. | |
| 1.9 | A force that does not dissipate mechanical energy; work done by it depends only on start and end positions, not path taken. | |
| 1.10 | A force such as friction or air resistance that converts mechanical energy to heat, so total mechanical energy decreases. |
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 When a force acts perpendicular to the direction of motion, the work done by that force is zero. T / F
2.2 Doubling an object’s speed doubles its kinetic energy, because KE is proportional to v. T / F
2.3 Conservation of mechanical energy can be applied whenever friction is mentioned in a problem. T / F
2.4 In the formula Wnet = ΔKE, Wnet is the sum of work done by all forces acting on the object. T / F
2.5 In ΔU = mgΔh, the symbol Δh refers to the distance measured along a slope, not the vertical height. T / F
2.6 At constant velocity on a flat road, the driving force of a car equals the total resistance force (not the car’s weight). 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:
conservative · displacement · friction · gravitational · net · quadruples · vertical · watt
Work is the energy transferred when a force acts through a ___________ in the direction of the force. Kinetic energy depends on speed squared; this means doubling speed ___________ the kinetic energy. The work-energy theorem states that the ___________ work done equals the change in kinetic energy. When calculating gravitational potential energy using ΔU = mgΔh, Δh is the ___________ height change, not the slope distance. Gravity is a ___________ force, meaning it does not dissipate mechanical energy as heat. By contrast, ___________ is a non-conservative force that converts mechanical energy to thermal energy. The SI unit of power is the ___________, equivalent to one joule per second. Gravitational potential energy is the energy stored due to an object’s position in a ___________ field.
4. Formula conditions recall
For each formula, state: (a) the condition required to use it, and (b) the most common exam error associated with it. Answer in 1–2 sentences each. 12 marks (2 per formula)
4.1 W = Fs cosθ
(a) Condition:
(b) Common exam error:
4.2 KE = ½mv²
(a) Condition:
(b) Common exam error:
4.3 Wnet = ΔKE
(a) Condition:
(b) Common exam error:
4.4 KE1 + U1 = KE2 + U2
(a) Condition:
(b) Common exam error:
4.5 ΔU = mgΔh
(a) Condition:
(b) Common exam error:
4.6 P = ΔE/Δt = Fv
(a) Condition:
(b) Common exam error:
5. Select the correct formula
For each scenario, circle the formula you would use first and give a one-line reason. 8 marks (1 formula + 1 reason each)
5.1 A ball falls from rest off a frictionless ramp. Find its speed at the bottom.
A W = Fs cosθ B KE1 + U1 = KE2 + U2 C Wnet = ΔKE D P = Fv
Reason:
5.2 A box slides down a rough slope (μk = 0.4). Find its speed at the bottom.
A W = Fs cosθ B KE1 + U1 = KE2 + U2 C Wnet = ΔKE D P = Fv
Reason:
5.3 A car travels at constant speed against a known resistance force. Find the required engine power.
A W = Fs cosθ B KE = ½mv² C Wnet = ΔKE D P = Fv
Reason:
5.4 An object slides 30 m along a slope inclined at 20°. Find the change in gravitational potential energy.
A ΔU = mgΔh (where Δh = 30 sin20°) B ΔU = mgΔh (where Δh = 30) C W = Fs cosθ D KE1 + U1 = KE2 + U2
Reason:
Q1 — Term–definition match
1.1 gravitational potential energy • 1.2 kinetic energy • 1.3 work • 1.4 work-energy theorem • 1.5 mechanical energy • 1.6 power • 1.7 joule • 1.8 watt • 1.9 conservative force • 1.10 non-conservative force.
Q2 — True / false with correction
2.1 True. When θ = 90°, cos90° = 0, so W = 0. The normal force and centripetal force are everyday examples.
2.2 False. KE = ½mv² — KE is proportional to vsquared. Doubling speed quadruples KE (since (2v)² = 4v²).
2.3 False. Conservation of mechanical energy applies only when no friction or other non-conservative forces act. When friction is present, you must use Wnet = ΔKE.
2.4 True. Wnet must include work done by every force — applied force, friction, gravity component along slope, etc.
2.5 False. In ΔU = mgΔh, Δh is the vertical height change only. For a slope: Δh = slope distance × sinθ.
2.6 True. On a flat road at constant velocity, Newton’s First Law gives Fdrive = Fresistance. Weight is vertical and does zero work horizontally.
Q3 — Cloze paragraph
In order: displacement / quadruples / net / vertical / conservative / friction / watt / gravitational.
Q4 — Formula conditions recall
4.1 W = Fs cosθ. (a) Use when calculating the energy transferred by a specific force through a known displacement at angle θ to motion. (b) Common error: using the angle between the force and the vertical instead of the angle between the force and the displacement.
4.2 KE = ½mv². (a) Use when finding the energy of motion at a given speed, or finding speed from known energy. (b) Common error: treating KE as proportional to v (linear) rather than v² (quadratic) — e.g. “doubling speed doubles KE.”
4.3 Wnet = ΔKE. (a) Use when friction or other non-conservative forces are present and mechanical energy is not conserved. (b) Common error: using only the applied force work rather than summing all forces including friction.
4.4 KE1 + U1 = KE2 + U2. (a) Use only when no friction or air resistance acts — only gravity (or springs) do work. (b) Common error: applying it when a rough surface or drag is mentioned, giving a speed that is too high.
4.5 ΔU = mgΔh. (a) Use when an object moves vertically in Earth’s gravitational field. (b) Common error: substituting the slope distance for Δh instead of the vertical height (Δh = slope × sinθ).
4.6 P = ΔE/Δt = Fv. (a) Use when finding the rate of energy transfer, or connecting force, speed, and power at constant velocity. (b) Common error: using weight (mg) as the driving force on a flat road instead of the resistance force from the problem.
Q5 — Select the correct formula
5.1 B — KE1 + U1 = KE2 + U2. No friction mentioned; frictionless surface means mechanical energy is conserved.
5.2 C — Wnet = ΔKE. Friction (μk = 0.4) is present, so mechanical energy is not conserved; net work theorem must be used.
5.3 D — P = Fv. Constant speed on a flat road means Fdrive = Fresistance; power is directly linked to force and speed.
5.4 A — ΔU = mgΔh where Δh = 30 sin20° = vertical height. The 30 m is slope distance; Δh must be calculated using the angle of inclination.