Physics • Year 11 • Module 2 • Lesson 7

Gravitational PE and Energy Conservation

Lock in the key vocabulary, the formulas, and the conditions for conservation of mechanical energy before tackling calculation problems.

Build · Vocab & Recall

1. Term–definition match

The definitions below are shuffled. In the right-hand column write the matching term from the list: gravitational potential energy, reference level, mechanical energy, conservation of mechanical energy, non-conservative force, kinetic energy, ΔU = mgΔh, v = √(2gΔh), E_lost, conservative force. 10 marks (1 each)

#	Definition	Matching term
1.1	Energy stored in an object due to its height in a gravitational field; depends on position relative to a reference level.
1.2	The chosen height at which gravitational PE is defined to be zero; only changes in PE matter, so this can be set anywhere convenient.
1.3	The sum of kinetic energy and gravitational potential energy at any point: E_mech = KE + U.
1.4	The principle that the total mechanical energy remains constant throughout the motion when only conservative forces act.
1.5	A force, such as friction or air resistance, that converts mechanical energy permanently to thermal energy and sound; cannot be recovered as motion.
1.6	Energy of motion; equal to ½mv².
1.7	The formula relating the change in gravitational PE to mass, gravitational acceleration, and vertical height change.
1.8	The formula giving the speed of an object that starts from rest and falls a vertical height Δh on a frictionless surface; derived when mass cancels from the conservation equation.
1.9	The energy converted from mechanical to thermal and sound forms by friction; equal to initial mechanical energy minus final mechanical energy.
1.10	A force, such as gravity or a spring, whose work depends only on start and end positions, not on the path taken; mechanical energy is conserved when only these forces act.

Stuck? Revisit the Key Terms panel and the Formula Reference in the lesson.

2. True or false — with correction

Circle T or F for each statement. If false, write the corrected version on the line below. 12 marks (1 T/F + 1 correction each)

2.1 The gravitational PE of an object depends on its height above the centre of Earth, not above any chosen reference level. T / F

2.2 A heavier rollercoaster car dropped from the same height as a lighter car will reach a greater speed at the bottom on a frictionless track. T / F

2.3 When friction is present, the conservation equation KE₁ + U₁ = KE₂ + U₂ cannot be used directly because mechanical energy is not conserved. T / F

2.4 Friction destroys energy — the total energy of the universe decreases when friction acts. T / F

2.5 The vertical height Δh in ΔU = mgΔh refers to the length of the slope, not the vertical rise. T / F

2.6 At the top of a frictionless rollercoaster drop (object at rest), all mechanical energy is stored as gravitational PE. T / F

Stuck? Revisit the Misconceptions panel and the “Why mass cancels” section in Card 2 of the lesson.

3. Fill-in-the-blank paragraph

Use the word bank to complete the passage. Each word or phrase is used once. 8 marks (1 per blank)

Word bank:

cancels · conservative · frictionless · gravitational potential energy · height · kinetic · reference level · thermal

___________ energy is stored in an object due to its position in a gravitational field. The formula ΔU = mgΔh uses the vertical ___________ change, not the path length along a slope. When only ___________ forces act (no friction), total mechanical energy is constant. This means that at any two points on a ___________ track, KE₁ + U₁ = KE₂ + U₂. The height at which PE = 0 is called the ___________ and may be chosen freely. When mass is cancelled from the conservation equation for an object starting from rest, mass ___________ and the speed at the bottom depends only on height. Friction converts mechanical energy into ___________ energy (heat) and sound. At the bottom of a frictionless drop (h = 0), all mechanical energy has converted to ___________ energy.

Stuck? Revisit Cards 1–3, the Formula Reference, and the “Copy into your books” section in the lesson.

4. Function recall

Answer each question in 1–2 sentences using precise terms from the lesson. 8 marks (2 each)

4.1 What two conditions must be satisfied for the equation KE₁ + U₁ = KE₂ + U₂ to be valid?

4.2 Why does mass cancel from the conservation of mechanical energy equation when an object starts from rest?

4.3 What formula is used to find the average friction force if you know the energy lost and the path length?

4.4 At what point on a frictionless rollercoaster track is the gravitational PE at a maximum? At what point is the kinetic energy at a maximum?

Stuck? Revisit the “Conservation of Mechanical Energy” card and the Vector Protocol checklist in the lesson.

5. Build a concept map

Draw labelled arrows between the six terms below to show how they relate. Each arrow must carry a linking phrase (e.g. “converts to”, “is conserved when”, “equals”, “calculated by”). Aim for at least 6 labelled arrows. 6 marks (1 per valid labelled arrow)

Supplied terms: gravitational PE · kinetic energy · mechanical energy · friction · height · reference level.

gravitational PE

kinetic energy

mechanical energy

friction

height

reference level

Stuck? Try: gravitational PE → converts to → kinetic energy (on frictionless track); height → determines → gravitational PE; mechanical energy → sum of → kinetic energy + gravitational PE; friction → reduces → mechanical energy; reference level → defines zero for → gravitational PE.

6. Formula identification — which equation to use?

For each scenario, write the correct formula or equation to use and state whether mechanical energy is conserved (Yes / No). 6 marks (1 per row)

#	Scenario	Formula to use	E_mech conserved?
6.1	A ball drops from rest off a cliff (no air resistance).
6.2	A skier slides down a rough slope losing energy to friction.
6.3	A pendulum swings in a vacuum from its highest point to its lowest.
6.4	A rollercoaster car starts from rest at 25 m; find speed at 10 m (frictionless).
6.5	A car brakes to a stop on a flat road (friction present).
6.6	A ball thrown upward with initial speed v₀; find speed at any height h (no air resistance).

Stuck? Revisit the Decision Flowchart SVG in the lesson and the “When to use which formula” copy-into-your-books section.

Answers — Do not peek before attempting

Q1 — Term–definition match

1.1 gravitational potential energy • 1.2 reference level • 1.3 mechanical energy • 1.4 conservation of mechanical energy • 1.5 non-conservative force • 1.6 kinetic energy • 1.7 ΔU = mgΔh • 1.8 v = √(2gΔh) • 1.9 E_lost • 1.10 conservative force.

Q2 — True / false with correction

2.1 False. Only changes in PE matter; the reference level (h = 0) can be set at any convenient point, not only at Earth’s centre. ΔU = mgΔh uses the vertical height change above the chosen reference level.

2.2 False. On a frictionless track, mass cancels from the conservation equation. Both cars reach the same speed at the bottom: v = √(2gh), which depends only on height, not mass.

2.3 True.

2.4 False. Friction does not destroy energy — it converts mechanical energy into thermal energy (heat) and sound. Total energy is conserved; only mechanical energy decreases.

2.5 False. Δh is the vertical height change, not the path length along a slope. A ball rolling 10 m down a 30° slope has Δh = 5 m (the vertical component).

2.6 True. At rest (KE = 0) at the top, all mechanical energy is stored as gravitational PE = mgh.

Q3 — Cloze paragraph

In order: Gravitational potential energy / height / conservative / frictionless / reference level / cancels / thermal / kinetic.

Q4 — Function recall

4.1 (1) No friction (no non-conservative forces) must act on the object. (2) The only force doing work must be gravity (a conservative force). Both conditions mean mechanical energy is not lost to heat or sound.

4.2 Starting from rest (v₁ = 0) at height h with h₂ = 0: mgh = ½mv². Dividing both sides by m gives gh = ½v², so mass cancels completely and v = √(2gh). The result depends only on g and h.

4.3 W_friction = F × s, so F = E_lost ÷ s. The average friction force equals the energy lost divided by the distance along the path.

4.4 Gravitational PE is at a maximum at the highest point on the track (minimum KE, often zero if starting from rest). Kinetic energy is at a maximum at the lowest point on the track (minimum height, therefore minimum PE).

Q5 — Sample concept map

Accept any valid labelled arrows. Examples:

gravitational PE —converts to→ kinetic energy (as object descends on frictionless track)
height —determines magnitude of→ gravitational PE
reference level —defines zero for→ gravitational PE
mechanical energy —equals sum of→ kinetic energy + gravitational PE
friction —reduces→ mechanical energy
mechanical energy —is conserved when no→ friction acts

Award 1 mark per valid labelled arrow (minimum 6, maximum 6 marked). Arrows must carry a meaningful linking phrase.

Q6 — Formula identification

6.1 v = √(2gΔh) | Yes (no air resistance, starts from rest).

6.2 KE₁ + U₁ = KE₂ + U₂ + E_lost; or find E_lost = initial E_mech − final E_mech | No.

6.3 KE₁ + U₁ = KE₂ + U₂ (frictionless, only gravity) | Yes.

6.4 KE₁ + U₁ = KE₂ + U₂, simplifies to g(h₁ − h₂) = ½v² | Yes.

6.5 E_lost = initial KE (use W_net = ΔKE) | No.

6.6 ½mv₀² + mgh₀ = ½mv² + mgh | Yes (no air resistance).