Physics • Year 12 • Module 5 • Lesson 14
Gravitational Potential Energy
Lock in the key formula U = −GMm/r, understand the physical meaning of the negative sign, and practise the vocabulary before tackling harder questions.
1. Term–definition match
The definitions below are shuffled. In the right-hand column write the matching term from the list: gravitational potential energy, zero-at-infinity convention, potential-energy change, centre-to-centre distance, near-surface approximation, work done by gravity, quasistatic external work, radial gravitational field, reference level, negative GPE. 10 marks (1 each)
| # | Definition | Matching term |
|---|---|---|
| 1.1 | The energy stored in a gravitational field; defined as U = −GMm/r for a mass m at distance r from mass M. | |
| 1.2 | The convention that sets GPE equal to zero when two masses are infinitely far apart. | |
| 1.3 | The signed difference ΔU = Uf − Ui between two stated positions. | |
| 1.4 | The distance measured from the centre of one body to the centre of another; equals Rplanet + h for orbiting objects. | |
| 1.5 | The formula ΔU ≈ mgh, which is only valid when the height h is much less than Earth’s radius. | |
| 1.6 | Energy transferred by the gravitational force; Wg = −ΔU. | |
| 1.7 | For a slow move with negligible change in kinetic energy, the work supplied from outside: Wext = +ΔU. | |
| 1.8 | A field directed along the line joining centres, with magnitude that depends on centre-to-centre radius. | |
| 1.9 | The chosen value from which potential-energy values are measured; for U = −GMm/r it is U = 0 at infinity. | |
| 1.10 | The value of GPE for any finite separation of two masses; it indicates the object has less energy than at infinite separation. |
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 Gravitational potential energy is always positive for any two masses separated by a finite distance. T / F
2.2 The zero reference point for gravitational potential energy is defined at Earth’s surface. T / F
2.3 As a satellite moves to a higher orbit, its gravitational potential energy increases (becomes less negative). T / F
2.4 When using U = −GMm/r, the variable r represents the height above Earth’s surface. T / F
2.5 The formula ΔU = mgh is a valid approximation only when the height h is much less than Earth’s radius. T / F
2.6 The negative sign in U = −GMm/r is simply a mathematical convention and has no physical meaning. 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:
attractive · infinity · less · negative · opposite · positive · quasistatic · reference
Gravitational potential energy is ___________ at finite separation because gravity is ___________ and the chosen ___________ is U = 0 at ___________. During an outward move U becomes ___________ negative, so ΔU is ___________. Work done by gravity has the ___________ sign, while for a ___________ move Wext = +ΔU.
4. Function recall
Answer each question in 1–2 sentences using precise terms from the lesson. 8 marks (2 each)
4.1 What does the negative sign in U = −GMm/r tell us physically about the gravitational interaction?
4.2 Why must the variable r in U = −GMm/r be the centre-to-centre distance rather than the altitude h above the surface?
4.3 State the condition under which ΔU ≈ mgh is a valid approximation and explain why this condition is necessary.
4.4 For an outward quasistatic move, compare the signs of ΔU, Wg and Wext.
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 defined at”, “indicates”, “is an approximation for”). Aim for at least 6 labelled arrows. 6 marks (1 per valid labelled arrow)
Supplied terms: gravitational potential energy · negative sign · zero at infinity · work by gravity · mgh · quasistatic external work.
Q1, Term–definition match
1.1 gravitational potential energy • 1.2 zero-at-infinity convention • 1.3 potential-energy change • 1.4 centre-to-centre distance • 1.5 near-surface approximation • 1.6 work done by gravity • 1.7 quasistatic external work • 1.8 radial gravitational field • 1.9 reference level • 1.10 negative GPE.
Q2, True / false with correction
2.1 False. GPE is always negative for any finite separation because gravity is attractive and U = −GMm/r; it only reaches zero at infinite separation.
2.2 False. The zero reference for GPE is defined at infinity (r → ∞), not at Earth’s surface. This is the zero-at-infinity convention.
2.3 True.
2.4 False. r is the centre-to-centre distance from Earth’s centre to the object, equal to REarth + h; using h alone would give an incorrect (and much smaller) value.
2.5 True.
2.6 False. With attractive gravity and U = 0 at infinity, every finite separation lies below the reference, so U is negative. Bound/unbound classification requires total mechanical energy rather than the sign of U alone.
Q3, Cloze paragraph
In order: negative / attractive / reference / infinity / less / positive / opposite / quasistatic.
Q4.1, Physical meaning of the negative sign
The negative sign follows from attractive gravity and the zero-at-infinity reference. A system at finite r has lower potential energy than it has at infinity, so positive external work is required for quasistatic separation.
Q4.2, Why r is centre-to-centre distance
The formula U = −GMm/r treats both bodies as point masses and r measures the distance between their centres of mass. Using altitude h ignores Earth’s radius (6.37 × 106 m), which would greatly underestimate the true separation and give an incorrect (far too negative) value of U.
Q4.3, Condition for the mgh approximation
The approximation is valid when h ≪ R (height much less than Earth’s radius). This is necessary because the derivation uses the approximation R + h ≈ R; at large h the approximation fails because g decreases significantly with altitude, yet mgh treats g as constant.
Q4.4, Signed work ledger
For an outward move, U becomes less negative and ΔU > 0. Gravity acts inward, so Wg = −ΔU < 0. If the move is quasistatic, Wext = +ΔU > 0.
Q5, Sample concept map
Award 1 mark per valid labelled arrow, minimum 6. Correct arrows include:
- gravitational potential energyis defined as zero at → zero at infinity
- work by gravityequals → −ΔU
- quasistatic external workequals → +ΔU
- mghis a near-surface approximation for → a change in gravitational potential energy
- negative signplaces U below → zero at infinity
- zero at infinitymakes → gravitational potential energy (negative at all finite r)