HSC Physics — Module 5
Gravitation — Flashcards & Quiz
Gravitation is the attractive force between any two masses, described by Newton's law F = GM₁M₂/r², and it underpins HSC Physics Module 5: Advanced Mechanics. You need to calculate gravitational field strength g = GM/r², use U = –GM₁M₂/r for gravitational potential energy (note the sign convention and the zero at infinity), and apply Kepler's third law T² ∝ r³ to satellites and planetary orbits.
Key Points
- Newton's law of universal gravitation: F = GM₁M₂/r², where G = 6.67 × 10⁻¹¹ N m² kg⁻² is the gravitational constant.
- Gravitational field strength g = GM/r²; on Earth's surface g ≈ 9.81 m s⁻².
- Gravitational potential energy U = -GM₁M₂/r — note the negative sign and zero at infinity. Objects bound to a mass have negative total energy.
- Kepler's third law: T² ∝ r³ (period squared is proportional to radius cubed) — derived from setting gravitational force equal to centripetal force.
- Escape velocity: v_esc = √(2GM/r) — the minimum velocity needed to escape to infinity from a gravitational well.
- Exam trap: don't confuse g (field strength, vector) with G (universal constant, scalar). Both symbols appear in exam formulas.
Common Mistakes to Avoid
- Confusing gravitational field strength g (vector, at a point) with the universal gravitational constant G (scalar).
- Forgetting the NEGATIVE sign in gravitational PE (U = -GM₁M₂/r) — zero at infinity.
- Using r as the distance from the surface instead of from the centre of the mass.
- Applying Kepler's third law to non-circular orbits without caveat — it works for ellipses but a is the semi-major axis.
- Mixing up weight (mg, force) with mass (scalar, amount of matter).
Exam Strategy
HSC Module 5 gravitation questions ask you to (1) calculate forces or field strengths, (2) derive Kepler's law, or (3) link PE to work done. Method: identify the given quantities, apply F = GM₁M₂/r² or g = GM/r², keep r as distance from mass centre, track signs carefully for PE.
Sample Flashcards
Q1: State Newton's Law of Universal Gravitation.
F = GMm/r², where F is the gravitational force, G = 6.674 × 10⁻¹¹ N·m²/kg² is the gravitational constant, M and m are the two masses, and r is the distance between their centres. The force is always attractive and acts along the line joining the centres.
Q2: What is gravitational field strength and how is it related to g?
Gravitational field strength g = F/m = GM/r² (N/kg or m/s²). It equals the acceleration due to gravity at that point. At Earth's surface: g ≈ 9.8 m/s². It decreases with altitude as r increases. Inside Earth, g decreases linearly to zero at the centre.
Q3: What is gravitational potential energy in the universal context?
U = -GMm/r (negative because work must be done AGAINST gravity to separate masses). At infinity, U = 0. As r decreases (closer to the central mass), U becomes more negative. The change in GPE: ΔU = GMm(1/r₁ - 1/r₂).
Q4: What is the gravitational field and how is it represented?
A gravitational field is the region around a mass where another mass experiences a gravitational force. Represented by field lines pointing toward the mass (direction a test mass would accelerate). Closer field lines = stronger field. For a uniform field (near Earth's surface), lines are parallel and equally spaced.
Q5: What is the total mechanical energy of an orbiting satellite?
E_total = KE + U = ½mv² + (-GMm/r). For a circular orbit: v² = GM/r, so KE = GMm/(2r). Therefore E_total = GMm/(2r) - GMm/r = -GMm/(2r). Total energy is negative (bound orbit) and equals half the potential energy.
Sample Quiz Questions
Q1: Gravitational force between two objects doubles when the distance between them is halved.
Answer: FALSE
F = GMm/r². If r is halved: F = GMm/(r/2)² = GMm/(r²/4) = 4GMm/r². The force QUADRUPLES (inverse square law). Doubling occurs when one mass doubles.
Q2: Gravitational field strength at a point depends on the mass of the test object placed there.
Answer: FALSE
Field strength g = GM/r² depends only on the SOURCE mass M and distance r. The test mass cancels out when deriving g = F/m. Field strength is a property of the field itself, not the test mass.
Q3: Gravitational potential energy is always negative for objects in bound orbits.
Answer: TRUE
U = -GMm/r is always negative (as r > 0). For bound orbits, total energy E = -GMm/(2r) is also negative. An object escapes when E ≥ 0.
Revision Tip
Gravitation is equation-heavy — drill Revizi flashcards with 10+ problems covering F, g, U, and escape velocity.
Related Concepts
Last updated: March 2026 · 6 flashcards · 5 quiz questions