Physics • Year 11 • Module 2 • Lesson 12

Conservation of Momentum

Lock in the law of conservation of momentum, the three collision types, and the key equations before tackling harder questions.

Build · Vocab & Recall

1. Term–definition match

The definitions below are shuffled. In the right-hand column write the matching term from this list: conservation of momentum, closed system, elastic collision, inelastic collision, perfectly inelastic collision, explosion from rest, impulse, recoil, kinetic energy, vector protocol. 10 marks (1 each)

#	Definition	Matching term
1.1	The principle that total momentum before any interaction equals total momentum after, provided no net external force acts.
1.2	A system in which no net external force acts, so total momentum is constant.
1.3	A collision in which both momentum and kinetic energy are conserved; objects do not deform permanently.
1.4	A collision in which momentum is conserved but kinetic energy is not; some KE is converted to heat, sound or deformation.
1.5	A special inelastic collision in which the objects stick together and move with a single final velocity; maximum KE is lost.
1.6	An interaction in which a system initially at rest separates into two or more parts moving in opposite directions, so total momentum remains zero.
1.7	The product of force and the time interval over which it acts; equal to the change in momentum of an object.
1.8	The backward motion of an object (such as a gun or spacecraft) following the forward ejection of another object, as required by conservation of momentum.
1.9	The energy an object possesses due to its motion; equal to ½mv².
1.10	The step-by-step method for solving momentum problems: define a positive direction, assign signs to all velocities, write the conservation equation, then state direction in the answer.

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 the statement is false, write the corrected version on the line below it. 12 marks (1 T/F + 1 correction each)

2.1 In a perfectly inelastic collision, all kinetic energy is always lost. T / F

2.2 Momentum is always conserved in a closed system, regardless of whether the collision is elastic or inelastic. T / F

2.3 In an explosion from rest, the two objects move apart with equal speeds because their momenta are equal and opposite. T / F

2.4 The law of conservation of momentum is derived from Newton’s Third Law of Motion. T / F

2.5 An object moving at constant velocity in a straight line has zero momentum. T / F

2.6 Gravity is an internal force in a ball–Earth collision system and therefore does not affect whether momentum is conserved. T / F

Stuck? Revisit the Conservation Law card and the Misconceptions section in the lesson.

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:

closed · conserved · equal · external · kinetic · opposite · perfectly inelastic · zero

The law of conservation of momentum states that the total momentum of a ___________ system remains constant, provided no net ___________ force acts. This means the total momentum before a collision is ___________ to the total momentum after. In all collision types, momentum is always ___________; however, ___________ energy is only conserved in elastic collisions. In a ___________ collision, the objects stick together and move with a common final velocity. In an explosion from rest, the total momentum before is ___________, so the momenta of the two objects after must be ___________ and opposite.

Stuck? Revisit the Formula Reference panel and the Conservation Law card 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 State the condition required for the law of conservation of momentum to apply.

4.2 Explain, using Newton’s Third Law, why the total momentum of a two-object system does not change during a collision.

4.3 What is the equation used to solve a perfectly inelastic collision, and what does each symbol represent?

4.4 Why does a bullet leaving a rifle cause the rifle to recoil, and why is the rifle’s recoil speed much smaller than the bullet’s speed?

Stuck? Revisit Cards 1 and 3, and the Explosion from Rest formula in the lesson.

5. Match each scenario to the correct conservation equation

Draw a line (or write the letter A, B, or C) to match each scenario to the equation that applies. 6 marks (1 per correct match, 1 per justification)

Scenarios

1. A 4 kg trolley moving at +3 m/s collides with a stationary 2 kg trolley and they lock together.

2. A 0.05 kg bullet is fired from a 3 kg rifle initially at rest.

3. A 2 kg ball at +5 m/s collides with a 3 kg ball at −2 m/s; the 2 kg ball bounces back at −1 m/s.

Equations

A. m₁v₁ + m₂v₂ = (m₁ + m₂)v_f

B. 0 = m₁v₁′ + m₂v₂′

C. m₁v₁ + m₂v₂ = m₁v₁′ + m₂v₂′

Scenario	Equation letter	Justification (one sentence)
1
2
3

Stuck? Revisit the “Three Scenario Setups” table in Card 2 of the lesson.

6. Classify each collision and complete the table

For each scenario, classify the collision type and state whether kinetic energy is conserved. 6 marks (1 per row)

#	Scenario	Collision type	KE conserved?
6.1	Two identical billiard balls collide; the first stops and the second moves at the first ball’s original speed.
6.2	Two clay balls collide and stick together.
6.3	A gun fires a bullet; both start at rest.
6.4	A tennis ball hits a stationary ball; the tennis ball slows down but does not stop; the second ball speeds up.
6.5	A car rear-ends a stationary car; they lock bumpers and slide together.
6.6	An astronaut at rest in space pushes off a spacecraft; both were initially stationary.

Stuck? Revisit Card 3 “Elastic vs Inelastic Collisions” and the classification flowchart in the lesson.

Answers — Do not peek before attempting

Q1 — Term–definition match

1.1 conservation of momentum • 1.2 closed system • 1.3 elastic collision • 1.4 inelastic collision • 1.5 perfectly inelastic collision • 1.6 explosion from rest • 1.7 impulse • 1.8 recoil • 1.9 kinetic energy • 1.10 vector protocol.

Q2 — True / false with correction

2.1 False. In a perfectly inelastic collision, kinetic energy is maximised in its loss (compared with other collision outcomes), but KE is only fully lost if the combined object ends up stationary (v_f = 0). If v_f ≠ 0, the combined object still has kinetic energy.

2.2 True. Momentum is always conserved in a closed system regardless of collision type.

2.3 False. In an explosion from rest the momenta are equal in magnitude and opposite in direction, but equal momenta do NOT mean equal speeds. Since p = mv, a smaller mass gets a larger speed and a larger mass gets a smaller speed to give equal momentum magnitudes.

2.4 True. Newton’s Third Law (equal and opposite forces acting for the same time interval) produces equal and opposite impulses, hence equal and opposite momentum changes, keeping total momentum constant.

2.5 False. An object moving at constant velocity has non-zero momentum (p = mv). Only an object with zero mass or zero velocity has zero momentum.

2.6 False. Gravity is an external force on a ball–Earth system (if only the ball is defined as the system). Gravity acts as an external force on the ball and can change its momentum. It is internal only if both the ball and the Earth are included in the system.

Q3 — Cloze paragraph

In order: closed / external / equal / conserved / kinetic / perfectly inelastic / zero / equal (in magnitude) and opposite (in direction). Note: the last blank requires “equal” (accept “equal in magnitude”); award ½ mark if student writes only “opposite”.

Q4.1 — Condition for conservation of momentum

No net external force must act on the system. The system must be closed — all forces involved are internal (between the objects themselves).

Q4.2 — Newton’s Third Law explanation

When object A exerts force F on B, B exerts an equal and opposite force −F on A (Newton’s Third Law). Both forces act for the same contact time Δt, so the impulse on A equals −(impulse on B), meaning Δp_A = −Δp_B. The total change in momentum (Δp_A + Δp_B) = 0, so the total momentum is unchanged.

Q4.3 — Perfectly inelastic equation

m₁v₁ + m₂v₂ = (m₁ + m₂)v_f, where m₁ and m₂ are the masses of the two objects, v₁ and v₂ are their velocities before the collision, and v_f is their common velocity after (since they stick together).

Q4.4 — Rifle recoil

By conservation of momentum, the gun–bullet system has zero total momentum before firing. When the bullet is expelled forward (positive momentum), the rifle must gain equal and opposite momentum (negative). Since p = mv and the rifle is far more massive than the bullet, the rifle’s recoil speed v_rifle = m_bulletv_bullet / m_rifle is much smaller than the bullet’s speed.

Q5 — Scenario-equation match

Scenario 1 → Equation A. Objects lock together → perfectly inelastic; use combined mass on the right side.
Scenario 2 → Equation B. System starts at rest → explosion from rest; total p = 0 both before and after.
Scenario 3 → Equation C. Objects separate after collision with different velocities → general two-object conservation equation.

Q6 — Collision classification

6.1 Elastic — KE conserved. Equal masses, complete momentum transfer, no deformation.
6.2 Perfectly inelastic — KE not conserved (maximum KE lost).
6.3 Explosion from rest (not a collision but an explosion) — KE increases from zero (chemical energy converts to KE).
6.4 Inelastic — KE not conserved (some lost to heat, sound, deformation); objects separate, not stuck.
6.5 Perfectly inelastic — KE not conserved.
6.6 Explosion from rest — KE increases from zero; momentum conserved (total = 0).