How do elastic and inelastic collisions differ?

Kinetic energy is conserved in an elastic collision and not in an inelastic one, while momentum is conserved in both.

What is special about equal-mass elastic collisions?

The two bodies simply swap velocities, so one stops and the other leaves with the original speed.

S4 Physics momentum paper 3: energy, flow and edge cases

2026-11-10

Tutor Prep Guide · S4 Physics Momentum and Impulse

Ten items combine momentum with energy: p squared over 2m, continuous flow, rocket thrust, rebound height and elastic formulae.

Direct answers　Items 01 to 03 cover energy from momentum, rebound force and bullets, 04 to 06 equal masses, elastic tests and steady flow, 07 to 09 sticky loss, thrust and rebound height, and 10 misusing the equal-mass result.

01　Paper details (check answers afterwards)

Item	Detail
Questions	10
Suggested time	25
Difficulty mix	Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1
Chapter	Chapter: S4 Physics Momentum and Impulse
Level	S4

02　Questions (10 items)

FoundationAn object has momentum 12 kg m/s and mass 3 kg. Find its kinetic energy.
FoundationA 0.2 kg ball hits a wall at 15 m/s and rebounds at 10 m/s after 0.05 s. Find the average force from the wall.
FoundationA 0.01 kg bullet at 300 m/s embeds in a stationary 1.99 kg block. Find the speed of the block afterwards.
IntermediateA 0.3 kg ball at 4 m/s hits an identical stationary ball in a perfectly elastic collision. Find both velocities after impact.
IntermediateA 1 kg ball at 2 m/s hits a stationary 3 kg ball and bounces back at 1 m/s. Find the 3 kg speed and say whether the collision is elastic.
IntermediateA hose delivers 0.5 kg of water per second at 20 m/s, and the jet is stopped by a flat plate. Find the average force on the plate.
ChallengeA 0.2 kg ball east at 4 m/s hits a 0.3 kg ball west at 2 m/s and they stick. Find the final velocity and the kinetic energy lost.
ChallengeA rocket ejects 5 kg of gas per second at 200 m/s relative to the rocket. Find the thrust.
ChallengeA 0.5 kg ball falls from 3 m and rebounds to 2 m. Find the size of its momentum change during the bounce, with g = 9.81 m/s2.
Error redoA 2 kg ball at 3 m/s hits a stationary 1 kg ball elastically. A student says the 2 kg ball stops and the 1 kg ball moves at 3 m/s; find the correct result.

03　Answers and one-line notes

#	Answer	One-line note
1	24 J	Kinetic energy is p squared over 2m: 144 / 6 = 24 J, which avoids finding the speed first.
2	100 N	The momentum change is 0.2 x 25 = 5 kg m/s, so the force is 5 / 0.05 = 100 N along the rebound direction.
3	1.5 m/s	The momentum is 0.01 x 300 = 3 kg m/s and the total mass is 2 kg, so v = 3 / 2 = 1.5 m/s.
4	First ball 0 m/s, second ball 4 m/s	Equal masses in an elastic collision simply swap velocities, so the first stops and the second moves off at 4 m/s with both momentum and energy conserved.
5	1 m/s, elastic with 2 J before and after	Momentum gives 2 = -1 + 3v, so v = 1 m/s; kinetic energy is 2 J before and 2 J after, no loss, so the collision is elastic.
6	10 N	The momentum stopped each second is 0.5 x 20 = 10 N, and the plate feels an equal force.
7	0.4 m/s east with 2.16 J lost	Total momentum is 0.8 – 0.6 = 0.2 kg m/s over 0.5 kg, giving 0.4 m/s; kinetic energy falls from 2.2 J to 0.04 J, so 2.16 J is lost.
8	1 000 N	The momentum given to the gas each second is 5 x 200 = 1 000 N, which is the thrust on the rocket.
9	6.97 kg m/s	Landing speed is 7.67 m/s and rebound speed is 6.26 m/s, so the change is 0.5 x (7.67 + 6.26), about 6.97 kg m/s.
10	2 kg ball 1 m/s, 1 kg ball 4 m/s in the same direction	The formulae give 1 m/s and 4 m/s; swapping velocities holds only for equal masses, and a lighter target always leaves faster than the original ball.

04　What to do after marking

After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
Repeat the same item two days later; move to the next paper only when both attempts are correct.
Parents only need the answer and note columns; there is no need to explain every item.

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