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Extended · Practice questions · Momentum and conservation

Before equals after.

Six original Cambridge-style questions on calculating momentum, conservation in collisions, handling direction signs, and the recoil or explosion case.

Original questions All questions on this page are original work, written in the Cambridge IGCSE style. They are not from past papers. They test the same concepts and skills the syllabus rewards.
Before you add

p = mv, and mind the signs.

01
[2 marks]

Define momentum, give the equation for it, and state its unit.

  • Momentum = mass × velocity; p = mv. ✓
  • Unit: kg m/s (it is a vector). ✓
02
Calculation
[2 marks]

Calculate the momentum of a 1500 kg car travelling at 12 m/s.

p = mv = 1500 × 12

18000 kg m/s

03
Analysis
[2 marks]

State the principle of conservation of momentum and the condition under which it applies.

  • The total momentum before an interaction equals the total momentum after it. ✓
  • This holds when no external resultant force acts (a closed system). ✓
04
Calculation
[3 marks]

A 3.0 kg trolley moving at 4.0 m/s collides with a stationary 1.0 kg trolley. They stick together. Calculate their common velocity afterwards.

before: p = 3.0 × 4.0 = 12 kg m/s after: 12 = (3.0 + 1.0) × v v = 12 ÷ 4.0

v = 3.0 m/s

05
Calculation
[3 marks]

A 0.50 kg ball moving at 6.0 m/s to the right strikes a stationary 1.0 kg ball. After the collision the 0.50 kg ball rebounds at 2.0 m/s to the left. Calculate the velocity of the 1.0 kg ball, taking the right as positive.

before: p = 0.50 × 6.0 = 3.0 kg m/s after: 3.0 = 0.50 × (−2.0) + 1.0 × v 3.0 = −1.0 + v  →  v = 4.0 m/s

v = 4.0 m/s to the right

the rebound makes the ball's velocity −2.0, not +2.0

06
Analysis
[3 marks]

A stationary firework explodes into two pieces that fly apart. Use the conservation of momentum to explain why the two pieces move in opposite directions.

  • Before the explosion the total momentum is zero (it is at rest). ✓
  • Momentum is conserved, so the total afterwards must also be zero. ✓
  • The two momenta must therefore be equal in size and opposite in direction, so the pieces move opposite ways. ✓