AS & A Level · Practice questions · Momentum and the conservation of momentum

Before equals after.

Six original Cambridge-style questions on momentum and its conservation in direct collisions, with full worked solutions.

Original questions All questions on this page are original work, written in the Cambridge AS & A Level style. They are not from past papers. They test the same concepts and skills the syllabus rewards.

The method

Diagram, signs, one equation.

Diagram: before and after, masses in kg, every velocity marked.
Positive direction: velocities the other way are negative.
Conserve: \(m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2\); coalescing uses \((m_1 + m_2)v\).
Interpret: a negative answer means the particle moves in the negative direction.
Chains: one collision at a time, then check whether another collision occurs.

Recall

[2 marks]

Find the magnitude of the momentum of (a) a ball of mass 150 g moving at \(20\ \text{m s}^{-1}\), (b) a van of mass 1200 kg moving at \(15\ \text{m s}^{-1}\).

(a) \(0.15 \times 20 = 3\ \text{kg m s}^{-1}\). ✓
(b) \(1200 \times 15 = 18\,000\ \text{kg m s}^{-1}\). ✓

Calculation

[2 marks]

A ball of mass 0.2 kg moving at \(15\ \text{m s}^{-1}\) hits a wall at right angles and rebounds at \(12\ \text{m s}^{-1}\). Find the magnitude of the change in momentum.

Towards the wall positive: before \(3\), after \(-2.4\ \text{N s}\). ✓
Change \(= -2.4 - 3 = -5.4\), magnitude 5.4 N s. ✓

Calculation

[3 marks]

A particle A of mass 4 kg moving at \(6\ \text{m s}^{-1}\) collides with a stationary particle B of mass 2 kg. After the collision A continues in the same direction at \(2\ \text{m s}^{-1}\). Find the speed of B.

\(4(6) + 0 = 4(2) + 2v_B\). ✓
\(24 = 8 + 2v_B\), so \(v_B = 8\ \text{m s}^{-1}\). ✓

Analysis

[3 marks]

Two particles, of masses 0.3 kg and \(m\) kg, move towards each other along a straight line with speeds \(4\ \text{m s}^{-1}\) and \(3\ \text{m s}^{-1}\). They collide and coalesce, and the combined particle is at rest. Find \(m\).

Total momentum after is zero, so total momentum before is zero. ✓
\(0.3(4) + m(-3) = 0\). ✓
\(m = 1.2 \div 3 = 0.4\). ✓

Analysis

[5 marks]

Particles A, B and C, of masses 0.2 kg, 0.3 kg and 0.5 kg, lie at rest in that order on a straight line on a smooth surface. A is projected towards B at \(5\ \text{m s}^{-1}\). After A hits B, A is at rest. B then hits C and they coalesce.

(a) Find the speed of B after the first collision.

(b) Find the speed of the combined particle, and explain why there are no further collisions.

(a) \(0.2(5) = 0.2(0) + 0.3v_B\), so \(v_B = \dfrac{1}{0.3} = 3.33\ \text{m s}^{-1}\). ✓
(b) \(0.3 \times \dfrac{10}{3} = 0.8v\), so \(1 = 0.8v\) and \(v = 1.25\ \text{m s}^{-1}\). ✓
A is at rest and the combined particle moves away from it, so they never meet again. ✓

Analysis

[5 marks]

A railway truck of mass 12 tonnes moving at \(3\ \text{m s}^{-1}\) runs into a stationary truck of mass 8 tonnes, and the two couple together.

(a) Find their speed immediately after coupling.

(b) Find the loss of kinetic energy in the collision.

(a) \(12\,000(3) = 20\,000v\), so \(v = 1.8\ \text{m s}^{-1}\). ✓
(b) KE before \(= \tfrac{1}{2}(12\,000)(3^2) = 54\,000\) J. ✓
KE after \(= \tfrac{1}{2}(20\,000)(1.8^2) = 32\,400\) J. ✓
Loss \(= 21\,600\) J. Momentum is conserved but kinetic energy is not. ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.