Mathematics 9709 · AS & A Level · Momentum

Momentum — practice question

Particles $P$ and $Q$, with masses $0.1\,\text{kg}$ and $0.3\,\text{kg}$ respectively, are initially stationary on a smooth horizontal plane. $P$ is sent directly towards $Q$ at speed $4u\,\text{m s}^{-1}$. At the same moment, $Q$ is sent directly towards $P$ at speed $u\,\text{m s}^{-1}$. Once $P$ and $Q$ have collided, $P$ travels at speed $2\,\text{m s}^{-1}$ and $Q$ travels at speed $4\,\text{m s}^{-1}$.
(a)[3]

Find the two possible values for $u$.

(b)[2]

Find the greatest possible loss of kinetic energy in the collision.

Worked solution & mark scheme

This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: Apply conservation of momentum, for example $0.1\times4u-0.3\times u=0.1\times2+0.3\times4$ or $0.1\times4u-0.3\times u=0.1\times(-2)+0.3\times4$

  • Full mark scheme, point by point
  • Step-by-step worked solution
  • Write your answer & get it marked instantly by AI