Edexcel M1 2017 January — Question 5 8 marks

Exam BoardEdexcel
ModuleM1 (Mechanics 1)
Year2017
SessionJanuary
Marks8
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicMomentum and Collisions
TypeCollision with two possible outcomes
DifficultyStandard +0.3 This is a standard M1 collision problem requiring impulse calculation and conservation of momentum. While it has a twist with two possible outcomes (P can move in either direction after collision), the solution follows routine mechanics procedures: apply impulse-momentum theorem to one particle, then use conservation of momentum to find k. The algebra is straightforward and the problem type is common in M1 textbooks.
Spec6.03a Linear momentum: p = mv6.03b Conservation of momentum: 1D two particles6.03e Impulse: by a force6.03f Impulse-momentum: relation

  1. Two particles \(P\) and \(Q\) have masses \(4 m\) and \(k m\) respectively. They are moving towards each other in opposite directions along the same straight line on a smooth horizontal table when they collide directly. Immediately before the collision the speed of \(P\) is \(3 u\) and the speed of \(Q\) is \(u\). Immediately after the collision both particles have speed \(2 u\) and the direction of motion of \(Q\) has been reversed.
    1. Find, in terms of \(k , m\) and \(u\), the magnitude of the impulse received by \(Q\) in the collision.
    2. Find the two possible values of \(k\).

\begin{enumerate}
  \item Two particles $P$ and $Q$ have masses $4 m$ and $k m$ respectively. They are moving towards each other in opposite directions along the same straight line on a smooth horizontal table when they collide directly. Immediately before the collision the speed of $P$ is $3 u$ and the speed of $Q$ is $u$. Immediately after the collision both particles have speed $2 u$ and the direction of motion of $Q$ has been reversed.\\
(a) Find, in terms of $k , m$ and $u$, the magnitude of the impulse received by $Q$ in the collision.\\
(b) Find the two possible values of $k$.\\

\end{enumerate}

\hfill \mbox{\textit{Edexcel M1 2017 Q5 [8]}}