Edexcel M1 Specimen — Question 2 7 marks

Exam BoardEdexcel
ModuleM1 (Mechanics 1)
SessionSpecimen
Marks7
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Mark schemeDownload PDF ↗
TopicMomentum and Collisions
TypeDirect collision, find mass
DifficultyModerate -0.3 This is a straightforward application of conservation of momentum to a collision problem. Part (a) requires setting up and solving a single linear equation using momentum conservation, while part (b) applies the impulse-momentum theorem directly. The problem involves no conceptual subtleties—the collision conditions are clearly stated, and the solution follows standard M1 procedures with algebraic manipulation of given quantities.
Spec6.03a Linear momentum: p = mv6.03b Conservation of momentum: 1D two particles6.03e Impulse: by a force6.03f Impulse-momentum: relation

Particle \(P\) has mass \(m\) kg and particle \(Q\) has mass \(3m\) kg. The particles are moving in opposite directions along a smooth horizontal plane when they collide directly. Immediately before the collision \(P\) has speed \(4u\) m s\(^{-1}\) and \(Q\) has speed \(ku\) m s\(^{-1}\), where \(k\) is a constant. As a result of the collision the direction of motion of each particle is reversed and the speed of each particle is halved.
  1. Find the value of \(k\). [4]
  2. Find, in terms of \(m\) and \(u\), the magnitude of the impulse exerted on \(P\) by \(Q\). [3]

Particle $P$ has mass $m$ kg and particle $Q$ has mass $3m$ kg. The particles are moving in opposite directions along a smooth horizontal plane when they collide directly. Immediately before the collision $P$ has speed $4u$ m s$^{-1}$ and $Q$ has speed $ku$ m s$^{-1}$, where $k$ is a constant. As a result of the collision the direction of motion of each particle is reversed and the speed of each particle is halved.

\begin{enumerate}[label=(\alph*)]
\item Find the value of $k$.
[4]

\item Find, in terms of $m$ and $u$, the magnitude of the impulse exerted on $P$ by $Q$.
[3]
\end{enumerate}

\hfill \mbox{\textit{Edexcel M1  Q2 [7]}}