OCR M2 2013 January — Question 3 9 marks

Exam BoardOCR
ModuleM2 (Mechanics 2)
Year2013
SessionJanuary
Marks9
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicMomentum and Collisions 1
TypeDirect collision with direction reversal
DifficultyStandard +0.3 This is a standard M2 collision problem combining kinematics on an inclined plane with conservation of momentum and coefficient of restitution. While it requires multiple steps (finding A's speed before collision, applying Newton's experimental law, using momentum conservation), all techniques are routine M2 material with no novel insight required. The multi-part structure and need to track signs carefully elevate it slightly above average difficulty.
Spec3.02d Constant acceleration: SUVAT formulae6.03b Conservation of momentum: 1D two particles6.03i Coefficient of restitution: e6.03k Newton's experimental law: direct impact6.03l Newton's law: oblique impacts

A particle \(A\) is released from rest from the top of a smooth plane, which makes an angle of 30° with the horizontal. The particle \(A\) collides 2 s later with a particle \(B\), which is moving up a line of greatest slope of the plane. The coefficient of restitution between the particles is 0.4 and the speed of \(B\) immediately before the collision is 2 ms\(^{-1}\). \(B\) has velocity 1 ms\(^{-1}\) down the plane immediately after the collision. Find
  1. the speed of \(A\) immediately after the collision, [4]
  2. the distance \(A\) moves up the plane after the collision. [2]
The masses of \(A\) and \(B\) are 0.5 kg and \(m\) kg, respectively.
  1. Find the value of \(m\). [3]

A particle $A$ is released from rest from the top of a smooth plane, which makes an angle of 30° with the horizontal. The particle $A$ collides 2 s later with a particle $B$, which is moving up a line of greatest slope of the plane. The coefficient of restitution between the particles is 0.4 and the speed of $B$ immediately before the collision is 2 ms$^{-1}$. $B$ has velocity 1 ms$^{-1}$ down the plane immediately after the collision. Find

\begin{enumerate}[label=(\roman*)]
\item the speed of $A$ immediately after the collision, [4]
\item the distance $A$ moves up the plane after the collision. [2]
\end{enumerate}

The masses of $A$ and $B$ are 0.5 kg and $m$ kg, respectively.

\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{2}
\item Find the value of $m$. [3]
\end{enumerate}

\hfill \mbox{\textit{OCR M2 2013 Q3 [9]}}