| Exam Board | OCR MEI |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2015 |
| Session | June |
| Marks | 20 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions 1 |
| Type | Direct collision with energy loss |
| Difficulty | Standard +0.3 This is a standard M2 collision problem requiring systematic application of conservation of momentum, energy loss conditions, and coefficient of restitution. Part (a) involves straightforward algebraic manipulation with given energy loss (showing v = 4 m/s), impulse calculation, and finding unknown velocities. Part (b) is routine projectile motion with restitution. All techniques are standard textbook exercises with no novel insight required, making it slightly easier than average A-level. |
| Spec | 3.02h Motion under gravity: vector form3.02i Projectile motion: constant acceleration model6.03a Linear momentum: p = mv6.03b Conservation of momentum: 1D two particles6.03j Perfectly elastic/inelastic: collisions6.03k Newton's experimental law: direct impact |
**Question 4 Total: 20 marks**
**Overall Total: 62 marks** (though document shows 16, 18, 18, 20 for the four sections tabulated)4
\begin{enumerate}[label=(\alph*)]
\item Two discs, P of mass 4 kg and Q of mass 5 kg , are sliding along the same line on a smooth horizontal plane when they collide. The velocity of P before the collision and the velocity of Q after the collision are shown in Fig. 4. P loses $\frac { 5 } { 9 }$ of its kinetic energy in the collision.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{71d839d8-12ca-4806-8f74-c572e7e21891-5_294_899_390_584}
\captionsetup{labelformat=empty}
\caption{Fig. 4}
\end{center}
\end{figure}
\begin{enumerate}[label=(\roman*)]
\item Show that after the collision P has a velocity of $4 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ in the opposite direction to its original motion.
While colliding, the discs are in contact for $\frac { 1 } { 5 } \mathrm {~s}$.
\item Find the impulse on P in the collision and the average force acting on the discs.
\item Find the velocity of Q before the collision and the coefficient of restitution between the two discs.
\end{enumerate}\item A particle is projected from a point 2.5 m above a smooth horizontal plane. Its initial velocity is $5.95 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ at an angle $\theta$ below the horizontal, where $\sin \theta = \frac { 15 } { 17 }$. The coefficient of restitution between the particle and the plane is $\frac { 4 } { 5 }$.
\begin{enumerate}[label=(\roman*)]
\item Show that, after bouncing off the plane, the greatest height reached by the particle is 2.5 m .
\item Calculate the horizontal distance between the two points at which the particle is 2.5 m above the plane.
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{OCR MEI M2 2015 Q4 [20]}}