| Exam Board | OCR |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Collision on inclined plane |
| Difficulty | Standard +0.8 This is a multi-stage mechanics problem requiring conservation of momentum during collision, followed by kinematics on an inclined plane for both particles. It demands careful tracking of two particles through multiple phases (collision, motion up/down the plane), sign conventions, and coordination of timing. The 14 marks and proof element indicate above-average difficulty, but the techniques are standard M1 content. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.03g Gravitational acceleration6.03b Conservation of momentum: 1D two particles |
\includegraphics{figure_7}
$PQ$ is a line of greatest slope, of length $4$ m, on a smooth plane inclined at $30°$ to the horizontal. Particles $A$ and $B$, of masses $0.15$ kg and $0.5$ kg respectively, move along $PQ$ with $A$ below $B$. The particles are both moving upwards, $A$ with speed $8$ m s$^{-1}$ and $B$ with speed $2$ m s$^{-1}$, when they collide at the mid-point of $PQ$ (see diagram). Particle $A$ is instantaneously at rest immediately after the collision.
\begin{enumerate}[label=(\roman*)]
\item Show that $B$ does not reach $Q$ in the subsequent motion. [8]
\item Find the time interval between the instant of $A$'s arrival at $P$ and the instant of $B$'s arrival at $P$. [6]
\end{enumerate}
\hfill \mbox{\textit{OCR M1 Q7 [14]}}