| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/3 (Pre-U Mathematics Paper 3) |
| Year | 2019 |
| Session | Specimen |
| Marks | 10 |
| Topic | Momentum and Collisions 1 |
| Type | Three-particle sequential collisions |
| Difficulty | Challenging +1.2 This is a multi-stage collision problem requiring systematic application of conservation of momentum and Newton's restitution law across three impacts. While it involves several steps and careful tracking of velocities, the techniques are standard A-level mechanics with no novel insights required. The 'show that' parts provide scaffolding that guides the solution path, making it moderately above average difficulty but not exceptionally challenging. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03k Newton's experimental law: direct impact |
\includegraphics{figure_9}
Three particles $A$, $B$ and $C$, having masses of 1 kg, 2 kg and 5 kg respectively, are placed 1 metre apart in a straight line on a smooth horizontal plane (see diagram). The particles $B$ and $C$ are initially at rest and $A$ is moving towards $B$ with speed 14 m s$^{-1}$. The coefficient of restitution between each pair of particles is 0.5.
\begin{enumerate}[label=(\alph*)]
\item Find the velocity of $B$ immediately after the first impact and show that $A$ comes to rest. [4]
\item Show that $B$ reversed direction after the impact with $C$. [3]
\item Find the distances between $B$ and $C$ at the instant that $B$ collides with $A$ for the second time. [3]
\end{enumerate}
\hfill \mbox{\textit{Pre-U Pre-U 9794/3 2019 Q9 [10]}}