| Exam Board | SPS |
|---|---|
| Module | SPS ASFM (SPS ASFM) |
| Year | 2020 |
| Session | May |
| Marks | 10 |
| Topic | Impulse and momentum (advanced) |
| Type | Multiple successive collisions |
| Difficulty | Challenging +1.8 This is a challenging multi-collision mechanics problem requiring systematic application of conservation of momentum and restitution equations across two collisions, followed by inequality analysis to determine when a second collision occurs. The algebraic manipulation is substantial, and finding the range of k values requires careful reasoning about relative velocities. While the techniques are standard A-level mechanics, the extended multi-step nature and the need to derive conditions for a second collision (rather than just analyzing one collision) places this well above average difficulty. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03k Newton's experimental law: direct impact |
Three particles, $P$, $Q$ and $R$, are at rest on a smooth horizontal plane. The particles lie along a straight line with $Q$ between $P$ and $R$. The particles $Q$ and $R$ have masses $m$ and $km$ respectively, where $k$ is a constant.
Particle $Q$ is projected towards $R$ with speed $u$ and the particles collide directly.
The coefficient of restitution between each pair of particles is $e$.
\begin{enumerate}[label=(\alph*)]
\item Find, in terms of $e$, the range of values of $k$ for which there is a second collision. [9]
Given that the mass of $P$ is $km$ and that there is a second collision,
\item write down, in terms of $u$, $k$ and $e$, the speed of $Q$ after this second collision. [1]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS ASFM 2020 Q9 [10]}}