| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2016 |
| Session | October |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions 1 |
| Type | Three-particle sequential collisions |
| Difficulty | Standard +0.3 This is a standard M2 momentum-collision problem requiring systematic application of conservation of momentum and Newton's restitution law across two collisions. While it involves multiple particles and algebraic manipulation with parameters, the approach is methodical and follows textbook procedures without requiring novel insight or particularly complex reasoning. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03i Coefficient of restitution: e6.03j Perfectly elastic/inelastic: collisions6.03k Newton's experimental law: direct impact |
8. Particles $A , B$ and $C$, of masses $4 m , k m$ and $2 m$ respectively, lie at rest in a straight line on a smooth horizontal surface with $B$ between $A$ and $C$. Particle $A$ is projected towards particle $B$ with speed $3 u$ and collides directly with $B$. The coefficient of restitution between each pair of particles is $\frac { 2 } { 3 }$
Find
\begin{enumerate}[label=(\alph*)]
\item the speed of $A$ immediately after the collision with $B$, giving your answer in terms of $u$ and $k$,
\item the range of values of $k$ for which $A$ and $B$ will both be moving in the same direction immediately after they collide.
After the collision between $A$ and $B$, particle $B$ collides directly with $C$. Given that $k = 4$,
\item show that there will not be a second collision between $A$ and $B$.\\
DO NOT WRITEIN THIS AREA
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 2016 Q8 [14]}}