| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2021 |
| Session | June |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions 1 |
| Type | Three-particle sequential collisions |
| Difficulty | Standard +0.8 This is a multi-stage collision problem requiring conservation of momentum and restitution equations for two separate collisions, followed by a proof that requires comparing velocities after the second collision. While the individual collision calculations are standard M2 fare, the sequential nature and the need to track three particles through multiple collisions, plus proving a second collision occurs, elevates this above routine exercises. |
| Spec | 6.03a Linear momentum: p = mv6.03b Conservation of momentum: 1D two particles6.03c Momentum in 2D: vector form6.03j Perfectly elastic/inelastic: collisions6.03k Newton's experimental law: direct impact |
\begin{enumerate}
\item Particles $A , B$ and $C$, of masses $2 m , m$ and $3 m$ respectively, lie at rest in a straight line on a smooth horizontal plane with $B$ between $A$ and $C$. Particle $A$ is projected towards particle $B$ with speed $2 u$ and collides directly with $B$.
\end{enumerate}
The coefficient of restitution between each pair of particles is $e$.\\
(a) (i) Show that the speed of $B$ immediately after the collision with $A$ is $\frac { 4 } { 3 } u ( 1 + e )$\\
(ii) Find the speed of $A$ immediately after the collision with $B$.
At the instant when $A$ collides with $B$, particle $C$ is projected with speed $u$ towards $B$ so that $B$ and $C$ collide directly.\\
(b) Show that there will be a second collision between $A$ and $B$.\\
\includegraphics[max width=\textwidth, alt={}, center]{e6e37d85-f8de-490a-82a9-8a3c16e2fdd0-27_2644_1840_118_111}
\hfill \mbox{\textit{Edexcel M2 2021 Q8 [13]}}