Challenging +1.2 This is a multi-step momentum problem requiring systematic application of conservation of momentum and Newton's restitution law across two collisions, with algebraic manipulation to show a specific result. While it involves multiple collisions and requires careful tracking of velocities, the techniques are standard for Further Mechanics and the question guides students to the conclusion rather than requiring novel insight.
2 Three particles, \(A , B\) and \(C\), of masses \(2 \mathrm {~kg} , 3 \mathrm {~kg}\) and 5 kg respectively, are at rest in a straight line on a smooth horizontal plane with \(B\) between \(A\) and \(C\).
Collisions between \(A\) and \(B\) are perfectly elastic. The coefficient of restitution for collisions between \(B\) and \(C\) is \(e\).
\(A\) is projected towards \(B\) with a speed of \(5 u \mathrm {~ms} ^ { - 1 }\) (see diagram).
\includegraphics[max width=\textwidth, alt={}, center]{709f3a7a-d857-4813-98ab-de6b41a3a8dc-02_190_885_1151_260}
Show that only two collisions occur.
2 Three particles, $A , B$ and $C$, of masses $2 \mathrm {~kg} , 3 \mathrm {~kg}$ and 5 kg respectively, are at rest in a straight line on a smooth horizontal plane with $B$ between $A$ and $C$.
Collisions between $A$ and $B$ are perfectly elastic. The coefficient of restitution for collisions between $B$ and $C$ is $e$.\\
$A$ is projected towards $B$ with a speed of $5 u \mathrm {~ms} ^ { - 1 }$ (see diagram).\\
\includegraphics[max width=\textwidth, alt={}, center]{709f3a7a-d857-4813-98ab-de6b41a3a8dc-02_190_885_1151_260}
Show that only two collisions occur.
\hfill \mbox{\textit{OCR Further Mechanics 2021 Q2 [8]}}