Challenging +1.8 This is a challenging M5 mechanics problem requiring conservation of angular momentum, Newton's experimental law (coefficient of restitution), and moment of inertia of a rod about an endpoint. It involves multiple equations and algebraic manipulation across 7 marks, with the coefficient e=1 providing a key constraint. The multi-step nature and need to coordinate linear/angular motion concepts place it well above average difficulty, though it follows a standard collision-with-rotation framework taught in M5.
A uniform rod \(AB\) of mass \(4m\) is free to rotate in a vertical plane about a fixed smooth horizontal axis, \(L\), through \(A\). The rod is hanging vertically at rest when it is struck at its end \(B\) by a particle of mass \(m\). The particle is moving with speed \(u\), in a direction which is horizontal and perpendicular to \(L\), and after striking the rod it rebounds in the opposite direction with speed \(v\). The coefficient of restitution between the particle and the rod is 1.
Show that \(u = 7v\).
[7]
A uniform rod $AB$ of mass $4m$ is free to rotate in a vertical plane about a fixed smooth horizontal axis, $L$, through $A$. The rod is hanging vertically at rest when it is struck at its end $B$ by a particle of mass $m$. The particle is moving with speed $u$, in a direction which is horizontal and perpendicular to $L$, and after striking the rod it rebounds in the opposite direction with speed $v$. The coefficient of restitution between the particle and the rod is 1.
Show that $u = 7v$.
[7]
\hfill \mbox{\textit{Edexcel M5 Q6 [7]}}