Challenging +1.8 This is a challenging M5 collision problem requiring conservation of angular momentum, Newton's experimental law (restitution), and manipulation of the rod's moment of inertia (I = 4ml²/3 for a uniform rod about one end). The e=1 condition with the 7v result requires careful algebraic manipulation across multiple equations. While the techniques are standard for M5, the multi-step coordination and algebraic complexity elevate this above routine mechanics questions.
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 2011 Q6 [7]}}