Standard +0.8 This is a two-stage collision problem requiring systematic application of conservation of momentum and Newton's restitution law across both collisions, with the need to work backwards from the final condition to find e. While the mechanics principles are standard M2 content, the algebraic manipulation across two linked collisions and solving the resulting system of equations elevates this above routine exercises.
Three particles \(A\), \(B\) and \(C\), of equal size and each of mass \(m\), are at rest on the same straight line on a smooth horizontal surface. The coefficient of restitution between \(A\) and \(B\), and between \(B\) and \(C\), is \(e\).
\(A\) is projected with speed \(7\) ms\(^{-1}\) and strikes \(B\) directly. \(B\) then collides with \(C\), which starts to move with speed \(4\) ms\(^{-1}\).
Calculate the value of \(e\). [10 marks]
Three particles $A$, $B$ and $C$, of equal size and each of mass $m$, are at rest on the same straight line on a smooth horizontal surface. The coefficient of restitution between $A$ and $B$, and between $B$ and $C$, is $e$.
$A$ is projected with speed $7$ ms$^{-1}$ and strikes $B$ directly. $B$ then collides with $C$, which starts to move with speed $4$ ms$^{-1}$.
Calculate the value of $e$. [10 marks]
\hfill \mbox{\textit{Edexcel M2 Q5 [10]}}