Standard +0.8 This is a multi-stage collision problem requiring conservation of momentum, Newton's law of restitution applied twice, and an energy condition linking both collisions. Students must track velocities through two separate collision events and solve a non-trivial equation involving e, going beyond standard single-collision exercises.
2 A small smooth sphere \(A\) of mass \(m\) is moving with speed \(u\) on a smooth horizontal surface when it collides directly with an identical sphere \(B\) which is initially at rest on the surface. The coefficient of restitution between the spheres is \(e\). Sphere \(B\) subsequently collides with a fixed vertical barrier which is perpendicular to the direction of motion of \(B\). The coefficient of restitution between \(B\) and the barrier is \(\frac { 1 } { 2 }\). Given that \(80 \%\) of the initial kinetic energy is lost as a result of the two collisions, find the value of \(e\).
2 A small smooth sphere $A$ of mass $m$ is moving with speed $u$ on a smooth horizontal surface when it collides directly with an identical sphere $B$ which is initially at rest on the surface. The coefficient of restitution between the spheres is $e$. Sphere $B$ subsequently collides with a fixed vertical barrier which is perpendicular to the direction of motion of $B$. The coefficient of restitution between $B$ and the barrier is $\frac { 1 } { 2 }$. Given that $80 \%$ of the initial kinetic energy is lost as a result of the two collisions, find the value of $e$.
\hfill \mbox{\textit{CAIE FP2 2016 Q2 [8]}}