Standard +0.3 This is a standard M4 collision problem requiring resolution of velocity components parallel and perpendicular to the wall, application of the coefficient of restitution formula, and calculation of kinetic energy. The method is routine for this module: component parallel unchanged (U cos α), component perpendicular reversed and scaled by e (eU sin α), then KE = ½m(v²). Straightforward application of well-practiced techniques with no conceptual surprises.
A smooth uniform sphere \(S\) of mass \(m\) is moving on a smooth horizontal plane when it collides with a fixed smooth vertical wall. Immediately before the collision, the speed of \(S\) is \(U\) and its direction of motion makes an angle \(\alpha\) with the wall. The coefficient of restitution between \(S\) and the wall is \(e\). Find the kinetic energy of \(S\) immediately after the collision.
[6]
A smooth uniform sphere $S$ of mass $m$ is moving on a smooth horizontal plane when it collides with a fixed smooth vertical wall. Immediately before the collision, the speed of $S$ is $U$ and its direction of motion makes an angle $\alpha$ with the wall. The coefficient of restitution between $S$ and the wall is $e$. Find the kinetic energy of $S$ immediately after the collision.
[6]
\hfill \mbox{\textit{Edexcel M4 2006 Q2 [6]}}