Standard +0.3 This is a standard direct collision problem requiring application of conservation of momentum and Newton's restitution law, followed by algebraic manipulation to find energy loss. While it involves multiple steps and algebraic work, it follows a well-established procedure taught in mechanics courses with no novel insight required—slightly easier than average for A-level Further Maths.
1 Two smooth spheres \(A\) and \(B\), of equal radii and of masses \(3 m\) and \(6 m\) respectively, are at rest on a smooth horizontal surface. Sphere \(A\) is projected directly towards \(B\) with speed \(u\). The coefficient of restitution between \(A\) and \(B\) is \(e\). Show that the kinetic energy lost in the collision between \(A\) and \(B\) is \(m u ^ { 2 } \left( 1 - e ^ { 2 } \right)\).
1 Two smooth spheres $A$ and $B$, of equal radii and of masses $3 m$ and $6 m$ respectively, are at rest on a smooth horizontal surface. Sphere $A$ is projected directly towards $B$ with speed $u$. The coefficient of restitution between $A$ and $B$ is $e$. Show that the kinetic energy lost in the collision between $A$ and $B$ is $m u ^ { 2 } \left( 1 - e ^ { 2 } \right)$.
\hfill \mbox{\textit{CAIE FP2 2012 Q1 [7]}}