Challenging +1.8 This is an oblique collision problem requiring resolution of velocities along the line of centres, application of conservation of momentum and Newton's restitution law in that direction, then vector reconstruction to find the impulse. The geometry (finding the angle from the 1.6r separation) adds complexity, and the multi-step nature with careful vector handling makes this significantly harder than standard direct impact questions, though it follows a well-established method for M4.
\includegraphics{figure_2}
Two smooth uniform spheres \(A\) and \(B\), of equal radius \(r\), have masses \(3m\) and \(2m\) respectively. The spheres are moving on a smooth horizontal plane when they collide. Immediately before the collision they are moving with speeds \(u\) and \(2u\) respectively. The centres of the spheres are moving towards each other along parallel paths at a distance \(1.6r\) apart, as shown in Figure 2.
The coefficient of restitution between the two spheres is \(\frac{1}{6}\).
Find, in terms of \(m\) and \(u\), the magnitude of the impulse received by \(B\) in the collision.
[10]
\includegraphics{figure_2}
Two smooth uniform spheres $A$ and $B$, of equal radius $r$, have masses $3m$ and $2m$ respectively. The spheres are moving on a smooth horizontal plane when they collide. Immediately before the collision they are moving with speeds $u$ and $2u$ respectively. The centres of the spheres are moving towards each other along parallel paths at a distance $1.6r$ apart, as shown in Figure 2.
The coefficient of restitution between the two spheres is $\frac{1}{6}$.
Find, in terms of $m$ and $u$, the magnitude of the impulse received by $B$ in the collision.
[10]
\hfill \mbox{\textit{Edexcel M4 2013 Q3 [10]}}