Standard +0.3 This is a standard M2 momentum question involving two collisions with given coefficients of restitution. Part (a) is direct impulse calculation, part (b) requires comparing velocities after collision using standard formulas, and part (c) uses an energy condition to find e. All techniques are routine for M2 with no novel insight required, making it slightly easier than average.
Two particles \(A\) and \(B\), of masses \(3 m\) and \(4 m\) respectively, lie at rest on a smooth horizontal surface. Particle \(B\) lies between \(A\) and a smooth vertical wall which is perpendicular to the line joining \(A\) and \(B\). Particle \(B\) is projected with speed \(5 u\) in a direction perpendicular to the wall and collides with the wall. The coefficient of restitution between \(B\) and the wall is \(\frac { 3 } { 5 }\).
Find the magnitude of the impulse received by \(B\) in the collision with the wall.
After the collision with the wall, \(B\) rebounds from the wall and collides directly with \(A\). The coefficient of restitution between \(A\) and \(B\) is \(e\).
Show that, immediately after they collide, \(A\) and \(B\) are both moving in the same direction.
The kinetic energy of \(B\) immediately after it collides with \(A\) is one quarter of the kinetic energy of \(B\) immediately before it collides with \(A\).
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\item Two particles $A$ and $B$, of masses $3 m$ and $4 m$ respectively, lie at rest on a smooth horizontal surface. Particle $B$ lies between $A$ and a smooth vertical wall which is perpendicular to the line joining $A$ and $B$. Particle $B$ is projected with speed $5 u$ in a direction perpendicular to the wall and collides with the wall. The coefficient of restitution between $B$ and the wall is $\frac { 3 } { 5 }$.\\
(a) Find the magnitude of the impulse received by $B$ in the collision with the wall.
\end{enumerate}
After the collision with the wall, $B$ rebounds from the wall and collides directly with $A$. The coefficient of restitution between $A$ and $B$ is $e$.\\
(b) Show that, immediately after they collide, $A$ and $B$ are both moving in the same direction.
The kinetic energy of $B$ immediately after it collides with $A$ is one quarter of the kinetic energy of $B$ immediately before it collides with $A$.\\
(c) Find the value of $e$.\\
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\hfill \mbox{\textit{Edexcel M2 2017 Q7 [14]}}