7. Three particles $A , B$ and $C$ lie at rest in a straight line on a smooth horizontal surface, with $B$ between $A$ and $C$. The particles $A$, $B$ and $C$ have mass $6 m$, 4 $m$ and $m$ respectively. Particle $A$ is projected towards $B$ with speed $3 u$ and $A$ collides directly with $B$. Immediately after this collision, the speed of $B$ is $w$. The coefficient of restitution between $A$ and $B$ is $\frac { 1 } { 6 }$.
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\item Show that $w = \frac { 21 } { 10 } u$.
\item Express the total kinetic energy of $A$ and $B$ lost in the collision as a fraction of the total kinetic energy of $A$ and $B$ immediately before the collision.

After being struck by $A$, the particle $B$ collides directly with $C$. The coefficient of restitution between $B$ and $C$ is $e$. After the collision between $B$ and $C$, there are no further collisions between the particles.
\item Find the range of possible values of $e$.\\

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\hfill \mbox{\textit{Edexcel M2 2017 Q7 [16]}}