Question

A smooth sphere A of mass 3m moving on a smooth horizontal table with speed 4u, impiges directly on another smooth sphere B of mass 2m, moving with speed u in the opposite direction to A. The coefficient of restitution between A and B is e.
(a) Find in terms of e and u, the speed of B after the impact.
(b) Show that e = 1/3
(c) Find the impulse exerted on A by the impact.

Answer 1

$\begin{cases} 12mu-2mu=3mx+2my,\\ 3m\cdot 16u^2+2mu^2=3mx^2+2my^2; \end{cases}$ $\begin{cases} 10u=3x+2y,\\ 50u^2=3x^2+2y^2; \end{cases}$

$\begin{cases} 100u^2=9x^2+12xy+4y^2,\\ 100u^2=6x^2+4y^2; \end{cases}$

$0=3x^2+12xy,$

$3x(x+4y)=0,$

$x=-4y,$

$-10y=10u,$

$y=-u,$

$x=4u.$