Question

Two blocks $A$ and $B$ of mass $m$ and $2m$ respectively are moving towards a massive (mass $>>2m$) cliff with velocities $2v$ and $v$ respectively. The cliff moves with a velocity $v$. If the coefficient of restitution of collision at the surface of the cliff is $e=\frac{1}{2}$. Find the work done by the cliff during collision.

Answer 1

$v_A=2v\hat{i},v_B=v\hat{i},v_{cl}=-v\hat{i}{v}_{B/cl}=2v\hat{i}e=\frac{1}{2}=-\frac{v_{fB/cl}}{v_{B/cl}}\Rightarrow v_{fB/cl}=-\frac{1}{2}{v}_{B/cl}\Rightarrow v_{fB/cl}=-v\hat{i}\Rightarrow v_{fB}=v_{fB/cl}+v_{cl}=-v\hat{i}-v\hat{i}=-2v\hat{i}WorkdonebythecliffchangesthekineticenergyofbodyB.W=\frac{1}{2}2m{v_{fB}}^2-\frac{1}{2}2m{v_B}^2=m(4v^2-v^2)=3m{v}^2$