Question

A particle of mass m is moving horizontally with a constant velocity v towards a rigid wall that is moving in opposite direction with a constant speed u. Assuming elastic impact between the particle and wall, the work done by the wall in reflecting the particle is equal to :

• A. $\left(1/2\right)m(u+v{)}^2$
• B. (1/2) m (u + v)
• C. (1/2) muv
• D. none of these

Answer 1

Answer: (D)

none of these

Given: Coefficient of restitution $e=1$

Speed of the wall $v_w=u$

Let the speed of the particle after collision be $v^{\prime }$

Using $\frac{v^{\prime }-v_w}{-v-v_w}=-e$

$\frac{v^{\prime }-u}{-v-u}=-1$ $⟹v^{\prime }=v+2u$

Work done by the wall $W=\frac{1}{2}m(v^{\prime }{)}^2-\frac{1}{2}m{v}^2$

$W=\frac{1}{2}m(v+2u{)}^2-\frac{1}{2}m{v}^2$

$⟹W=2mu(v+u)$