First slide

Coefficient of restitution

Question

A ball moving with a velocity v strikes a wall moving towards the ball with a velocity u as shown in fig. An elastic impact occurs. Consider the mass of the wall to be infinitely great. The work done by the wall during collision is

Moderate

A

2mu(v+u)
B

mv²
C

$\frac{1}{2} {mv}^{2} + \frac{1}{2} {mu}^{2}$
D

$m (v + u)^{2}$

Solution

$Initial K . E = \frac{1}{2} {mv}^{2}; Final K.E == \frac{1}{2} m (v + 2 u)^{2} \begin{array}{l} \frac{1}{2} {mv}^{2} + ΔW = \frac{1}{2} m (v + 2 u)^{2} \\ ΔW = \frac{m}{2} \cdot 4 u^{2} + 2 mvu = 2 mu (u + v) \end{array}$

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