Question

A ball of mass 'm' moving with a speed 2v strikes a heavy wall elastically, which is moved with a velocity 'v'. The work done by the heavy wall on the ball is

Answer 1

Given:

A ball of mass 'm' moving with a speed 2v strikes a heavy wall elastically, which is moved with a velocity 'v'.

To find:

Work done by the heavy wall on the ball.

Calculation:

Let final Velocity of ball be v_(2)

For elastic collision , coefficient of restitution is equal to 1 ;

$\therefore \: e = 1$

$= > \dfrac{v - v_{2}}{2v - 0} = 1$

$= > \dfrac{v - v_{2}}{2v } = 1$

$= > v - v_{2} = 2 v$

$= > v_{2} = - v$

Therefore , work done by the wall on the ball will be equal to the change in kinetic energy of the ball as per Work-Energy theorem:

$W = \dfrac{1}{2} m {(2v)}^{2} - \dfrac{1}{2} m {( - v)}^{2}$

$= > W = \dfrac{4}{2} m {v}^{2} - \dfrac{1}{2} m {v}^{2}$

$= > W = 2 m {v}^{2} - \dfrac{1}{2} m {v}^{2}$

$= > W = \dfrac{3}{2} m {v}^{2}$

So, final answer is:

$\boxed{ \sf{ W = \dfrac{3}{2} m {v}^{2} }}$

Answer 2

Answer:

pic is attached down below

Explanation:

pic