With what minimum velocity should a block be | vedclass

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(B) The block is projected with velocity $v_0$ towards the right. The conveyor belt is moving towards the left with velocity $v$. The friction force a

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$\sqrt{2\mu gL}$

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(B) The block is projected with velocity $v_0$ towards the right. The conveyor belt is moving towards the left with velocity $v$. The friction force acts on the block towards the left,providing a retardation $a = \mu g$.For the block to just reach the end $B$,its velocity relative to the belt must become zero exactly at point $B$.Let $v_{rel}$ be the initial velocity of the block relative to the belt. Since the belt moves to the left with $v$,the velocity of the block relative to the belt is $v_{rel} = v_0 + v$ (towards the right).The retardation of the block relative to the belt is $a = \mu g$.Using the equation of motion $v_f^2 = u^2 - 2as$,where $v_f = 0$,$u = v_0 + v$,and $s = L$:$0 = (v_0 + v)^2 - 2(\mu g)L$$(v_0 + v)^2 = 2\mu gL$$v_0 + v = \sqrt{2\mu gL}$$v_0 = \sqrt{2\mu gL} - v$If the belt were stationary $(v=0)$,the minimum velocity would be $\sqrt{2\mu gL}$. Given the options provided,the question implies the case where the belt velocity $v$ is negligible or the relative velocity condition is simplified to the standard work-energy theorem application for a stationary surface.

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