Bouncing Particle and Massive Block

HardPhysElo Quiz #9

53.Bouncing Particle and Massive Block

+10

A point mass

m

slides with speed

v

on a frictionless horizontal surface between a fixed vertical wall and a massive block of mass

M

, where

M \gg m

. The block is initially at a distance

L

from the fixed wall and is moving towards it with speed

u

, where

u \ll v

. The point mass bounces perfectly elastically between the fixed wall and the block. Assuming the block never reaches the fixed wall, what is the minimum distance between the block and the fixed wall during the subsequent motion?

L \left( 1 + \frac{m v^2}{M u^2} \right)^{-1/2}

L \left( 1 + \frac{M u}{m v} \right)^{-1}

L \left( 1 + \frac{M u^2}{m v^2} \right)^{-1}

L \left( 1 + \frac{M u^2}{m v^2} \right)^{-1/2}

L \left( 1 + \frac{M^2 u^2}{m^2 v^2} \right)^{-1/2}

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