(i) Show that the coeffecient of the restitution between the particle and the wall is given by √(1-2E/mu^2).

Question

A particle of mass 'm' is traveling on a straight line with speed 'u' on a horizontal floor. It strikes a fixed smooth vertical wall normally. If the kinetic energy lost by the particle due to the collision is 'E',

Answer 1

e=v/u where v is the rebound speed magnitude with velocity direction opposite to u. Therefore v=-eu.

Energy equation is: mu^2/2-E=mv^2/2=me^2u^2/2.

e^2=(mu^2-2E)/(mu^2)=1-2E/mu^2, so e=√(1-2E/mu^2).

Comments

Please in the other approach v=eu. But this approach v=-eu. Is it correct in both cases? Thank you

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Actually, it doesn't matter whether it's positive or negative because v is squared,

so (eu)^2=(-eu)^2=e^2u^2.

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OK I understand it now Thank u very much