(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

The speed of rebound is v=eu where e=coeff of restitution.

Loss (negative) of KE is E so mu^2/2-E=mv^2/2=mu^2e^2/2.

mu^2/2-mu^2e^2/2=E.

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

Comments

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