Dynamics | Part IA, 2006

Two light, rigid rods of length 22 \ell have a mass mm attached to each end. Both are free to move in two dimensions. The two rods are placed so that their two ends are located at (d,+2),(d,0)(-d,+2 \ell),(-d, 0), and (+d,0),(+d,2)(+d, 0),(+d,-2 \ell) respectively, where dd is positive. They are set in motion with no rotation, with centre-of-mass velocities (+V,0)(+V, 0) and (V,0)(-V, 0), so that the lower mass on the first rod collides head on with the upper mass on the second rod at the origin (0,0)(0,0). [You may assume that the impulse is directed along the xx-axis.]

Assuming the collision is elastic, calculate the centre of-mass velocity v\boldsymbol{v} and the angular velocity ω\boldsymbol{\omega} of each rod immediately after the collision.

Assuming a coefficient of restitution ee, compute v\boldsymbol{v} and ω\boldsymbol{\omega} for each rod after the collision.

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