A projectile of mass m moves to the right with aspeed v i . The projectile strik

Question

A projectile of mass m moves to the right with aspeed vi. The projectile strikes andsticks to the end of a stationary rod of mass M, oflength d, that is pivoted about a frictionless axlethrough its center.
(a) Find the angular speed ofthe system right after the collision. (Use v_ifor vi, m, M, and d as appropriate in yourequation.)

(b) Determine the fractionalloss in mechanical energy due to the collision. (Use v_ifor vi, m, M, and d as appropriate in yourequation.)

(a) Find the angular speed ofthe system right after the collision. (Use v_ifor vi, m, M, and d as appropriate in yourequation.)

(b) Determine the fractionalloss in mechanical energy due to the collision. (Use v_ifor vi, m, M, and d as appropriate in yourequation.)

Explanation / Answer

(a)according to the law of conservation of momentum wehave m * vi + M * u = (m + M) * V or V = [m * vi + M * u/(m + M)] u = 0 or V = [m * vi + M * 0/(m + M)] = [m *vi/(m + M)] the angular momentum of the system right after the collisionis L = m * V * (d/2) we know that L = I * w or m * V * (d/2) = I * w or w = [m * V * (d/2)/I] I = (M * d2/3) or w = [m * V * (d/2)/(M * d2/3)] or w = (3/2) * (m * V/M * d) (b)the frational loss in mechanical energy due to thecollision is K = Kf - Ki where Ki = (1/2)m * vi2 andKf = (1/2)(M + m) * V2 or K = [(1/2)(M + m) * V2 - (1/2)m *vi2] = (1/2) * ((M + m) * V2 - m *vi2)

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