a mass moving m moving to the right with speed v, strikes a stationary rod of le

Question

a mass moving m moving to the right with speed v, strikes a stationary rod of length l and mass m is pivoted at its center. the rod is free to rotate about the frictionless pivot point (Icam,rod=1/12 Ml^2) a. find angualr speed after collision b. determine the ractional loss of energy of the ssystem due to the collision

Explanation / Answer

conserve angular momentum Now, moment of inertia of particle + rod system after the particlehaving stuck : I = M*L*L/12   + m*L/2*L/2 And, initial angular momentum = m*v*L/2 So, if final angular speed be w, I*w = mvL/2 => w = mv/2(ML/12 + mL/4) = mv/(ML/6 + mL/2) initial energy = m*v*v/2 final energy = I*w*w/2 => loss of energy = m*v*v/2 - [M*L*L/12 + m*L/2*L/2]* mv*mv / 2*[(ML/6 + mL/2)*(ML/6 + mL/2)] = m*v*v/2 - mv*mv*/(2M/3 + 2m) = m*v*v * [ 1/2 -   m/(2M/3 + 2m)] =m*v*v* [ M/(M + 3m)] So, fractional loss = [(m*v*v)*(M/(M+3m)] / [(m*v*v) *(1/2)] = 2M/(M+3m)

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