Question

A projectile of mass m moves to the right with a speed vi. The projectile strikes and sticks to the end of a stationary rod of mass M, of length d, that is pivoted about a frictionless axle through its center.

(a) Find the angular speed of the system right after the collision. (Use v_i for vi, m, M, and d as appropriate in your equation.)
(b) Determine the fractional loss in mechanical energy due to the collision. (Use v_i for vi, m, M, and d as appropriate in your equation.)
fractional loss of energy


I got part a correct and it's (12mv_i^2)/((m+M)d^2)
For part b is it just the final kinetic energy over the initial kinetic energy? If so, why do I keep getting the same answer as part a?

Answer 1

for part b, your final KE is rotational KE which is now 1/2 I w^2 where I consists of the rod mass distributed, and the mass of the initial stuff at some rotational distance. You cant get the same answer as a), as the units are different. THe units in a) are sec^-1, and in b) should be unitless.

Answer 2

so would it be (Iw^2)/(mv^2)?

Answer 3

Yes, depending on what you put in for final I, w, and the intial v.

Answer 4

actually, since b) asked for fractional loss, it would be that fraction subtracted from 1.

Answer 5

What did you put in for I