Question

A projectile of mass m moves to the right with a speed vi (Fig. P11.50a). 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 (Fig. P11.50b).

a) Find the angular speed of the system right after the collision. (Use vi, m, M, and d as appropriate in your equation.)

(b) Determine the fractional loss in mechanical energy due to the collision. (Use vi, m, M, and d as appropriate in your equation.)

Answer 1

The initial angular momentum of the projectile about the pivot O is, With the projectile stuck to the end of the rod, the rotational inertia of the projectile and the rod combined about O is, 212 4 12 Using conservation of angular momentum, we have Therefore, combine (1), (2) and (3), we have mv 4 12 mv 3m M 12 12 6mv, (3m+M)d

The initial kinetical energy is given by, The final energy is rotational kinetical energy omv 2L12 (M+3m)d 3mv, 2M +6m KE KE The fractional loss in mechanical energy is 3m M +3m M +3m