Question

A small block of mass 2m initially rests on a track at the bottom of the circular, vertical loop-the-loop shown, which has a radius r. The surface contact between the block and the loop is friction less. A bullet of mass m strikes the block horizontally with initial speed v_o and remains embedded in the block as the block and bullet circle the loop.

 Determine each of the following in terms of m, v_o,  r, and g.

a. The speed of the block and bullet immediately after impact

b. The kinetic energy of the block and bullet when they reach point P on the loop

c. The speed v_min of the block at the top of the loop to remain in contact with track at all times

d The new required entry speed v_o' of the block and bullet at the bottom of the loop such that the conditions in part c apply.

e. The new initial speed of the bullet to produce the speed from part d above. 

Answer 1

(a) Apply momentum conservation perfect inelastic

(c) The minimum speed to stay in contact is the limit point at the top where F_n just becomes zero. So set F_n = 0 at the top of the loop so that only mg is acting down on the block. The apply F_net(C)

(e) Apply momentum conservation, perfect inelastic with v_f as the speed found above and v_i unknown