How Does Bullet Speed Affect Pendulum Motion?

[mathematical]

Homework Statement

diagram: http://goo.gl/uPl0

Part A
A bullet of mass 0.0175 kg and speed v_b passes completely through a pendulum bob of mass 1.3 kg. The bullet emerges with a speed 0.5v_b. The pendulum bob is suspended by a stiff rod of length 1.1 m and negligible mass. The acceleration of gravity is 9.8 m/s². What is the critical value v, such that when v_b > v , the pendulum bob will barely swing through a complete vertical circle?

Part B

Suppose that the pendulum bob is suspended from a light flexible cord instead of a stiff rod.
Now what is the minimum value of v such that the pendulum bob will swing through a
complete vertical circle?

2. The attempt at a solution

I was able to get part A by using conservation of momentum and conservation of energy and ended up with 975.61 m/s for v.

However, I am stuck on part B and do not know how to proceed. I know it has something to do with the tension of the cord, but am not exactly how to factor that in.

Any help would be much appreciated. Thanks!

 

[mathematical]

help anyone?

 

[mathematical]

never mind, i got it! i figured out that at the top of the pendulum, centripetal force had to be equal to the force of gravity because there is no tension to support the bob.