Conservation of Energy, Momentum

[abpandanguyen]

Homework Statement

A bullet of mass m = .010 kg and speed v passes completely through a pendulum bob of mass M = 1.2 kg. The bullet emerges with a speed of v/2. The pendulum bob is suspended by a rigid rod of length l = 0.50 m and negligible mass that can pivot about the center point.


What minimum speed v_p must the pendulum bob have to just make it to the top of the arc at point A (top of the circle, pendulum starting at the bottom)?

What is the speed of the bullet just before hitting the pendulum bob for the situation described in part a?

What is the magnitude of the force in the rod just after the bullet emerges?

Homework Equations

F_r = mv²/r

The Attempt at a Solution

I solved for parts a and b already, and I also got C (answer is 58.8N), but I'm having trouble understanding why this number is the answer. At the bottom of the circle would the magnitude of the force in the rod be:

F_r + mg?

that gets the answer, but aren't these forces going in different directions at the bottom of the circle?

 

[ideasrule]

Fr = mv2/r is the centripetal force required to keep the bob on the string. Since tension must provide this centripetal force and counteract gravity, T=mv^2/r + mg.

 

[abpandanguyen]

Fr = mv2/r is the centripetal force required to keep the bob on the string. Since tension must provide this centripetal force and counteract gravity, T=mv^2/r + mg.

if it was counteracting gravity, doesn't that mean it would be - mg? I don't think I'm quite understanding here.