Solving Pendulum Motion: Vo, Angle 48', Horizontal & Vertical Positions

[Inkyspider]

1. There is a pendulum of Length 2.1m. Its bob has speed Vo when the cord makes the angle 48' with the vertical.
a) what is the speed of bob in lowest posotioin if Vo=8m/s?
What is the least value Vo could have is pendulum is to swing down and then up to:
b) a horizontal position
c) a vertical position with cord remaining straight



2. I understand that this is a conservation of energy problem and K1 + U1 = K2 + U2 and i tried using this with K=1/2mv^2 and U=mgy but it didn't work.
Also, i know the answer to c involves something to do with tension, but I'm not sure how to use it.


Thanks for any help!

 

[Doc Al]

2. I understand that this is a conservation of energy problem and K1 + U1 = K2 + U2 and i tried using this with K=1/2mv^2 and U=mgy but it didn't work.

Show what you did.

Also, i know the answer to c involves something to do with tension, but I'm not sure how to use it.

Hint for c: Analyze the forces on the bob when it is in the vertical position and apply Newton's 2nd law to find the minimum speed required at that position to maintain a straight cord.