What Is the Minimum Speed Needed for a Whirling Ball to Taut a String?

[Callen9]

Homework Statement

A 2.0 kg ball is attached to a vertical post with two strings, one 2.0 m long and the other 1.0 m long as shown in the figure. If the ball is set whirling in a horizontal circle, what is the minimum speed necessary for the lower string to be taught? If the ball has a constant speed of 6 ms-1, find the tension on each string.

The picture would look something like this

|\
| \
| \ 2m
1.73m | \
| \
| ____O <--- 2kg
| 1m
|

Homework Equations

I know I have to use this equation at some point --> F=(mv^2)/r

The Attempt at a Solution

I've went throw a few sheets of paper already trying to find the answer. If someone could give me a push in the right direction would be great. This is what I know for sure. There are 3 forces at work here, Gravity, Tension of the upper line, Tension of the lower line. After that I get confused as to what to do. If I could get the first step on what to do and why to do it I think I could figure the rest out.

Any help and I would be extremely grateful!

 

[Callen9]

It screwed up my picture so i'll try this again.

|\
| \
| \
| \
| \
|___O
|
|
|

 

[ideasrule]

Try starting out by drawing a free-body diagram on the ball, labeling all forces, and writing out Newton's second law for both the horizontal and the vertical direction. (Remember that centripetal acceleration is v^2/r). Now you can solve the second problem, where the ball is moving at 6 m/s. You'll get 2 equations with the tensions as the 2 unknowns, so you can solve for the unknowns.

For the first problem, what's the tension in the bottom string when the string is barely taught? Use this value in the 2 equations you found before to solve for the speed.