Suspended ball

[Punchlinegirl]

A mass m= 9.3 kg is suspended from a sting of length L=1.57 m. It revolves in horizontal circle. The tangential speed of the mass is 3.14 m/s. What is the angle theta between the string and the vertical in degrees?

I started off by using the equations Lsin theta= mv^2/ r and Lcos theta=mg
Solving the second one for L and plugging into the first gave me mgsin theta/ cos theta= mv^2/r. I then plugged in my numbers to get 91.14 sin theta/ cos theta = 116.8. Since sin/cos= tan, I simplified to get 91.14 tan theta= 116.8, using inverse tan to get an answer of 52 deg. This wasn't right... can someone help me?

Thanks

[jamesrc]

First, I think you mean T (as in the tension of the string) when you wrote L.

Second, it looks like you decided that r=L/2; what made you decide that? r is the distance between the mass and the axis it rotates about. Look at the geometry again to find r as a function of θ.