Centripetal Force and Tangential Velocity

[x0ji11y]

Homework Statement

Suppose a string of negligible mass can support a mass of .025 kg when hanging vertically. The string is 4.23 m long (radius). If you add another weight and spin the string horizontally in a circular pattern above your head, the string will break upon reaching a tangential velocity of 5.1 m/s. What is the mass of the weight?

Homework Equations

Angular displacement = (arc length) / (radius)
Centripetal Force = (mass)(tangential velocity)(tangential velocity) / (radius)
Centripetal Force= (mass)(radius)(angular speed)(angular speed)
Tangential Velocity=(angular speed)(radius)

The Attempt at a Solution

I have no idea where to get started, considering you're given neither the mass nor the force to work with. I'm thinking that you need to start by using the fact that it can support a 25 g mass vertically, but i don't know how to calculate the force from that, given that the tangential velocity is zero. Any help would be greatly appreciated! Thank you! :)

 

[vela]

Start by drawing the free-body diagram for the 25-g mass when it's suspended vertically. You should be able to find the tension in the string easily.