What Is the Minimum Speed for a Stone to Stay Taut in a Vertical Circle?

[quantumlolz]

Homework Statement

A stone is tied to a string of length l. Someone whirls the stone in a vertical circle. Assume that the energy of the stone remains constant as it moves around the circle. Calculate the minimum speed that the stone must have at the bottom of the circle, if the string is to remain taut at the top of the circle

Homework Equations

Equations that I'm sure are relevant:

Kinetic energy = 1/2*m*v^2
Gravitational potential energy = mgh

Equations that are probably relevant:

Centripetal force = (m*v^2)/r

The Attempt at a Solution

Taking the zero of potential energy at the bottom of the circle.

At the top, kinetic energy = 0, gravitational potential = mg(2l) [as 2l] is the height above the bottom of the circle.

At the bottom, kinetic energy = 1/2*m*v^2. gravitational potential = 0.

Conservation of energy gives:

2mgl = 0.5*m*v^2
4gl = v^2
---> v=sqrt(4gl)

I'm not sure if my method is right or not. I'd really appreciate it if someone could have a quick look and point out any mistakes if they can see any. Cheers :)

 

[Maybe_Memorie]

Looks fine to me.

 

[housemartin]

You did it like the string was rigid and massless, so you found speed with witch stone just reach top of the circle and stays there (very complicated thing in real world ;] ). The question, however, is different i think - (I don't know English well) - its like what minimum speed at the bottom must be so stone keeps moving in circle of radius L with minimum tension on the string