Using energy to solve circular motion problems

[flyingpig]

Homework Statement

[PLAIN]http://img251.imageshack.us/img251/1764/66016056.jpg

Solutions

[PLAIN]http://img213.imageshack.us/img213/6821/99132292.jpg

The Attempt at a Solution

Now here is my question, why exactly can we not approach this problem using Energy to part a) by setting spring energy = kinetic energy?

I tried it and I got an answer similar, except there is a square root

 

[kuruman]

Now here is my question, why exactly can we not approach this problem using Energy to part a) by setting spring energy = kinetic energy?

I tried it and I got an answer similar, except there is a square root

Based on what principle should the kinetic energy be equal to the spring energy? Why should there be a 50-50 split of the energy initially added to the mass?

 

[flyingpig]

Kinetic energy of the stone (the tangential speed) is equal to the spring energy? What do you mean 50-50 split?

 

[kuruman]

Kinetic energy of the stone (the tangential speed) is equal to the spring energy? What do you mean 50-50 split?

It was your idea.

Now here is my question, why exactly can we not approach this problem using Energy to part a) by setting spring energy = kinetic energy?

Total energy = Kinetic energy + spring energy
If, as you say, spring energy = kinetic energy, then there is a 50-50 split of the total energy. I am wondering why you think that is true.