Conservation of Energy + circular motion

[anotherghost]

Quick question:

I'm having trouble understanding a concept: say you've got a mass hanging from a peg by a string. Using conservation of energy, you can figure out what the minimum velocity is that the mass has to have initially so that it goes around the circle: at the top, mv^2/r = mg, so it just makes it around once. However, I'm having trouble with this - how do you calculate the minimum initial velocity so that it goes around the circle twice?

Confusion.

 

[kuruman]

Say it goes around once. If mechanical energy is truly conserved, then it should go around the circle twice, thrice, four times and so on. In other words, if it has enough kinetic energy at the bottom to make it through the top and energy is not lost anywhere, then it will keep on going forever. However, in real life, energy is lost to friction and air resistance so this does not happen