# Homework Help: Circular motion of a loop-the-loop machine

1. Sep 6, 2006

### busted

A loop-the-loop machine has radius R of 18m.
a)What is the minimum speed at which a cart must travel so that it will safely loop the loop?

I am unsure which formula to use as I know it has something to do with KE and GPE. I was thinking it might be :

v = square root ____(2GM)______
r

but it cant be as we don't the mass.

any ideas???

2. Sep 6, 2006

### Hootenanny

Staff Emeritus
Hi there busted and welcome to PF,

Your an the right tracks with energy. Energy must be conserved, ignoring friction all the kinetic energy at the bottom of the loop will be converted into potential energy and the top of the loop. Therefore, at the minimum speed the initial kinetic energy must equal the potential energy at the top of the loop. Do you follow?

3. Sep 6, 2006

### Tomsk

The trick to this is to remember it needs to have some excess velocity (and therefore KE) to get round, it can't have v=0 at the top, else it would fall vertically. The constraint for the particle at the top of the turn is centripetal acc=g.

Also, the mass cancels.

Last edited: Sep 6, 2006
4. Sep 6, 2006

### busted

thanks guys i'll hav a go working it out