# Beads on a hoop that cause elevation

1. Feb 24, 2012

### michelle15g

1. The problem statement, all variables and given/known data
There are two beads at the top of a hoop that is tied by a string. The beads start moving downward on the hoop on each side. M is the hoop's mass and m represents each bead's mass.
What is that mass ratio that will cause the hoop to elevate.

2. Relevant equations
T>= (M +2m)g

3. The attempt at a solution
I know that the momentum on the x axis isn't relevant since the beads cancel each other out.
I'm not sure how to use the hoop as a constraint. I can find the difference in potential energy but I can't seem to connect it to the force - only to the momentum.
I would really appreciate the help.

2. Feb 24, 2012

### tiny-tim

welcome to pf!

hi michelle! welcome to pf!
assume the hoop is fixed, and use conservation of energy to find the bead-speed at a general angle θ

(i expect you've already done that )

then find the acceleration of the beads,

then the reaction force on the beads …

what do you get?

3. Feb 24, 2012

### michelle15g

Thank you very much. My problem was that I kept skipping to the bottom instead of finding the speed at every angle in which case the integral was irrelevant.