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 tried to go about this question but I couldn't finish the equations. 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.
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?
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.