Beads on a hoop that cause elevation

  1. 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.
  2. jcsd
  3. tiny-tim

    tiny-tim 26,016
    Science Advisor
    Homework Helper

    welcome to pf!

    hi michelle! welcome to pf! :wink:
    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 :wink:)

    then find the acceleration of the beads,

    then the reaction force on the beads …

    what do you get? :smile:
  4. 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.
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