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-   -   Beads on a hoop that cause elevation (http://www.physicsforums.com/showthread.php?t=580855)

michelle15g Feb24-12 03:12 AM

Beads on a hoop that cause elevation
 
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.

tiny-tim Feb24-12 04:42 AM

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

Quote by michelle15g (Post 3781504)
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.

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:

michelle15g Feb24-12 05:57 AM

Re: Beads on a hoop that cause elevation
 
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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