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Values of Velocity at which the body will move without bouncing

  1. Oct 14, 2011 #1
    1. The problem statement, all variables and given/known data
    A small point mass is fixed to the inside of a thin rigid ring(hoop) of radius R and mass equal to that of the point mass. The hoop rolls without slipping over on a horizontal plane; at the moments when the point mass gets into lower position, the center of the hoop moves with velocity V0. At what values of V0 the hoop will move without bouncing ?

    2. The attempt at a solution

    As the point mass m attached to the hoop moves up it gains potential energy. Since total energy must be conserved, the kinetic energy of the (hoop+point mass system) reduces and thus the rotating hoop slows down. the hoop will have its maximum tendency to jump off the ground when the point mass is located at the highest point due to centrifugal force, that's all I can think about.
     
  2. jcsd
  3. Oct 15, 2011 #2
    Does this make sense?

    Edit, in my sketch my v = 2V_o
     

    Attached Files:

    Last edited: Oct 15, 2011
  4. Oct 15, 2011 #3
    In a perfect world, no bouncing, just diminished G's. In the real world, imperfections in the hoop and "road" surface could easily create bouncing. Isn't this why we balance rotational bodies?
     
  5. Oct 15, 2011 #4
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