Rotating hoop with body fixed inside of same mass

[lavankohsa]

Homework Statement

A small body A is fixed to the inside of a thin rigid hoop of radius R and mass equal to that of the body A. The hoop rolls without slipping over a horizontal plane; at the moments when the body A gets into the lower position, the center of the hoop moves with velocity v0. At what values of v0 will the hoop move without bouncing?

Homework Equations

mgcos(θ)−N=mv²/R
One equation will be the energy equation. The velocity of hoop and mass A will reduce as the body A is gaining the potential energy.

The Attempt at a Solution

 

[Andrew Mason]

Homework Statement

A small body A is fixed to the inside of a thin rigid hoop of radius R and mass equal to that of the body A. The hoop rolls without slipping over a horizontal plane; at the moments when the body A gets into the lower position, the center of the hoop moves with velocity v0. At what values of v0 will the hoop move without bouncing?

Homework Equations

mgcos(θ)−N=mv²/R
One equation will be the energy equation. The velocity of hoop and mass A will reduce as the body A is gaining the potential energy.

The Attempt at a Solution

What will cause the hoop to bounce? Think of the force on the mass A and the centripetal force required to keep it rotating when mass A is at its highest point (highest velocity).

AM