Solving the Mystery of Two Beads and a Frictionless Hoop

[zheng89120]

Homework Statement

Two beads of mass m are initially at rest at the top of a frictionless hoop of mass M and radius R, which stands vertically on the ground. The beads are given tiny kicks, and they slide down the hoop, one to the rigth and one to the left. What is the largest value of m/M for which the hoop will never rise up off the ground?

Homework Equations

classical mechanics

The Attempt at a Solution

2mg cos^2(theta from top) = Mg ?

please help me get started, as this is an assignment question

 

[tiny-tim]

hi zheng89120!

(have a theta: θ and try using the X² tag just above the Reply box )

2mg cos^2(theta from top) = Mg ?

where did that come from?

start with conservation of energy to find the speed as a function of θ

then find the acceleration

then find the force from the hoop on each mass

then find the force on the hoop from each mass …

when will that be enough to lift the hoop? ​