- #1
Buffu
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Homework Statement
Homework Equations
The Attempt at a Solution
For ##0 \ge \theta \ge \pi/2##
Forces on the ring,
##Mg + 2N\cos \theta = F\qquad 1##
Forces on the beads ##mv^2/R = - N + mg \cos \theta##
By conservation of energy when the bead has fallen through some angle ##\theta##,
##mg (2R) = \dfrac12 mv^2 + mg(R + R\cos \theta)##
From this equation and above we get
##F = -4m\cos\theta + 6m\cos^2 \theta + M##
The discriminent is ##\Delta = 16m^2 - 24 m M \ge 0 \implies m \ge \dfrac32M##
The rise will start when the vertical force on the ring is zero,
So ##\theta = \arccos\left( \dfrac{2m + \sqrt{4m^2 - 6Mm}}{6m}\right)##
Is this correct ? why did we omit ##m = 3/2 M## ?
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