A ring of mass M and radius R is suspended from a light inextensible thread, and two beads (each of mass m) are constrained to slide on it without friction, as shown in the figure below. The beads are released simultaneously from the top of the ring (at = 0) and they slide down opposite sides symmetrically. At the instant of release, the tension in the thread is initially positive. The ring may start to rise depending on the mass ratio M/m.

Principles of Physics: A Calculus-Based Text
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Chapter6: Energy Of A System
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A ring of mass M and radius R is suspended from a light inextensible thread, and two
beads (each of mass m) are constrained to slide on it without friction, as shown in the
figure below. The beads are released simultaneously from the top of the ring (at 0 = 0)
and they slide down opposite sides symmetrically. At the instant of release, the tension
in the thread is initially positive. The ring may start to rise depending on the mass ratio
M/m.
Fixed support
m
Thread
Bead mass
Ring
mass
=
M
1. Use Newton's 2nd law to derive the equations of motion for the bead and the
ring.
2. Use the work and energy principle for the bead to derive an additional equation.
Use the above two to drive the following equation?
3cos^20-2cose + M/2m=0
Transcribed Image Text:A ring of mass M and radius R is suspended from a light inextensible thread, and two beads (each of mass m) are constrained to slide on it without friction, as shown in the figure below. The beads are released simultaneously from the top of the ring (at 0 = 0) and they slide down opposite sides symmetrically. At the instant of release, the tension in the thread is initially positive. The ring may start to rise depending on the mass ratio M/m. Fixed support m Thread Bead mass Ring mass = M 1. Use Newton's 2nd law to derive the equations of motion for the bead and the ring. 2. Use the work and energy principle for the bead to derive an additional equation. Use the above two to drive the following equation? 3cos^20-2cose + M/2m=0
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