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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) 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. 9] m ring,M a) i) Draw a free-body diagram for the ring. thread m R bead ii) Draw a free body diagram for one of the beads. b) i) Use Newton's 2nd law to derive the equations of motion for the bead and the ring. ii) Use the work and energy principle for the bead to derive an additional equation. iii) Use your results from i) and ii) to show that the condition for which the tension in the thread is zero is governed by the following quadratic equation: M 3 cos² 0 - 2cose + = 0 2m

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. 9] m ring,M a) i) Draw a free-body diagram for the ring. thread m R bead ii) Draw a free body diagram for one of the beads. b) i) Use Newton's 2nd law to derive the equations of motion for the bead and the ring. ii) Use the work and energy principle for the bead to derive an additional equation. iii) Use your results from i) and ii) to show that the condition for which the tension in the thread is zero is governed by the following quadratic equation: M 3 cos² 0 - 2cose + = 0 2m

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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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) 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. 9] m ring,M a) i) Draw a free-body diagram for the ring. thread m R bead ii) Draw a free body diagram for one of the beads. b) i) Use Newton's 2nd law to derive the equations of motion for the bead and the ring. ii) Use the work and energy principle for the bead to derive an additional equation.
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) 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. 9] m ring,M a) i) Draw a free-body diagram for the ring. thread m R bead ii) Draw a free body diagram for one of the beads. b) i) Use Newton's 2nd law to derive the equations of motion for the bead and the ring. ii) Use the work and energy principle for the bead to derive an additional equation.
iii) Use your results from i) and ii) to show that the condition for which the tension in the thread is zero is governed by the following quadratic equation: M 3 cos² 0 - 2cose + = 0 2m
Transcribed Image Text:iii) Use your results from i) and ii) to show that the condition for which the tension in the thread is zero is governed by the following quadratic equation: M 3 cos² 0 - 2cose + = 0 2m
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