The collar of mass m slides on the rough horizontalshaft under the action of the force F

Chapter 3, Problem 3/191

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The collar of mass m slides on the rough horizontal shaft under the action of the force F of constant magnitude \(F \leq m g\) but variable direction. If \(\theta=k t\) where k is a constant, and if the collar has a speed \(v_1\) to the right when \(\theta=0\), determine the velocity \(v_2\) of the collar when \(\theta\) reaches \(90^{\circ}\). Also determine the value of F which renders \(v_2=v_1\).

                                                           

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