Chapter 12.1, Problem 12.68P

The 3-kg collar B slides on the frictionless arm AA′. The arm is attached to drum D and rotates about O in a horizontal plane at the rate $\stackrel{\dot{}}{\theta }=0.75t$ where $\stackrel{\dot{}}{\theta }$ and t are expressed in rad/s and seconds, respectively. As the arm-drum assembly rotates, a mechanism within the drum releases cord so that the collar moves outward from O with a constant speed of 0.5 m/s. Knowing that at t = 0, r = 0, determine the time at which the tension in the cord is equal to the magnitude of the horizontal force exerted on B by arm AA′.

Fig. P12.68