The 6-lb 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 θ = 0.8t, where θ 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 1.5 ft/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??.

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4' O D 8