Problem

A cord, which is wrapped around the inner radius of the spool of mass m = 35 kg, is pulled...

A cord, which is wrapped around the inner radius of the spool of mass m = 35 kg, is pulled vertically at A by a constant force P = 120 N (the cord is pulled in such a way that it remains vertical), causing the spool to roll over the horizontal bar BD. The inner radius of the spool is R = 0.3 m, and the center of mass of the spool is at G, which also coincides with the geometric center of the spool. The spool’s radius of gyration is kG = 0.18 m. Assuming that the spool starts from rest, that the cord’s inertia and extensibility can be neglected, and that the spool rolls without slip, determine the speed of the spool’s center 3 s after the application of the force. In addition, determine the minimum static friction coefficient for rolling without slip to be maintained during the time interval in question.