An ideal rope or bicycle-type chain of length L and mass ρ per unit length is resting on...

An ideal rope or bicycle-type chain of length L and mass ρ per unit length is resting on a smooth horizontal surface when end A is doubled back on itself by a force P applied to end A. End B of the rope is secured to a fixed support. Determine the force P required to give A a constant velocity v. (Hint: The action of the loop can be modeled by inserting a circular disk of negligible mass as shown in the separate sketch and then taking the disk radius as zero. It is easily shown that the tensions in the rope at C, D, and B are all equal to P under the ideal conditions imposed and with constant velocity.)