Replace the pile of chain in Prob. 4/92 by a coil of rope of mass ρ per unit length and...

Replace the pile of chain in Prob. 4/92 by a coil of rope of mass ρ per unit length and total length L as shown and determine the velocity of the falling section in terms of x if it starts from rest at x = 0. Show that the acceleration is constant at g/2. The rope is considered to be perfectly flexible in bending but inextensible and constitutes a conservative system (no energy loss). Rope elements acquire their velocity in a continuous manner from zero to v in a small transition section of the rope at the top of the coil. For comparison with the chain of Prob. 4/92, this transition section may be considered to have negligible length without violating the requirement that there be no energy loss in the present problem. Also determine the force R exerted by the platform on the coil in terms of x and explain why R becomes zero when x = 2L/3. Neglect the dimensions of the coil compared with x.