Replace the chain of Prob. 4/90 by a flexible rope or bicycle chain of mass ρ per unit l...

Replace the chain of Prob. 4/90 by a flexible rope or bicycle chain of mass ρ per unit length and total length L. The free end is released from rest at x = 0 and falls under the influence of gravity. Determine the acceleration a of the free end, the force R at the fixed end, and the tension T₁ in the rope at the loop, all in terms of x. (Note that a is greater than g. What happens to the energy of the system when x = L?)