A uniform rope of mass M and length a is held at rest with its two ends close together and the rope hanging symmetrically below. (In this position, the rope has two long vertical segments connected by a small curved segment at the bottom.) One of the ends is then released. It can be shown by energy conservation (see Problem 9.8) that the velocity of the free end when it has descended by a distance x is given by
v2=(a−xx(2a−x))g.
Find the reaction R exerted by the support at the fixed end when the free end has descended a distance x. The support will collapse if R exceeds 23Mg. Find how far the free end will fall before this happens.