Classical Mechanics (Kibble & Berkshire) · Problem 9.8
The linear momentum principle — T.W.B. Kibble, F.H. Berkshire
Physics — Mechanics · ropes-energy-conservation
Problem
A uniform heavy rope of 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. Find the velocity of the free end when it has descended by a distance x.
Deduce a similar formula for the acceleration of the free end and show that it always exceeds g. Find how far the free end has fallen when its acceleration has risen to 5g.