(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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 that the velocity of the free end when it has descended by a distance x is given by

v^2= (x(2a-x))g/(a-x)

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 3/2Mg. Find how far the free end will fall before this happens.

2. Relevant equations

dp/dt= Mg-R, dp/dt is change in momemtum and R is the reaction force.

3. The attempt at a solution

Mass of moving rope is changing. At rest, T=0 . When rope is release T=1/2*Mv^2 and V= Mgh_{r}+Mgh_{l}.

h_{l}=x, h_{r}=1/2(a-x)

R=Mg-dp/dt

should I differentiate v^2 in order to obtain dv/dt and then should I proceed to multiply dv/dt by M in order to get dp/dt. Now that I have dp/dt I can calculate the R now right?

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# Homework Help: Linear momemtum principle problem

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