Problem Newtonian mechanics French

[leoleo]

A prisoner in jail decides to escape by sliding to freedom down a rope provided by an
accomplice. He attaches the top end of the rope to a hook outside his window; the
bottom end of the rope hangs clear of the ground. The rope has a mass of 10 kg, and the
prisoner has a mass of 70 kg. The hook can stand a pull of 600 N without giving way. If
the prisoner's window is 15 m above the ground, what is the least velocity with which he
can reach the ground, starting from rest at the top end of the rope?

My solution:

For the hook I calculate:

M-mass rope 10 kg

m-mass prisoner 70 kg

F –force max. on the hook 600 N

h-height 15 m





(1) F>T+Mg

(2) ma=mg-T

From 1 T < F-M and from 2 mg-ma<F-Mg

Ma>(m+M)*g-F

a>((m+M)*g-F)/M

Now v=SQRT(2*a*h) I can find h.



But I am not sure for two free body diagram : (1) and (2). Is (1) probably F>T+Mg+mg because prisoner is on the rope or in (2) there is influence of mass of rope or not on the prisoner?

Please help how to think at this problems.

 

[leoleo]

Now v=SQRT(2*a*h) I can find h.

It should be: I can find v

 

[haruspex]

Is (1) probably F>T+Mg+mg

It is impossible to answer your question since you have not defined T.