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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.

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.