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This is a problem that I encountered while solving problems related to constrained motion:

With all the data given in the above question, I believe that the monkey just holds on to the rope and does not climb it up or slip down. So if that is the case , and assuming that the string is inextensible, shouldn’t the monkey and the block have the same accelerations? However, when I saw the solution to the above problem, the monkey and the block have different accelerations. How is that possible?

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First of all the monkey is trying to climb up the rope. For that he is applying a force of 80 N downward on the rope. As per newton's third law of motion the rope exerts a force of 80 N upwards on the monkey.

If we take the up direction as '$+$' and down direction as '$-$', then force on monkey is $Mg=-100$ N, and rope force = $+80$ N. By $F=ma$ we get acceleration (monkey) = $-2$ ms$^{-2}$.

Now as the string is massless we get tension in string = $80$ N. This $T$ will lift the $5$ kg block. Applying $F=ma$ on $5$ kg block (forces are $T$ and $Mg$) we get a (rope) = $+6$ ms$^{-2}$.

Now, the acceleration of the Monkey relative to rope = $A$(monkey) — $A$(rope) $= -2-6 = -8$ (downward direction).

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  • $\begingroup$ Here, acc. of rope and 5 kg block is same. $\endgroup$ – Brijesh Shah Nov 26 '17 at 3:48
  • $\begingroup$ Ohhhh so it means that if the monkey didnt climb up , he wouldnt exert a force of $80N $? $\endgroup$ – Aditi Nov 26 '17 at 4:14
  • $\begingroup$ Yes if the monkey did not climb up then he would not exert a 80 N force on the rope. And in such a case the acc. of the rope and monkey will be same. $\endgroup$ – Brijesh Shah Nov 26 '17 at 4:36
  • $\begingroup$ Ohhhh thank you very much ! I was really confused , but now it’s clear to me. $\endgroup$ – Aditi Nov 26 '17 at 6:22
  • $\begingroup$ If the monkey is accelerating downward at 2 and the rope on his side of the pulley is accelerating downward at 6 , then his acceleration relative to the rope is upward at 4 (m/sec^2). $\endgroup$ – R.W. Bird Aug 31 '19 at 17:51

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