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Consider the following figure. A man sits in a pan and tries to raise himself by pulling the rope downwards. Will he be able to raise himself up? Explain.

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I understand that it is not possible as like sitting on chair, one can't pull the chair up. But would anyone give a proper justification with necessary mathematical support. Please.

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  • $\begingroup$ @VincentThacker Not properly. Need a mathematical explanation... $\endgroup$ Commented Jun 17, 2021 at 5:20
  • $\begingroup$ It is well possible. $\endgroup$ Commented Jun 17, 2021 at 5:21
  • $\begingroup$ @VladimirKalitvianski Is it.. Please explain in details $\endgroup$ Commented Jun 17, 2021 at 5:22
  • $\begingroup$ Put this set horizontally, only friction is employed. It is self evident that one can move oneselfwith pulling a rope. $\endgroup$ Commented Jun 17, 2021 at 5:34
  • $\begingroup$ see for math youtube.com/watch?v=ayUuD2RyI5w and playground youtube.com/watch?v=5JQ43_-pyzw $\endgroup$
    – anna v
    Commented Jun 17, 2021 at 6:48

3 Answers 3

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This is by all means possible:

The person just need to apply a pulling force on the rope greater than their weight and the pan's weight combined. "Mathematically", the resulting force on the pan is: \begin{align} F &= F_{pull} - (M_{pan} + M_{person})g = (M_{pan} + M_{person})a \end{align} and the resulting acceleration is \begin{align} a &= \frac{F_{pull}}{(M_{pan} + M_{person})} - g. \end{align}

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This is like like pulling up yourself on a tree branch. The key is that the Newton third law pairs do not cancel, since they act on different objects -- the rope is attached to the pulley which is attached to some rigid structure. If the pulley was attached to you this would fail.

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There is a clear difference between the two cases you point to, in your example you are trying to pull up the chair while sitting in it, just apply Newton's third law of motion. as you pull the chair up you need to push on something down which happens to be the chair so you are nullifying any force you apply.

If you leverage against some other surface like the floor or ceiling then you have a net force that can act on the chair hence making it possible to move it. In the question given, you are pulling against the ceiling to apply an equal force to the pan making it possible to pull yourself up.

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