# Consider the following figure. A man sits in a pan and tries to raise himself by pullingthe rope downwards [duplicate]

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.

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.

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

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}