Some time ago I came across this simple task. Instead of describing it a lot I will just post a picture and try to explain like that.
So the man and the weight on the other side of the rope have the same mass, everything is in perfect condition, meaning there is no traction on the roll (only traction needed for human to hold on to the rope).
So the question is what will happen when the human tries to climb up the rope? Where will the weight go? Up, down or remain still?
Answer
If the man pulls a length $L$ of rope through his hands, both he and the counterweight will rise by $L/2$. The rope is assumed to be massless, and hence the force of tension is uniform throughout it at all times. As the man does work to pull the rope through his hands, he increases the magnitude of the tension force in the rope to greater than his weight. Since tension is uniform and the counterweight has the same mass, both he and the counterweight accelerate upwards at the same rate.
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