Tension and acceleration comprehension

[seanhead42]

If a man hanging on to a rope with just his hands tries to climb the rope, does the tension on the rope increase? Why?

I think no, but my argument isn't very rigorous.

If the man is stationary and holding on to the rope with just his hands, the weight of his body is pulling down on his arms which is pulling down on the string which is pulling on the ceiling. The tension on the rope and his arms is equal to his weight.

When he climbs up the rope, at some point he must bend his arms to pull his body upward. This is when the accelaration occurs. He pulls his body up, so there must be a positive force from the muscles in his arms acting on his body. I make a very large intuitive leap here and say that since his body is accelerating, there need not be any increase in the tension of the rope. If I am right, why am I right?

 

[Aero]

You are wrong. Remember Newton's third law. There are two forces here: the man pulling down on the rope, and the rope pulling up on the man. The former is the force in his muscles, and the latter is the tension in the string.

If the man exerts a 10N force downwards on the string, the string will exert a 10N force upwards on the man, accelerating him. This 10N force is added to the tension in the string.

 

[seanhead42]

Thankyou for your help