Understanding Forces in a Bosun Chair System

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In a bosun chair system, when the man pulls himself up at a constant speed, the force he exerts must equal the weight of the man, represented as T + T = mg, due to the two tensions acting on him. If someone else holds the rope, only one tension is present, leading to the equation T = mg for maintaining constant speed. The force exerted by the ceiling on the system varies between the two scenarios, necessitating a free body diagram for clarity. Understanding the number of tensions acting on the pulley is crucial for analyzing the forces involved. This discussion emphasizes the importance of correctly identifying forces in different configurations of the system.
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A man is on a bosun chair attached to a frictionless massless pulley and is holding onto the other end of a rope. (at ground level)

a. What is the force he must pull himself up at if he is to move at a constant speed?
Is the set up T + T = mg?

b. If instead the rope is held by someone else, what is the force needed to pull him up at a constant speed?

And is this set up as T = mg?

c. What is the force exerted by the ceiling on the system for both cases?

This one I am lost on since I need to do a free body diagram for each case.

I don't understand why there is such a difference, in essence.
 
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a and b, you are correct. In a, there are "two tensions" pulling up on the guy in the sling. In b, there is only one tension pulling on the guy.

c:

how many tensions are pulling down on the pulley?
 
Draw a free body diagram from the pulley. That should help.
 

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