Is it friction or tension acting on the person hanging on a rope?

[aiqing]

Homework Statement

First question is only for reference for the second question.
1. Block A of mass $m/2$ is connected to one end of light rope which passes over a pulley as shown in figure. A man of mass $m$ climbs the other end of rope with a relative acceleration of $g/6$ with respect to rope. Find the acceleration of block A and tension in the rope.

2. A monkey of mass $m$ is climbing a rope hanging from the rod with acceleration $a$. The coefficient of static friction between the body of the monkey and the rope is $\mu$. Find the direction and value of friction force on the monkey and tension in the string.

Relevant Equations

$\sum F_{net} = ma$

The first question statement was under the chapter $Newton's Laws Of Motion (Without Friction)$. Whereas, the second question was under $Friction$.
The free body diagram for the first question is given as:

And the free body diagram for the other question is given as:

In the first question, the tension is acting directly on the person gripping the rope.
In the second question, tension is not directly acting on the body but the friction is. Thus, the solution says that the equations for the second question are $$f-mg=ma,$$ $$f=T$$

If there was no friction, there would be sliding between the gripping hand of the body and the rope. But, there is no sliding. Hence, there is static friction due to the tendency of relative motion for the hand downwards.

So, the static friction for the body will be acting upwards and for the rope, it will be acting downwards because static friction acts opposite to the direction of tendency of relative motion. So, I get the second equation very clearly.

But the problem arises that shouldn't the first equation be:
$$T+f-mg=ma$$
Shouldn't the tension be acting on the body too in their free body diagram. I know intuitively that i am wrong but don't seem to come up with any logical reasoning behind it. And I made the chapter names clear because I think that it could be because we weren't familiar with friction, that is why, the first problem didn't mention friction in it and subtly tried to solve the problem by skipping the step of equating tension with friction.
Still, i would like to have a logical statement as to why the tension is not acting directly on the body.

 

[Aurelius120]

How can tension act directly on a person? Friction joins the person with the rope. Lizards have suction but the person needs friction to hold the rope.

 

[haruspex]

Shouldn't the tension be acting on the body too in their free body diagram.

It depends where you want to put the boundary around a system.
Tension acts all along the rope, down to the part in contact with the monkey. The part of the rope in contact with the monkey interacts through tension with the rope above it and through friction with the monkey's hand. The monkey's hand… etc.

 

[aiqing]

It depends where you want to put the boundary around a system.
Tension acts all along the rope, down to the part in contact with the monkey. The part of the rope in contact with the monkey interacts through tension with the rope above it and through friction with the monkey's hand. The monkey's hand… etc.

Thank you so much! All my other doubts regarding this have been solved with just this statement. The problem was that I was not considering any boundary and just doing it all in air. I built misconceptions because I've rarely come across problems that don't have a singular body as the boundary and always, by default, thinking of only a singular body as the boundary. Thus, missing the minute detail but a very important question that on what exactly are we drawing the free body diagram of.

Conclusion:
The first question's Free Body Diagram is also correct as they have much larger system into view compared to the second question and they cancel out the internal forces (friction here).
And the second question's Free Body Diagram had a micro level system to understand what is exactly going on in the micro level and how friction helps.

Thank you again for the insight!

 

[aiqing]

How can tension act directly on a person? Friction joins the person with the rope. Lizards have suction but the person needs friction to hold the rope.

The actual problem was that I was not considering any boundary, thank you for your input!