Is the Tension Force in an Atwood Machine Only Transmitted Between Blocks?

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Homework Statement


When talking about an Atwood machine, a student states:
"All strings can do is transmit forces from other objects. That means that the string in the Atwood's machine just transmits the weight of one block to the other."
Is the student correct or incorrect? Why?

Homework Equations


Tension = mg + ma

The Attempt at a Solution


This is how it is making sense in my mind, but correct me if I'm wrong.
I am thinking that the student is incorrect, because the tension force on the string holds objects together. The weight of one block isn't transmitted from one block to another, but the forces on the blocks are a result of one another through the string.
 
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I think I could argue either way... but it reads like you've said the same thing as "the student", but in different words.