How Do Tension Forces Distribute in a System with a Diagonal Rope?

[adam3music]

Homework Statement

Homework Equations

SUM OF FORCES / BALANCING

The Attempt at a Solution

Hey all, the question and my illustration are posted above. My main question is which blocks do the three Tension values I circled go? Are they all tied into the diagonal where the rope meets or do they go in the force equations for their respective blocks? Once I figure that out I can use the force equations and balance everything to find the mass of the hanging block. Thank you for any help, I appreciate it

EDIT* Also if my illustration is just flat out wrong , I apologize and will give it another shot. I feel like it's right but I'm still learning the very basics and struggling. Thank you!

 

[haruspex]

Are they all tied into the diagonal where the rope meets or do they go in the force equations for their respective blocks?

The standard procedure is to consider each rigid body separately. In this case, you can treat the meeting point of the three cords as a massless rigid body. Write out the force balance equations for each.
You seem to have T₂ as the tension in both the diagonal cord and the vertical cord. They will not be the same.

 

[scottdave]

Yes adam3music is correct in that the tension holding up the weight, is not the same as the tension in the angled rope.
Here are some things to consider:
The vertical components of the tension in the upper (angled) rope will balance the vertical components of the other ropes.
Does the horizontal rope contribute any vertical component?
How much vertical component does the rope which the weight is suspended?
How can you split the tension in the angled rope to its vertical and horizontal components?
All horizontal components must also balance out?
What is the maximum possible horizontal tension in the horizontal rope, before the mass starts sliding?