How to handle string intersection in static friction calculation?

[joemama69]

Homework Statement

a mass m is supported as shown in the figure by ideal strings connected to a rigid wall and to tal mass 3m sitting on a horizontal surface. what is the minimum coefficient of static friction between the larger mass and the surface that permits the system to remain in equilibrium in the situation shown

Homework Equations

The Attempt at a Solution

Big block

F_x = u3mg - T = 0

Little block & strongs

F_x = T - mgsin60 = 0

T = us3mg - mgsin60


I don't think this is correct. How do u deal with the string intersection

 

[rl.bhat]

For big block Fx = μ*3mg - T*sin30 = 0
For smaller block Fy = ...?

 

[joemama69]

Why is the tension have the sin 30 doesn't the tension come directly in the x plain

so is Fy = mg - Tcos30 = 0

 

[rl.bhat]

Correct.
Eliminate T and find the value of μ.

 

[joemama69]

u3mg -Tsin30 = 0
mg - t cos30 = 0 t = mg/cos30
u3mg - mgsin30(cos30) = 0
u = tan30/3

 

[rl.bhat]

Correct.