Equilibrium of a particle

1. The problem statement, all variables and given/known data
Determine the maximum weight W of the block that can be suspended in the position shown if each cord can support a max tension of 80lb. also what is the angle [tex]\theta[/tex] for equilibrium?


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2. Relevant equations



3. The attempt at a solution
the free body diagram should be:
-force A to B is 60[tex]^{o}[/tex] from the positive x axis
-force from the block is in the negative y direction
-tension is in the third quadrant at and angle of [tex]\theta[/tex] from the negative y axis

putting the forces in their respected x and y components:
**note: i'm using 30[tex]^{o}[/tex] instead of the 60 from the x axis**

F[tex]_{x}[/tex] = 80sin30 - Wsin[tex]\theta[/tex] = 0
F[tex]_{y}[/tex] = 80cos30 - Wcos[tex]\theta[/tex] - W = 0

from F[tex]_{x}[/tex] : W = [tex]\frac{80sin30}{sin\theta}[/tex]

sub into F[tex]_{y}[/tex]:

0=80cos30 - [tex]\frac{80sin30}{sin\theta}[/tex]cos[tex]\theta[/tex] - [tex]\frac{80sin30}{sin\theta}[/tex]

then i get:
cot30 = [tex]\frac{cos\theta - 1}{sin\theta}[/tex]
form here i'm not sure how to solve for [tex]\theta[/tex]. the angle should b 60 deg, but from the solution, it seems to me lyk a random guess....

any help would b appreciated.
cheers
1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution
 
any1????
 

LowlyPion

Homework Helper
3,055
4
Is θ constrained to be less than 90°?

Because at greater than 90° more weight can be supported it seems, because the Tension of the rope no longer has a negative y component.
 

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