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unknown_2
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Homework Statement
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?
Homework Equations
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