(adsbygoogle = window.adsbygoogle || []).push({}); 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?

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

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# Homework Help: Equilibrium of a particle

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