Statics Questions - Equilibrium in a pulley system

[Wilson123]

Homework Statement

Find the value of W to maintain equilibrium

Homework Equations

The Attempt at a Solution

I have split the system into two, creating a triangle. From this I have a right angle triangle with an adjacent of 2m, opposite of 0.6m and an hypotenuse of 2.088m (calculated through pythag). I have then worked out the angle at the pulley as 16.7 degrees. However I do not know how to now find W, I think it may have something to do with the equation 40kg x g x cos(90-16.7) + 40kg x g x sin(90-16.7), but this isn't given me the kind of answer I expected so I'm not sure if it's right.

Any help on the next step would be much appreciated!

 

[Doc Al]

How about analyzing the forces acting at the point where the ropes connect to the 80 kg mass. Apply the conditions for equilibrium.

 

[Wilson123]

How about analyzing the forces acting at the point where the ropes connect to the 80 kg mass. Apply the conditions for equilibrium.

Am I right in thinking the forces are acting like this?

 

[Doc Al]

Am I right in thinking the forces are acting like this?

Yes, that's exactly right. And if you set up the equilibrium equations, you can solve for T.