Equilibrium of weight on pulley

[drkidd22]

Homework Statement

A 15lb weight at a on frictionless rod at a distance of 16" from a pulley can move up and down and it has counter-force on pulley of 17lb. What should the height of weight on rod be so that system is in equilibrium

Homework Equations

Cosine Law
Sine Law

The Attempt at a Solution

I have tried to draw the problem so that it would be better to understand. I'm not given any angles and not sure to get started here.

 

[Doc Al]

What's the tension in the pulley cable? What angle must the cable make with respect to the weight on the rod. (Redo your force diagram to show the forces acting on the 15lb weight.)

 

[drkidd22]

I'm having difficulty trying to understand the problem as is. The tension in the cable would be the sum of all components of both weights, but I'm not given angles to find them. Wouldn't the tension be 32lb anyways?

 

[Doc Al]

The tension in the cable would be the sum of all components of both weights,

No, that's not true.

but I'm not given angles to find them. Wouldn't the tension be 32lb anyways?

No.

To find the tension in the cable, analyze the forces acting on the 17lb mass. That mass must be in equilibrium also.