Static Equilibrium Pulley and free body diagram

[sharp12]

Homework Statement

Attached is the picture of the problem and my free body diagram.
The system is in equilibrium.

Homework Equations

Fy = 0 Fx = 0

The Attempt at a Solution

I'm having trouble solving the two equations that I arrive with...

I use +x to the right, and +y up.

For the forces in x: -T_acCos(60) + T_acCos(20) - 2000Sin(theta) = 0

For the forces in y: T_acSin(60) + T_acSin(20) - 2000Cos(theta) = 0

When trying to solve these two equations, I tried adding them together and setting them equal to each other but I've had no luck. What am I doing wrong or missing here?

 

[ehild]

Hi sharp,

I guess you need to find theta and the tension so as the pulley is n equilibrium.

Your equations look correct. Move the term with theta on the other side, then divide the equations: the tension will cancel and you can solve for theta.

ehild

 

[sharp12]

Hi sharp,

I guess you need to find theta and the tension so as the pulley is n equilibrium.

Your equations look correct. Move the term with theta on the other side, then divide the equations: the tension will cancel and you can solve for theta.

ehild

Hi ehild,

Thank you! That worked out quite nicely. :)!

 

[ehild]

You are welcome. I was really pleased with your suggestive pictures. Remember the method. ehild

 

[asteriatic]

I would first commend you on correctly setting up the free body diagram and using the correct equilibrium equations. It seems that you are on the right track in terms of solving the equations, but you may be missing a key component in the problem.

In order to fully solve the equations, you need to know the values of the tensions in the two ropes, Tac and Tbc. These tensions can be calculated using trigonometric relationships and the given angles and forces. Once you have these values, you can substitute them into your equations and solve for the unknown variable, theta.

Additionally, it may be helpful to draw a separate free body diagram for each pulley in the system, as this can help you visualize the forces acting on each object and make it easier to solve the equations.

Overall, it seems like you have a good understanding of the concepts involved in this problem. Keep working at it and don't hesitate to ask for help if you get stuck. Good luck!