Static Equilibrium Pulley and free body diagram

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Homework Help Overview

The discussion revolves around a problem involving static equilibrium in a pulley system, where the original poster presents a free body diagram and equations related to the forces acting on the system.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to solve two equations derived from the equilibrium conditions but expresses difficulty in manipulating them to find the unknowns. Some participants question the approach taken to combine the equations and suggest methods to isolate variables.

Discussion Status

Participants have provided guidance on how to rearrange the equations to isolate the variable theta and suggested that the tension terms may cancel out. The conversation indicates a productive exchange of ideas, although no consensus on a final solution has been reached.

Contextual Notes

The original poster's equations are based on specific angles and forces, but the exact values or additional constraints related to the problem setup are not fully detailed in the discussion.

sharp12
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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: -TacCos(60) + TacCos(20) - 2000Sin(theta) = 0

For the forces in y: TacSin(60) + TacSin(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?
 

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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
 
ehild said:
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. :)!
 
You are welcome. :smile: I was really pleased with your suggestive pictures. Remember the method. ehild
 

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