What Angle \(\phi\) Balances the Pulley in Static Equilibrium?

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SUMMARY

The discussion focuses on determining the angle \(\phi\) that balances a pulley in static equilibrium, where a 50 lb weight is supported by a wire attached to the pulley at point B. The tension in wire ABC is specified as 70 lb. To find the angle \(\phi\), participants emphasize the importance of drawing a free body diagram (FBD) of the pulley and applying Newton's first law in both the x and y directions to solve for the angle. The equation F=ks is referenced, indicating the relationship between force and spring constant in the context of the problem.

PREREQUISITES
  • Understanding of static equilibrium principles
  • Knowledge of free body diagrams (FBD)
  • Familiarity with Newton's laws of motion
  • Basic concepts of tension in cables and pulleys
NEXT STEPS
  • Study the application of Newton's first law in static systems
  • Learn how to construct and analyze free body diagrams for complex systems
  • Explore the relationship between tension and weight in pulley systems
  • Investigate the effects of different angles on tension and equilibrium
USEFUL FOR

This discussion is beneficial for physics students, engineering students, and anyone studying mechanics, particularly those focusing on static equilibrium and pulley systems.

msds1502
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Homework Statement


statics.jpg
(rotate picture 90 degree clockwise)
A 50 lb weight is supported by a wire attached to a pulley at point B. The Pulley rests on wire ABC. If the tension in wire ABC is equal to 70lb determine the angle \phi necessary to keep point B in balance


Homework Equations


F=ks



The Attempt at a Solution



I Know there is some force acting from C to D. There is also some spring force acting from C to E. What I don't understand is how to model the FBD with the tension force ABC and 50lb weight at point C
 
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msds1502 said:

Homework Statement


statics.jpg
(rotate picture 90 degree clockwise)
A 50 lb weight is supported by a wire attached to a pulley at point B. The Pulley rests on wire ABC. If the tension in wire ABC is equal to 70lb determine the angle \phi necessary to keep point B in balance


Homework Equations


F=ks



The Attempt at a Solution



I Know there is some force acting from C to D. There is also some spring force acting from C to E. What I don't understand is how to model the FBD with the tension force ABC and 50lb weight at point C
The problem is asking for the angle \phi when the pulley is in equilibrium. Draw a free body diagram of the pulley only. The weight is given and the tension in the rope on each side of the pulley is give. So use Newton's first law in the x direction and in the y direction, to solve for the angle.
 

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