Equilibrium Problem: Help Solving

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SUMMARY

The discussion focuses on solving an equilibrium problem using Lami's theorem and trigonometric identities. The user attempted substitution but found it complicated, leading to a request for assistance. Key equations derived from free body diagrams (FBD) include relationships between forces and angles, specifically using sine functions. The solution involves substituting known values and applying trigonometric identities to form a quadratic equation for θ.

PREREQUISITES
  • Understanding of Lami's theorem
  • Familiarity with trigonometric identities, specifically sine and cosine functions
  • Ability to manipulate quadratic equations
  • Knowledge of free body diagrams (FBD)
NEXT STEPS
  • Study Lami's theorem applications in static equilibrium problems
  • Review trigonometric identities, focusing on sine and cosine addition formulas
  • Practice solving quadratic equations derived from trigonometric relationships
  • Explore free body diagram techniques for analyzing forces in equilibrium
USEFUL FOR

Students in physics or engineering courses, particularly those studying statics and equilibrium problems, as well as educators looking for examples of applying Lami's theorem and trigonometric identities in problem-solving.

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Homework Statement


[PLAIN]http://img148.imageshack.us/img148/7880/95204069.jpg


Homework Equations





The Attempt at a Solution


Im not sure how to solve, i tried substitution but it gets really messy and trig identities are needed, some of which i don't know.

[PLAIN]http://img7.imageshack.us/img7/716/lastscantq.jpg
 
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Can someone please help?
 
You can apply the Lami's theorem.

For FBD-C

E/sin(150 + θ) = T(CB)/sin(90 + 30) ...(1)

For FBD - F

F/sin(135 - θ) = T(BC)/sin(90 + 45)...(2)

T(CB) = - T(BC)

E*sin(90 + 30)/sin(150 + θ) = T(CB)

F*sin(90 + 45)/sin(135 - θ) = T(BC)

E*sin(90 + 30)/sin(150 + θ) = - F*sin(90 + 45)/sin(135 - θ)

Substitute the known values.

Using sin(A+B) =sinAcosB + cosAsinB

and sin(A-B) = sinAcosB - cosAsinB

Find cosθ in terms of sinθ.

Using the identity cos^2(θ) = 1 - sin^2(θ), form a quadratic equation and then solve for sinθ and hence θ.
 

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