Solving Statics Problem: Equilibrium of Forces

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Discussion Overview

The discussion revolves around solving a statics problem involving the equilibrium of forces. Participants are attempting to derive equations from given conditions and solve for unknowns related to forces acting in both the x and y directions.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant presents the equations derived from summing forces in the x and y directions, specifically C*cos(30) - B*cos(phi) = 0 and C*sin(30) + B*sin(phi) - D = 0.
  • Another participant suggests dividing the second equation by the first to derive a relationship involving tan(30) and proposes squaring both sides to solve for phi.
  • A later reply indicates confusion regarding the division step, presenting an alternative form of the equation and questioning if something was missed in the process.
  • Another participant confirms the division is correct and advises to square both sides and simplify further.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the steps taken to solve the problem, as there is a noted confusion regarding the manipulation of the equations. Multiple approaches and interpretations of the equations remain present.

Contextual Notes

There are unresolved mathematical steps and potential dependencies on the correct interpretation of the equations derived from the force balance.

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I have having trouble solving this statics problem, I sum up the forces and have

C*cos(30) - B*cos(phi) = 0 in the positive x direction
and
C*sin(30) + B*sin(phi) - D =0 in the positive y direction

B = 275 lbs and D = 300lbs
I need to solve for C and phi, I have tried substitution, division, not matrices because it wouldn't work
 
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C*cos(30) = B*cos(phi)...(1)
C*sin(30) = - B*sin(phi) + D ...(2)
Divide (2) by (1).You get
tan(30) = B*cosφ/(B*sinφ - D)
Square both the sides. Write cos^2(φ) = 1 - sin^2(φ) and solve the quadratics to find φ.
 
Thanks for the reply,

I divided (2) by (1) but I have

Tan(30) = (-B*sin(φ) + D)/ (B*cos(φ))

Am I missing something?
 
No.
Now square both sides. And simplify.
 

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