Cables, pulleys, 2 weights

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SUMMARY

The discussion centers on solving a static equilibrium problem involving two weights connected by cables and pulleys. The equations of motion are established as Fx = 0 and Fy = 0, leading to the relationships ABcos(a) + 3.2737cos(b) - 3.738 = 0 and ABsin(a) + 3.237sin(b) - 2.158 = 0. A critical insight shared is the application of vector addition to form a closed polygon, which simplifies finding the tension in cable AB. The participant successfully resolves the issue after recognizing the importance of vector closure in static systems.

PREREQUISITES
  • Understanding of static equilibrium principles
  • Familiarity with vector addition and trigonometric functions
  • Knowledge of tension in cables and pulleys
  • Basic algebra for solving equations
NEXT STEPS
  • Study the principles of static equilibrium in physics
  • Learn about vector addition and its applications in mechanics
  • Explore tension calculations in cable systems
  • Review trigonometric identities and their use in solving physics problems
USEFUL FOR

Students studying physics, particularly those focusing on mechanics, engineers working with cable systems, and anyone interested in understanding static equilibrium and vector analysis.

DylanMurfly
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Homework Statement
I've been struggling with this question for a while now, and for the life of me i cant see what i'm missing, the picture is in the solution attempt along with the equations i've been using. Any assistance would be amazing. Find: Tension AB and Angle a
Relevant Equations
W1 = 330g
W2 = 440g
1713386600869.png

Fx = 0 = ABcos(a)+BCcos(b)-BDcos(30)
Fy = 0 = ABsin(a)+BCsin(b)-BDsin(30)

==

Fx = 0 = ABcos(a) + 3.2737cos(b) - 3.738
Fy = 0 = ABsin(a) + 3.237sin(b) - 2.158

But i cant find a third equation to use. I've tried a+b = 90 but that produced a number of errors. Thank you.
Edit: angle b is the angle string CB makes with horizontal
 
Last edited:
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Please post the question that the problem asks. What are you looking for? The homework statement must be as was given to you.
 
kuruman said:
Please post the question that the problem asks. What are you looking for? The homework statement must be as was given to you.
updated, sorry about that
 
Finding the tension AB is easy. You are missing that when the sum of N vectors is zero and you draw the vector addition diagram, the ensuing shape is a closed polygon with N sides. Apply this idea here.
 
Thank you sir, got it all fixed up now, didn't even think to go about it that way, earlier response was a brain fart as its quite early in the morning and i haven't had a coffee yet.
 

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