Boom held by 3 cables (Statics)

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Discussion Overview

The discussion revolves around a statics problem involving a boom supported by three cables. Participants are attempting to determine the tension in one of the cables given the tensions in two others, while analyzing the forces and torques acting on the system. The scope includes homework-related problem-solving and technical reasoning about equilibrium and forces.

Discussion Character

  • Homework-related
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant expresses difficulty in analyzing the problem with the information provided, particularly regarding the resultant tensions at point A of the boom.
  • Another participant suggests that if the sum of the torques is zero, it could satisfy the conditions of the problem, questioning if that is sufficient to find the unknown tension.
  • A later reply indicates that if the cable forces are directed along AB, then the force in the boom is also directed along AB, proposing to take moments about point B to simplify the analysis.
  • One participant shares their realization about the nature of the forces involved and mentions that the problem can be approached as an equilibrium problem using plane forces.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the best approach to solve the problem, as there are multiple suggestions and methods proposed without agreement on a definitive solution.

Contextual Notes

Participants reference the need to understand angles between cables and the boom, as well as the concept of moments, indicating that certain assumptions about the setup and forces may be necessary for a complete analysis.

Who May Find This Useful

This discussion may be useful for students studying statics, particularly those working on problems involving equilibrium and forces in cable systems.

masterflex
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Homework Statement


I've included a picture of the problem so you can see the diagram too. The question is asking for the tension of 1 cable, when 2 are given (problem# 41).

Homework Equations


no equations per se.

The Attempt at a Solution


I resolved cable AC and cable AD, but don't know how to proceed. How do you even analyze it with the given info that "the resultant of the tensions exerted at point A of the boom must be directed along AB"? This is hard. Thanks for helping me.
 

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Seems like if the sum of the torques were zero, that would satisfy the situation. Is that enough to figure it out? (I don't know offhand)
 
berkeman said:
Seems like if the sum of the torques were zero, that would satisfy the situation. Is that enough to figure it out? (I don't know offhand)

If the sum of the cable forces is directed along AB, the force in the boom is also directed along AB.

So if you take moments about a point on the line AB, the unknown force in the boom (which you are not asked to find) has zero moment. Point B will do nicely.

Hint: first work out the angle between each cable and the boom AB, then taking the moments is easy.
 
I understand

Thanks a lot for your help guys. I got this solution from a random professor that I just walked in the door to talk to. I also realized what I was struggling with: there's a force along the line of AB (but not necessarily constrained to that physical distance; just in line with it), but I didn't know what to make of that force even though the problem said it was there. One easy way to know how many forces are in play at any given point is to look at the number of things (booms, cables, hanging things, whatever).

The moment solution should work -- I mean it sounds good :D, and I'll give it a try. Thanks for that.

By the way, the prof approached this like an equilibrium problem just using plane forces. I've attached my work.
 

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  • 2.41_equilibrium.JPG
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