How Do You Calculate the Design Angle θ for Strut AB in Vector Problems?

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Discussion Overview

The discussion revolves around calculating the design angle θ for strut AB in a vector problem involving forces. Participants explore how to determine θ such that a specified horizontal force has a particular component directed from point A towards point C. The conversation includes attempts at solutions, clarifications on the problem setup, and considerations of the forces involved.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Rybka expresses uncertainty about how to derive the AC component with the given information.
  • Another participant suggests that the forces must form a closed triangle and emphasizes the importance of the struts' directional contributions.
  • One participant claims to have found a solution, stating θ = 53.5° and ForceAB = 621lb.
  • A later reply indicates that the initial diagram's strut positions are confusing, but rearranging them clarified the problem for that participant.
  • Another participant reiterates the solution of θ = 53.5° and ForceAB = 621lb, while also requesting clarification on the significance of the angle ϕ = 40°.
  • One participant points out that the drawing does not provide accurate dimensions, suggesting potential issues with the problem setup.

Areas of Agreement / Disagreement

There is no clear consensus on the solution, as participants express differing views on the problem's setup and the accuracy of the provided diagram. Some participants have proposed solutions, while others raise concerns about the clarity and correctness of the information given.

Contextual Notes

Participants note that the problem's diagram may not accurately represent dimensions, which could affect the understanding of the forces involved. There is also ambiguity regarding the role of the angle ϕ = 40° in the context of the problem.

Rybka
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Homework Statement



"Determine the design angle θ (0° ≤ θ ≤ 90°) for strut AB so that the 400-lb horizontal force has a component of 500lb directed from A towards C. What is the component of force acting along member AB? Take ϕ = 40°"


Homework Equations



x-component: magnitude*cos(θ)
y-component: magnitude*sin(θ)

The Attempt at a Solution



I understand what is being asked, I'm just unsure as to how I would get that AC component with what is given.

-Rybka
 

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Hi Rybka. http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif

Take ϕ = 40°
Please correct this.

You have 3 forces, they must form a closed triangle. Struts exert their force in line with their length, so this tells you the directions of their contributions.

Are you given the correct answer?
 
Last edited by a moderator:
Good evening!

The solution is: θ = 53.5°, ForceAB = 621lb
 
I figured it out.

The position of the struts in the first diagram is confusing, but the fact that we're solving for θ means their shape is variable.

Once I moved things around a little bit, it all became clear. :smile:
 

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Rybka said:
The solution is: θ = 53.5°, ForceAB = 621lb
It's always useful to know the answer. I was hoping you'd edit your post so it tells us exactly what is 40°. That would be useful for someone following along.

Good to know you worked it out.
 
The problem in the drawing does not give accurate dimensions
 

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