Statics - 3 forces acting at a point -- angle α maxima

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Discussion Overview

The discussion revolves around a statics problem involving two wires attached to a pole and the forces acting at a point. Participants are attempting to determine the angle α that maximizes the tension in one of the wires, as well as the corresponding tensions in both cables. The context is primarily homework-related, focusing on the application of static equilibrium principles.

Discussion Character

  • Homework-related, Mathematical reasoning, Technical explanation

Main Points Raised

  • One participant requests assistance in solving the problem, specifically in finding the angle α for maximum tension and the corresponding tensions in the cables.
  • Another participant suggests summing the forces in the x-direction as a potential approach to the problem.
  • A different participant asks about the force balances that can be established in the scenario.
  • One participant expresses frustration at being unable to visualize the forces or vector locations necessary for the solution.
  • Another participant advises focusing on the forces acting on the top of the pole and suggests introducing a variable for any unknown quantities.
  • The original poster acknowledges the feedback and indicates they will continue working on the problem.

Areas of Agreement / Disagreement

Participants appear to be exploring various approaches to the problem without a consensus on the specific method to solve it. There is no clear agreement on the next steps or the necessary forces involved.

Contextual Notes

Participants have not fully defined all forces or vectors involved in the problem, and there are unresolved aspects regarding the setup of the equations necessary for a solution.

SFG
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Homework Statement



Please if anyone could help me with this question .

Two wires AC and BC are attached to the top of pole CD . The force exerted by the pole at C is vertical and the 2.5 kN force applied at C is horizontal and makes an angle α with the direction of the x-axis .

Find the angle α for which the tension in AC is a maximum and the corresponding tension in each cable .

as per pdf diagram

Homework Equations



Cos ^2 ɸx + Cos ^2 ɸy + Cos ^2 ɸz = 1

F = √Fx^2 + Fy^2 + Fz^2

Cos ɸz = Fz/F

The Attempt at a Solution

Formulate a quadratic then differentiate to get a maxima .

Sorry I cannot find the start point for this solution . Please help
 

Attachments

Physics news on Phys.org
Try summing forces in the x-direction.
 
Which force balances do you see that you can set up?
 
guys I am looking . seriously I am blanked without knowing another force or vector locations . regards SFG
 
The top of the pole is the only thing that can move, so it is useful to look at forces acting on that.
If you do not know a quantity, introduce a variable for it. That is something you will have to do frequently and everywhere.
 
ok thanks guys . i'll work on this overnight . regards
 

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