Did I Solve the Vertical Post Problem Correctly Using SOH CAH TOA?

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Homework Help Overview

The discussion revolves around a problem involving a vertical post supported by two cables, with participants analyzing the angles and forces involved in maintaining the post's stability. The subject area includes concepts from static equilibrium and trigonometry, particularly the use of SOH CAH TOA for resolving forces.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the balance of horizontal and vertical components of tension in the cables, questioning the correctness of an angle calculation. Some express confusion regarding the conditions under which the vertical components of tension are considered equal.

Discussion Status

The discussion is ongoing, with participants providing insights into the mechanics of the problem and questioning assumptions made in the calculations. Some guidance has been offered regarding the conditions for equilibrium, but no consensus has been reached on the correct angle.

Contextual Notes

There is mention of a textbook answer that differs from the participants' calculations, leading to questions about the assumptions made in the setup. The original poster expresses uncertainty about the validity of their approach and the implications of the angles calculated.

Ryan Lau
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Homework Statement


A vertical post is held in place by two cables as shown.

Homework Equations


SOH CAH TOA

The Attempt at a Solution


http://postimg.org/image/6rgssb1j5/

The answer in the textbook is 63 degrees. Is this an issue or did I do something terribly wrong?
 
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The tension in the cables keep the post in vertical position. Its top point can not move sideways, the horizontal components of the tensions balance each other.
The vertical components do not need to be equal, as they are balanced by the force from the ground.
 
ehild said:
The tension in the cables keep the post in vertical position. Its top point can not move sideways, the horizontal components of the tensions balance each other.
The vertical components do not need to be equal, as they are balanced by the force from the ground.
Unfortunately, I do not fully comprehend this explanation. My question is why 33 degrees is not the correct angle for Theta.
 
Ryan Lau said:
Unfortunately, I do not fully comprehend this explanation. My question is why 33 degrees is not the correct angle for Theta.
You calculated theta from the condition that the vertical components of the tensions are equal, which is wrong .
 
ehild said:
You calculated theta from the condition that the vertical components of the tensions are equal, which is wrong .

I believe I understand this comment now.

Overview:
To keep the vertical post upright, both the left and right side of the ground by the tensional strings will be equal to each other.

1500cos50 = 964.1814 N = Adjacent Side (floor)
Cos Inv. (964.1814/2100) = 62.6688 N (angle required to keep the pole upright)
 
And the rounded value is 63°.
 

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