What is the Correct Method for Calculating Tension in Equilibrium?

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Discussion Overview

The discussion revolves around the method for calculating tension in a system in equilibrium, specifically focusing on the application of free body diagrams and equilibrium equations. Participants are attempting to solve a problem involving tension in wires connected to points in a structure, sharing their calculations and seeking clarification on their methods.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant describes their approach of using free body diagrams and equilibrium equations to calculate tension but expresses confusion about their results.
  • Another participant suggests checking the calculations, indicating that the method appears correct but points out potential errors in the working shown in an image.
  • A participant shares their own calculations based on the provided equations, arriving at a different tension value than previously mentioned.
  • There is a question raised about the reasoning behind combining tensions, specifically why two tensions would be added together in the calculations.
  • Further calculations are presented, showing a step-by-step approach to derive the tension value, which differs slightly from earlier estimates.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct tension value, as different calculations yield slightly varying results. There is ongoing discussion about the methods used and the potential errors in calculations, indicating that multiple views and uncertainties remain.

Contextual Notes

Some calculations depend on specific assumptions about angles and trigonometric functions, which may not be fully resolved in the discussion. The reliance on images for clarity may also limit the understanding of the problem setup.

Who May Find This Useful

This discussion may be useful for students or individuals interested in learning about tension calculations in physics, particularly in the context of equilibrium problems and the application of free body diagrams.

blubbulf
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I don't manage to get this task right. See the pictures. First i take point D and draw a free body diagram. Then i use the equation for equilibrium. I can then calculate the tension in the wires that goes from D to B and from D to C. I then take point B and draw a free body diagram, but all the answers i get is wrong. Can somebody please see what i have done wrong?
 

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Method looks ok. Check your working at the bottom of image Task1.jpg. The third line up looks ok. Last two look wrong.

I got...

TDB (1.11) = 490
so
TDB = 441N
 
Thanks for your reply, and sorry for just putting up pictures. My first time, so i will try to put things together a little nicer. I don't see how to solve that equation. I move 490.5 to the right, divide that with (cos45/cos30)(*sin30) so i stand with TDB+TDB sin45. divide with sin 45 and at last i divide with 2, beacuse TDB+TDB=2TDB. But apparently somewhere this got terribly wrong, and i don't se where.
 
Ah, now i see what you did, but want you get 2TDB when you add them together?
 
Here is my working starting with your equation...

TDB*cos45*sin30/cos30 + TDB*SIN45 - 490.5 = 0

Take TDB outside brackets..

TDB*(cos45*sin30/cos30 + SIN45) - 490.5 = 0

Rearrange..
TDB = 490.5/(cos45*sin30/cos30 + SIN45)

Substitute values..
= 490.5/(0.707*0.5/0.866 + 0.707)
= 490.5/(1.12)
= 438N
Not quite the 441N I got earlier.
 
Thank you so much!
 

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