What is the Centroid of a Wire and How to Calculate It Using Geometry?

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Homework Help Overview

The discussion revolves around calculating the centroid of a wire using geometric principles. Participants are examining the application of the equation ƩxiLi=0 in the context of this problem.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants are attempting to apply the centroid formula and are discussing the factors in the equation, particularly the division by 2 for certain terms. Questions arise regarding the reasoning behind specific components of the equation.

Discussion Status

The discussion is active, with participants questioning the validity of certain factors in the equation. Some have reached clarity on the necessity of dividing by 2, while others are still exploring the implications of their calculations.

Contextual Notes

There appears to be some confusion regarding the setup of the problem and the interpretation of the lengths involved, particularly concerning the positioning of the centroid relative to the origin.

yaro99
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Homework Statement


2C7ksNe.png



Homework Equations


ƩxiLi=0


The Attempt at a Solution


Using geometry to find the lengths and rotating so AB is horizontal, I have:
CQ8E20S.png



ƩxiLi=0: [((64/80)*L)/2]*L + (-64/2)*80 + (-14/2)*100 = 0

L = 90.28mm
 
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yaro99 said:
ƩxiLi=0: [((64/80)*L)/2]*L + (-64/2)*80 + (-14/2)*100 = 0
I'm not getting the 14/2 factor. Everything else looks good to me.
 
TSny said:
I'm not getting the 14/2 factor. Everything else looks good to me.

The centroid of line AB is right in the middle, 50mm from either edge. Looking at the left side, 64-50=14, and it is negative because it is to the left of the origin.
 
But why divide the 14 by 2?
 
TSny said:
But why divide the 14 by 2?

Oh, wow haha, you're right. Didn't need to divide by 2, now the equation works for me.
 
OK, good.
 

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