Find Centroid: Solve Homework Statement

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SUMMARY

The discussion focuses on calculating the centroid using the formula \(\bar{Y}A_{TOT}=\bar{Y_1}A_1+\bar{Y_2}A_2+\bar{Y_3}A_3\). The user provided values for \(\bar{Y_1}\), \(\bar{Y_2}\), and \(\bar{Y_3}\) as 7.5mm, 82.5mm, and 215mm respectively, with areas \(A_1\) and \(A_2\) both calculated as 2250mm² and \(A_3\) as 7854mm², leading to a total area \(A_{TOT}\) of 12354mm². The calculated centroid \(\bar{Y}\) was found to be 153.1mm, which is slightly off from the book's answer of 154mm, prompting the user to question potential rounding errors in their calculations.

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Homework Statement



http://img170.imageshack.us/img170/214/centroidssk4.th.jpg


Homework Equations



\bar{Y}A_{TOT}=\bar{Y_1}A_1+\bar{Y_2}A_2+\bar{Y_3}A_3

The Attempt at a Solution



by observation:

\bar{Y_1}=7.5mm
\bar{Y_2}=82.5mm
\bar{Y_3}=215mm
A_1=(15mm)(150mm)=2250mm^2
A_2=(15mm)(150mm)=2250mm^2
A_3=(\pi)(50mm^2)=7854mm^2

A_{TOT}=12354mm^2

\bar{Y}=\frac{1891110mm^3}{12354mm^2}

\bar{Y} = 153.1mm

The book says the answer is 154mm, I know that its not off by far but am I doing something wrong, or is the book rounding off somewhere? I am slightly off on every single question I attempt!
 
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suspenc3 said:
\bar{Y_2}=82.5mm
Correct this one.
 
Righhhht, Dumb Mistake

Thanks
 

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