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

[yaro99]

Homework Statement

Homework Equations

Ʃx_iL_i=0

The Attempt at a Solution

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

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

L = 90.28mm

 

[TSny]

Ʃx_iL_i=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.

 

[yaro99]

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.

 

[TSny]

But why divide the 14 by 2?

 

[yaro99]

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.

 

[TSny]

OK, good.