What is the centroid of a C-shape?

[nobodyuknow]

Homework Statement

http://prntscr.com/fcbm8

Find the centroid - All dimensions are in mm

Homework Equations

xbar = (A₁X₁+A₂X₂) / (A₁+A₂)

Similarly for Ybar I assume

The Attempt at a Solution

I got the y co-ordinate to be 20.428mm, and would assume that the x coordinate would be 5mm.

Is this right?

 

[CWatters]

You can divide the shape into three rectangular parts several different ways but I used two vertical lines in the obvious places. I assumed the origin is in the bottom left corner.

xbar = (A1X1+A2X2+A3X3) / (A1+A2+A3)

= (700*5 + 800*30 +400*30) / (700+800+400)
= 20.789

ybar = (A1Y1+A2Y2+A3Y3) / (A1+A2+A3)

= (700*35 + 800*10 + 400*65) / (700+800+400)
= 30.789

Best show your working as my answer is quite different.

 

[nobodyuknow]

This is what confused me, does this mean the centroid is not on the shape itself?

 

[CWatters]

In this case yes. Where would the centroid of a doughnut be?

 

[HallsofIvy]

In this case yes. Where would the centroid of a doughnut be?

In the center, of course. That's what the "centroid" is- the geometric center. If you were to represent the doughnut as two circled in the in the xy-plane, centered at the origin with radii r and R, and then have other circles as the thickness of the doughnut, the centroid would be at (0, 0, 0).

 

[CWatters]

I know. I was using it as an obvious example for the OP to think about. eg a shape that has a centroid that's not on the surface of the shape.

 

[nobodyuknow]

Yeah, I was probably thinking more about a centroid of a mass, but even then, there's still the donut which proves me redundant.