Center of mass of composite body

[aaronfue]

Homework Statement

In the image below, calculate the center of mass (x-bar,y-bar) of the composite body.

Homework Equations

I've used all of the equations for area for the shapes needed (triangle, square, circle).

The Attempt at a Solution

I have attached my calculations and would appreciate if someone could verify that they are correct.

Thanks!

 

[mfb]

x and y for the triangle look strange, and your area calculations are wrong.

 

[SteamKing]

The table in your figure contains mostly formulas with no data.

 

[aaronfue]

@Steamking: I've attached both the images with formulas and with the answers to the calculations to view.

@mrb: I believe it is NOT an equilateral triangle therefore the formula should be correct. And the area calculations for the rest of the shapes I've verified to be correct as well.

 

[mfb]

@mrb: I believe it is NOT an equilateral triangle therefore the formula should be correct.

Who is mrb?
Of course it is not equilateral, it has 1 and sqrt(5/4) as sidelengths.
Judging from your formulas in columns F and G and rows 3 to 5, columns D and E are supposed to have the center of mass position of the geometric object. y=1.75 is certainly not the y-position of its center of mass (it is outside the whole object), and x=0.5 is wrong as well.

And the area calculations for the rest of the shapes I've verified to be correct as well.

Consider the square, for example: It has a height of 1 and a width of 1, so its area is 1. Your formula, however, gives 1.5. Even worse: It gives the same area for the hole, which is obviously wrong.

 

[aaronfue]

Sorry...mfb.

I did notice those errors for the areas and they should be correct...now.

 

[mfb]

That looks good now.