# Homework Help: Center of mass of composite body

1. Nov 21, 2012

### aaronfue

1. The problem statement, all variables and given/known data

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

2. Relevant equations

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

3. The attempt at a solution

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

Thanks!

#### Attached Files:

File size:
14.7 KB
Views:
239
• ###### Capture.JPG
File size:
33.6 KB
Views:
166
2. Nov 21, 2012

### Staff: Mentor

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

3. Nov 21, 2012

### SteamKing

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

4. Nov 22, 2012

### 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.

#### Attached Files:

File size:
31.2 KB
Views:
197
• ###### Calculations.JPG
File size:
26.7 KB
Views:
140
5. Nov 22, 2012

### Staff: Mentor

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.

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.

6. Nov 22, 2012

### aaronfue

Sorry.....mfb.

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

7. Nov 23, 2012

### Staff: Mentor

That looks good now.