# Center of Mass (Subtraction over addition)

1. Jul 20, 2017

### Ignitia

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

Find the coordinates for the center of mass in the picture above. Plate is uniform.

2. Relevant equations
Since it's uniform, the lengths can be converted to the mass. So:

coord x =(M1X1 +M2X2 + M3X3 + ... +MiXi)/(M1 +M2 + M3 + ... +Mi)
coord y =(M1Y1 +M2Y2 + M3Y3 + ... +MiXi)/(M1 +M2 + M3 + ... +Mi)

I saw it as 3 pieces: the original square, 6x7, and two missing pieces, 2x2 and 4x4.

I'll only put the X equation since Y is similar.

s = plate (shown)
1 = 4x4 missing piece
2 = 2x2 missing piece.
I simply need to find Xs = coords of the plate.

coord x (total, 6x7 square) = 1 = (MsXs +M1X1 + M2X2) / (Ms +M1 + M2)

(Ms +M1 + M2) * 1 = (MsXs +M1X1 + M2X2)
Ms +M1 + M2 - M1X1 - M2X2= MsXs
Ms/Ms +M1/Ms + M2/Ms - M1X1/Ms - M2X2/Ms = Xs

Plugged in the values, it didn't come out correctly. Same for the Y coordinate.

Edit:
Ms/Ms +M1/Ms + M2/Ms - M1X1/Ms - M2X2/Ms = Xs
22/22 + 16/22 + 4/22 - (16/22 (2)) - (4/22 (3)) = -0.090

3. The attempt at a solution
I was shown the solution of cutting up the plate into 4 pieces, and finding the CM that way. That came out correct. But I want to know what went wrong when I went 'take whole plate, remove two pieces, find CM' There's probably something really obvious that I'm missing.

Last edited: Jul 20, 2017
2. Jul 20, 2017

### jbriggs444

I do not understand your notation here. Or the equations that you assert. But if M1 is missing then M1 should be regarded as negative.

3. Jul 20, 2017

### jerromyjon

Or is it 0? It doesn't take much to prove me wrong sometimes, but I see this as 1's and 0's... is it 1 and -1 or am I totally missing the concept...

4. Jul 20, 2017

### Ignitia

Sorry, guess I didn't explain it clearly.

The original plate is grey + red + green, where its CM is x=1. So what I wanted to do was find the X coord of they grey plate only, but I could deduce the red and green's x coords, and their area as well.

So, X (grey+red+green aka total plate) = 1 = (MgreyXgrey + MredXred + MgreenXgreen) / (Mgrey + Mred + Mgreen)

5. Jul 20, 2017

### haruspex

Looks fine to there. Please post subsequent working.

6. Jul 20, 2017

### Ignitia

Ms/Ms +M1/Ms + M2/Ms - M1X1/Ms - M2X2/Ms = Xs
22/22 + 16/22 + 4/22 - (16/22 (2)) - (4/22 (3)) = -0.090

7. Jul 20, 2017

### haruspex

It could not possibly be that close to the left hand edge of the shape. -0.09 is correct.

8. Jul 20, 2017