Center of Mass (Subtraction over addition)

[Ignitia]

Homework Statement

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

Homework 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
However, answer given is -0.90

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.

 

[jbriggs444]

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

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.

 

[jerromyjon]

M1 should be regarded as negative.

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...

 

[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)

 

[haruspex]

Ms/Ms +M1/Ms + M2/Ms - M1X1/Ms - M2X2/Ms = Xs

Looks fine to there. Please post subsequent working.

 

[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
However, answer given is -0.90

 

[haruspex]

answer given is -0.90

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

 

[Ignitia]

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

But the given answer -

...

You know what, I'll just accept the fact I spent an hour unable to figure out why my correct answer wasn't the given answer. Thank you.