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Center of Mass (Subtraction over addition)

  1. Jul 20, 2017 #1
    1. The problem statement, all variables and given/known data
    b06OECX.png
    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
    However, answer given is -0.90

    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. jcsd
  3. Jul 20, 2017 #2

    jbriggs444

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    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.
     
  4. Jul 20, 2017 #3
    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...
     
  5. Jul 20, 2017 #4
    Sorry, guess I didn't explain it clearly.

    mr9Em2z.png

    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)
     
  6. Jul 20, 2017 #5

    haruspex

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    Looks fine to there. Please post subsequent working.
     
  7. Jul 20, 2017 #6
    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
     
  8. Jul 20, 2017 #7

    haruspex

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    It could not possibly be that close to the left hand edge of the shape. -0.09 is correct.
     
  9. Jul 20, 2017 #8
    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.
     
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