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Classical mechanics-coordinates

  1. May 12, 2013 #1
    1. The problem statement, all variables and given/known data

    Attached is the picture of a dumbbell. I do not understand how the coordinate of M1 is
    M2 R/ (M1 + M2)

    It is not an assignment question but an example from a book.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. May 12, 2013 #2

    ehild

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    The origin is at the centre of mass. You certainly know how to determine the position of the CM?

    ehild
     
  4. May 12, 2013 #3
    CM= (R1m1+R2M2)/M1+M2
    because CM=0, I get M1 R1 = -R2 M2
    which further gives me
    R1= RM2 / (M2-M1)

    =|
     
  5. May 12, 2013 #4

    ehild

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    What do you mean on R1 and R2? If they are coordinates of the spheres with respect to the CM, the formula is correct, but use parentheses. (R1m1+R2M2)/(M1+M2)=0

    How are R1 and R2 related to the distance R between the spheres?

    ehild
     
  6. May 12, 2013 #5
    R= R_1 + R_2
    where R_i is the distance to M_i from CM.
     
  7. May 12, 2013 #6
    In the book R_1 = R M2/ (M1 + M2) but mine is R1= R M2 / (M2-M1)
     
  8. May 12, 2013 #7

    ehild

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    If x1, x2 are coordinates of m1, m2, respectively, the x coordinate of the CM is (x1m1+
    x2m2)/(m1+m2).
    If they are distances from the CM, the coordinate of m2 is negative: m1R1-M2R2=0

    ehild
     
    Last edited: May 12, 2013
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