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HELP Center of Mass

  1. Nov 12, 2007 #1
    A 3kg mass is positioned at (0,8) and 1 kg mass is positioned at (12,0). What are the coordinates of a 4 kg mass, which will result int he center of mass of the system of three masses being located at the origin (0,0)?

    I know that m1x1+m2x2...etc but I don't understand how you can do it with actual coordinates, can someone explain?
  2. jcsd
  3. Nov 12, 2007 #2
    Have you tried finding the distance between the points and the origin?
  4. Nov 12, 2007 #3
    This will sound dumb, but I do not remember the distance formula....
  5. Nov 12, 2007 #4
    distance= square root of [(x2-x1)^2 + (y2-y1)^2]
  6. Nov 12, 2007 #5
    so the 3 kg is 8 units away and the 1 kg is 12 units away. would that mean that the 4kg had to be 9 units away? and how do you know which way/what coordinates?
  7. Nov 12, 2007 #6
    You know that the 3kg is due north and the 12kg is to the east of the origin. Therefore, you know that the third mass must be placed south-west of the origin to mantain equilibrium. Bear in mind that this is the y=x line.
  8. Nov 12, 2007 #7
    i know to use the m1x1+m2x2+m3x3/(m1+m2+m3) but i still don't understand how you get 2 points from this equation
  9. Nov 12, 2007 #8
    so the coordinates are oging to (-n,-n) but i still dont see how the formula works
  10. Nov 12, 2007 #9
    you will need to think of the vectors in terms of their components, and realize that the third mass will have a vector with components to cancel out the other two masses' vectors.

    edit: also, the post saying it's on the x=y line is misinformed. the answer is not in the form (-n,-n).
    Last edited: Nov 12, 2007
  11. Nov 12, 2007 #10
    so 3 kg directly up 8 units, 1 kg directly right 12 units and 4 kg in quardrant III. the sum equals 36 so the 4 kg would have to be 9 units away from the origin? I dont think i'm doing this right
  12. Nov 12, 2007 #11
    not the sum. the vectors are at right angles. the y component of the 4kg mass equals the 3kg mass's vector, and the x component is the 1kg mass's vector
  13. Nov 12, 2007 #12
    that would give me (-8,-12) right?
  14. Nov 12, 2007 #13
    Then use (m1y1+m2y2+m3y3)/(m1+m2+m3) to find the y-coordinate of the CM.
  15. Nov 12, 2007 #14
    i dont know m3y3 so is it (m1y1+m2y2)/(m1+m2+m3) = m3y3?
  16. Nov 12, 2007 #15
    no, its 0, remember its stated on the problem.. (0,0) is the CM
  17. Nov 12, 2007 #16
    List everything you know:

    m1, x1, y1
    m2, x2, y2
    CM(x), CM(y)

    You need to find x3 and y3.

    So set up the equation to find the center of mass,

    CM{}_x{} = (m{}_1{}x{}_1{} + m{}_2{}x{}_2{} + m{}_3{}x{}_3{}) / (M)

    Solve it for what you're looking for.

    EDIT: To be clearer, a value x1, x2, x3, etc. is the x-coordinate of the position of that mass m1, m2, m3...
  18. Nov 12, 2007 #17
    maybe this will help you visualize it.. I am not sure if you are familiar of adding vectors using unit vectors--> i(hat) and j(hat). But if you do it like that.. you will have
    3(0i+8j) <-- i can multiply by three because mass is a scaler.
    12i + 24j
    0i+ 0j <-- center of mass..

    Ok, that is more than enough of information.. you should be able to solve it.
  19. Nov 13, 2007 #18
    i just don't understand, i give up
    Last edited: Nov 13, 2007
  20. Nov 13, 2007 #19
    It's much easier than you are making it. The equation

    [tex]CM_{x} = \frac{m_{1}x_{1} + m_{2}x_{2} + m_{3}x_{3}}{m_{1} + m_{2} + m_{3}}

    Will give you the x-coordinate for the position of the center of mass: [tex]CM_{x}[/tex]. You are looking for the position of the 4-kg mass, so solve this equation for x3.

    And this second equation

    [tex]CM_{y} = \frac{m_{1}y_{1} + m_{2}y_{2} + m_{3}y_{3}}{m_{1} + m_{2} + m_{3}}

    will give you the y-coordinate for the center of mass ([tex]CM_{y}[/tex]). Since you're looking for the position of that m3, solve this second equation for y3.
  21. Nov 13, 2007 #20
    (3*8)+(1*12)/(3+1+4) =4.5/4 = 1.125

    this is what i've done and i'm getting nothing close to the answer. the answer is (-3,-6)
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