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Homework Help: Adding Couples in 3D

  1. Sep 24, 2010 #1
    1. The problem statement, all variables and given/known data
    Replace the three couples with a single resultant couple. Specify its magnitude and direction of its axis using angles to the positive x, y, and z axes.

    yphi0.jpg


    2. Relevant equations

    M = r x F (r cross F)

    3. The attempt at a solution

    I'm pretty sure I want to resolve the moments into their force components, but to do that I would need to set an r. But since I have no measurements other than the angle of inclines I don't see how I can do that.
     
  2. jcsd
  3. Sep 24, 2010 #2

    PhanthomJay

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    The nice thing about couples is that they are independent of 'r'....the moment of a couple about any point is the couple itself. The couple can be represented by a vector pointing perpendicular to the plane of the couple, following the right hand rule method for its direction (+ or - ) perpendicular to the plane. Then solve the resultant couple as a vector located anywhere on the plane, but with a certain magnitude and direction.
     
  4. Sep 25, 2010 #3
    Then I guess this question isn't that complicated at all. If you number the couples 1-3 going from left to right:
    M1x=0
    M1y=1.5cos20
    M1z=1.5sin20

    M2x=0
    M2y=1.5
    M2z=0

    M3x=0
    M3y=1.75cos25
    M3y=-1.75sin25

    Therefore MRx=0
    MRy=4.496
    MRz=-0.2265

    MR has a magnitude of 4.5012

    And the angles are 0 with the +x axis, 2.91 with the +y axis, and 87.1 with the -z axis (using simple trig)

    Barring any issues with significant digits, I think that makes some sense since the resultant is almost vertical.
     
  5. Sep 25, 2010 #4

    PhanthomJay

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    You may have your plus/- signs mixed...the y component points down, are you calling that the positive y axis? Otherwise, your work is very good.
     
  6. Sep 25, 2010 #5
    I did. Good catch and thanks a lot
     
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