1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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.


    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


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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:



    Therefore MRx=0

    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


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook