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Statics Problem, Moment About an Axis

  1. Jun 9, 2013 #1
    1. The problem statement, all variables and given/known data
    Problem 3.60:
    BgRMJLy.png


    2. Relevant equations

    [itex]M_{AD}= \begin{vmatrix}
    \lambda_x & \lambda_y & \lambda_z \\
    x_{B/A} & y_{B/A} & z_{B/A} \\
    F_x & F_y & F_z &
    \end{vmatrix}
    [/itex]


    3. The attempt at a solution

    Looking at the figure, these are the unit vector components for line AD:

    [itex]\lambda_x=1 \ m
    \\ \lambda_y= 0 \ m
    \\ \lambda_z = -0.75 \ m
    [/itex]

    And these are the coordinates for point B where the force is applied:

    [itex]x_{B/A}=0.5 \ m
    \\ y_{B/A}= 0 \ m
    \\ z_{B/A} = 0 \ m
    [/itex]

    The force vector for the tension in BG:
    [itex]\mathbf{T_{BG}}= 450*(\frac{-0.5\hat{i}+0.925\hat{j}-0.4\hat{k}}{1.125})= -200\hat{i}+370\hat{j}-160\hat{k} \ N[/itex]

    Plugging these values into the matrix above, I get -138.75 N*m, but the answer is supposed to be -111.0 N*m

    Edit: Changed the mistake I made in the second row. Still getting the wrong answer.
     
    Last edited: Jun 9, 2013
  2. jcsd
  3. Jun 9, 2013 #2

    SteamKing

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    Staff Emeritus
    Science Advisor
    Homework Helper

    Shouldn't λx^2+λy^2+λz^2 = 1 if these are the components of a unit vector?
     
  4. Jun 9, 2013 #3
    Yes, I actually just figured it out. I had messed up when I took the unit vector components and didn't divide by the magnitude.
    Is there a way I can close this thread?
     
  5. Jun 9, 2013 #4

    berkeman

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    Staff: Mentor

    We don't delete threads that have responses. Glad that you figured it out. :smile:
     
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