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Statics - Moment using both vector and scalar approaches

  1. Sep 28, 2015 #1
    1. The problem statement, all variables and given/known data
    Capture.PNG

    2. Relevant equations
    Mo=Fd
    Mo=r x F

    3. The attempt at a solution
    Alright guys, I did the whole process but I'm pretty sure I just made a little bump somewhere in my calculations which screwed up my answers.

    First I found everything I could find
    OA = 350j, so the unit vector of OA is 1j

    OB = ( 350sin(33°) )i + ( 350 + 350cos(33°) )j
    = 191i + 644j

    tan(θ) = (300/350), θ = 40.6°

    AC = √(300)^2 + (350^2) = 461 mm
    OC = 461 sin(33°+40.6°) + (350 + 461cos(33°+40.6°), = 442i + 480j

    Then,
    AB = OB - OA
    = 191i + 644j -350j
    = 191i + 294j
    Unit vector of AB = 0.545i + 0.839j

    Given force is F = 130k

    AC = OC - OA
    = 442i + 130j

    Vector Approach:
    MA = AC x F
    = (442i + 130j) x (130k)
    = 16900i -57460j
    In the position of AB = MA * Unit vector AB
    MAB = 39000 N * mm

    MOA = MA ⋅ Unit vector OA
    = (16900, -57460) ⋅ (0,1,0)
    = 57500 N * mm


    Scalar Approach:
    MAB = F x d
    = 130 x 300
    = 39000 N * mm

    h = AC sin (40.6° + 33°)
    = 461 sin (73.6°)
    = 442 mm

    MOA = F x h
    =130 x 442
    =57500 N * mm

    My answers match, so I'm not sure where I went wrong, any help would be greatly appreciated!
     
  2. jcsd
  3. Sep 28, 2015 #2
    Omg, all I didn't do what convert to N * m, :blushing:
    I'm dumb.

    Check your units boys and girls.
     
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