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Early Statics Question

  1. Sep 18, 2016 #1
    1. The problem statement, all variables and given/known data
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    Given: A 300 kg walkway supported by two rollers(at points A and B) with center of mass at G.
    Find: The tension T in the horizontal cable attached to the cleat at point B and the force under the roller at A.

    2. Relevant equations
    ∑M = 0
    ΣFx = 0
    ΣFy = 0

    3. The attempt at a solution
    Free body diagram of the bridge has Normal force vertically upwards with point of application A(Na) , Weight(W) vertically downwards at G, Normal force perpendicular to walkway directed away from water(Nb), and Tension(T) horizontal to the right at point B.

    ∑Mb = 0 (moment at point B)
    0 = +W(4cos30°) - Na(8cos30°)
    Na = (W(4cos30°))/(8cos30°)
    Na = 1472 N

    So far this answer is known to be correct for Na.

    ΣFx = 0
    0 = T - Nbcos30°
    T = Nbcos30°
    ΣFy = 0
    0 = Na - W + Nbsin30°
    Nbsin30° = W - Na
    Nb = (W - Na) / sin30°

    Plugging in the known values and Na that we solved for yields the incorrect answer. Why can't I add up the components of the force vectors or what am I doing incorrectly?




     
  2. jcsd
  3. Sep 18, 2016 #2

    PhanthomJay

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    Science Advisor
    Homework Helper
    Gold Member

    Check your trig again when determining the x and y components of the normal force at B.
     
  4. Sep 18, 2016 #3

    NascentOxygen

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    Staff: Mentor

    Check this.
     
  5. Sep 18, 2016 #4
    OK the horizontal component of Nb should be Nbcos60° and the vertical component of Nb should be Nbsin60°. I think I was tired and messed up the trig. Thanks for the help.
     
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