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Static Equilibrium of a tree sapling

  1. Dec 2, 2008 #1
    1. The problem statement, all variables and given/known data

    Three forces are applied to a tree sapling, as shown in the figure, to stabilize it. If vector F A = 380 N and vector F B = 260 N, find vector F C in magnitude and direction.
    http://www.webassign.net/gianpse4/12-45.gif


    2. Relevant equations



    3. The attempt at a solution
    I am not sure where to begin...Help!!
     
  2. jcsd
  3. Dec 2, 2008 #2

    fluidistic

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    Gold Member

    Hint : To stabilize the tree, the sum of the three forces must be [tex]0N[/tex].
     
  4. Dec 2, 2008 #3
    Fa=380N
    Fbsin(15)=67.29

    380N-67.29=fcsinθ
    312.71N=Fcsinθ


    Fbcos(15)=Fccosθ

    Fbcos(15)= 251.14

    so Fccosθ=251.14

    we now know Fcsinθ and Fccosθ

    tanθ=opp/adj

    θ=arctan(312.71/251.14)= 51.23 degrees

    so the angle Fa to Fc equals 51.23 degrees+ 90 degrees=141.23 degrees

    the magnitude of Fc= √Fcx2+Fcy2

    magnitude of Fc= 401N which doesn't seem to be correct...any help??
     
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