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3D tension problem (static equilibrium)

  1. Jan 31, 2013 #1
    1. The problem statement, all variables and given/known data
    A block of weight 50N is hung by 3 cables from the ceiling. Each rope ZA, ZB, ZC converges at Z so that they form a tetrahedron. (ZA=ZB=ZC=AB=BC=CA). Find the magnitude of the tension of each cable.

    a=0
    tetrahedron symmetry


    2. Relevant equations
    F=mg


    3. The attempt at a solution
    I realized that T1=T2=T3 due to the symmetrical nature of tetrahedrons. The angles weren't given but each side of a tetrahedron is composed of 3x60 degree angles.

    My approach was to represent the problem in 2D since there were some obvious vector symmetries in the x,y plane.
    I proceeded to decompose the F(x,y) components, which cancel each other out. Can be proven with a simple qualitative 2D vector sum, even though the quantities weren't given.
    I then tried: F(z) = T1 sin + T2 sinβ + T3 sinβ = 50N.
    or
    (3)(T)(sinβ) = 50N

    But then I couldn't figure out how to find β. Initially I assumed it was 60 degrees, but after checking my work the math didn't work out.
    I'm basically curious as to what is the thought process required to solve a problem like this, or a more general case where there aren't any nice symmetric features.
     
    Last edited: Jan 31, 2013
  2. jcsd
  3. Jan 31, 2013 #2

    SammyS

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    You could check out the Wikipedia article on tetrahedrons .
     
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