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Homework Help: Find tension and Direction

  1. Mar 7, 2010 #1
    During a storm, a tree limb breaks off and comes to rest across a barbed wire fence at a point that is not in the middle between two fence posts. The limb exerts a downward force of 164 N on the wire. The left section of the wire makes an angle of 12° relative to the horizontal and sustains a tension of 447 N. Find the magnitude and direction of the tension that the right section of the wire sustains.
    I got the tension in the rope which is 440N, I am having trouble finding the Direction.

    ° (counterclockwise from x-axis) ?

    I tried 1/cos of 164/440...its wrong




    ]
     
  2. jcsd
  3. Mar 7, 2010 #2

    lightgrav

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    Homework Helper

    how did you get 440 N?
    you _should_ keep vertical Forces and horizontal Forces separate .
     
  4. Mar 7, 2010 #3
    i will look thru my notes and see how i came to it.
     
  5. Mar 7, 2010 #4
    this is how i got the 440N: we break the tensions into x- & y- components

    So x- direction....-447N*cos(12) + T2*cos(θ2) = 0...So T2*cos(θ2) = 437.2 [eqn 1]
    and in the y- direction 447*sin(12) + T2*sin(θ2) - 146 = 0..
    so T2*sin(θ2) = 146 - 447*sin(12) = 53.1 [eqn 2]

    Now divide eqn 2 by eqn 1 giving sin(θ2)/cos(θ2) = 53.1/437.1

    or tan(θ2) = 0.1214....so θ2 = arctan(0.1214) = 6.92o

    Now plug back into eqn 1 to get T2...T2 = 437.1/cos(6.92) = 440N
     
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