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Object Lifted By Cord (Stress/Tension Problem)

  1. Apr 24, 2009 #1
    1. The problem statement, all variables and given/known data
    A 25kg object is being lifted by pulling on the ends of a 1.10mm diameter nylon cord that goes over two 3.50m high poles that are 4.8 m apart. How high above the floor will the object be when the cord breaks?

    2. Relevant equations
    F=EA
    F=ma

    3. The attempt at a solution
    I thought that by using this equation, I could find the tension in the cord.
    F=(500 x 10^6)(pi)(.00055)^2=475

    X-dir force
    Tcos θ + Tcos θ = 2Tcos θ=0

    Y-dir force
    Tsin θ + Tsin θ -mg=0
    2Tsin θ=mg

    I think my equations are incorrect. I didn't know how to account for the height and weight of the cord. Help would be much appreciated.
     
  2. jcsd
  3. Apr 24, 2009 #2

    tiny-tim

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    Hi kritzy! :smile:

    (what does the weight have to do with it? :confused:)

    Use the triangle whose length is 3.5 - h and whose width is 2.4 to find cosθ and sinθ :wink:
     
  4. Apr 24, 2009 #3
    I tried to solve for sinθ and cosθ but I end up with to many unknowns.
    T=tension
    cosθ=2.4/T
    sinθ=(3.5-h)/T
    I tried to substitute for T. I got
    tanθ=(3.5-h)/2.4
    I still have two unknowns and only one equation.
    Can you give me another hint?
    I attached a file which shows the diagram. Maybe it will help
     

    Attached Files:

  5. Apr 24, 2009 #4

    tiny-tim

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    I'm confused … isn't T the breaking strength, which I assume is given in the question? :confused:

    and I'm off to bed now :zzz: …
     
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