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Static equilibrium with Youn modulus

  1. Nov 20, 2012 #1
    1. The problem statement, all variables and given/known data
    In Figure, a 103 kg uniform log hangs by two steel wires, A and B, both of radiuses 1.20 mm. Initially, wire A was 2.50 m long and 2.00 mm shorter than wire B. The log is now horizontal. What are the magnitudes of the forces on it from Wire A, and Wire B?
    Ysteel= 2.00*10^(11) Pa


    [url=http://www.freeimagehosting.net/rsgtl][PLAIN]http://www.freeimagehosting.net/t/rsgtl.jpg[/url][/PLAIN]
    2. Relevant equations

    Young Modulus = (F(perpendicular)/Area)/(ΔL/L(initial))

    3. The attempt at a solution



    This is static equilibrium
    so

    Summation of Forces:
    F: Ta-Tb-Wb =0

    Not sure where to take it from here. Can somebody give me a direction?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
    Last edited: Nov 20, 2012
  2. jcsd
  3. Nov 21, 2012 #2

    SteamKing

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    For a wire under tension, what is the formula for the amount it stretches?
     
  4. Nov 21, 2012 #3
    Would it be tensile strain?

    Tensile strain=ΔL/L
     
  5. Nov 21, 2012 #4

    SteamKing

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    Yeah, but what is the formula for calculating delta L?
     
  6. Nov 21, 2012 #5
    Lfinal minus Linitial right
     
  7. Nov 21, 2012 #6

    SteamKing

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    Read your problem carefully. You have two wires, one of which is slightly shorter than the other when there is no load (no tension) applied. After the log is suspended, it is perfectly horizontal, suggesting that both wires under tension are now the same length. How would you use the equation for Young's Modulus to calculate the tension in each wire?
     
  8. Nov 21, 2012 #7
    If wire A had a length of L0A = 2.5 meters before it was loaded, and wire A had a length 2 mm shorter than wire B before it was loaded, what was the length L0B of wire B before it was loaded?

    If FA is the force in wire A, and FB is the force in wire B, what is the equation for the strain εA and εB in each of these wires in terms of Young's modulus?

    From this, and knowing the unloaded lengths of the two wires, write an equation for the loaded lengths of the two wires LA and LB. Since the log is horizontal, what does this tell you about the relationship between LA and LB? This should give you a single relationship between FA and FB.

    How are FA and FB related to the weight of the log? This should give you your second relationship between the unknowns FA and FB.
     
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