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Thermal Expansion Problem

  1. Jan 23, 2013 #1
    1. The problem statement, all variables and given/known data

    As shown in attachment a steel cable is stretched between two poles. In 20°C temperature the cable remains horizontal (the length of the cable 10m). At a higher temperature θ°C the cable bends like in attachment. The lamp hanging from the mid-point could be thought as weightless. The linear expansion coefficient for steel is 12 * 10^-6. What is the value of θ?


    2. Relevant equations

    l' = l [1 + αθ] ------- 1


    3. The attempt at a solution

    I first used pythagorian to find the expanded length so,

    L^2 = 25 + 64 * 10^-4

    that gives L = 5.0064
    so the total expanded length 2L = 10.0128

    And applying it to the (1) equation
    I get a value for θ = 126 °C !!! obviously absurd.

    So anyone got a hint on what i'm doing wrong?
     

    Attached Files:

  2. jcsd
  3. Jan 23, 2013 #2

    haruspex

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    Pls post the steps between calculating the expanded length and getting theta.
     
  4. Jan 23, 2013 #3

    ehild

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    You miss some zeroes. I think it is just typing error. I got the same result a you.
    Edit: We both forgot to divide the change of length by the original length.


    ehild
     
    Last edited: Jan 23, 2013
  5. Jan 23, 2013 #4

    haruspex

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    Strange - I get 30.7C.
    Fractional expansion = 0.000128 = 1.28E-4. Dividing by 12E-6 gives a bit over 10.
     
  6. Jan 23, 2013 #5

    ehild

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    You are right, I forgot to divide by Lo. :redface:

    ehild
     
  7. Feb 1, 2013 #6
    Thks guys. It really helped. I think I've made some miscalculations. But now i get it. :D
     
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