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Homework Help: About tension

  1. Nov 11, 2004 #1
    I have the following problem:
    The specimen (rod) is hanging vertically. Weight=P. Young's modulus = E. Area = S. What is the ε-?
    ε = dL/L

    As I know Energy U=V*(E*ε ^2)/2, where V-volume
    And the work is A=P*dL(dL of center of mass)
    In this case A=p*dL/2
    So it must be that ε =P/(E*S)
    But the correct answer is ε =P/(2*E*S)
    Where is the mistake?
     
    Last edited: Nov 11, 2004
  2. jcsd
  3. Nov 11, 2004 #2

    Doc Al

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    Staff: Mentor

    I can't quite figure out what you're doing with energy and volume. But I suspect that your mistake is in treating the rod as if the tension were the same throughout, which is not the case.
     
  4. Nov 11, 2004 #3
    Ok. In final moment Energy is equal U=V*(E*ε ^2)/2=V*(σ*ε/2),
    where σ-stress (tension), (σ=F/S=E*ε (Hook's law)
    But the "tension is not the same throughout".
    It changes from 0 to P/S.
    What I should do?
     
  5. Nov 11, 2004 #4

    Doc Al

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    Staff: Mentor

    The stress ranges from 0 (at the bottom) to P/S at the top. So the average stress is 1/2 P/S. Thus the overall strain is P/(2 E S), where E is Young's modulus.
     
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