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Finding the change in length of a nylon string

  1. Oct 19, 2009 #1
    1. The problem statement, all variables and given/known data
    A nylon tennis string on a racket is under a tension of 225 N. If its diameter is 0.97 mm, by how much is it lengthened from its untensioned length of 29.6 cm?

    Li= 29.6cm =.296 m
    r= 4.85e-4 m
    A= 7.389811319e-7
    F= 225 N
    E= Young's Modulus for Nylon= 5 x 10^9
    Solving for deltaL

    2. Relevant equations
    A=pi(r)^2
    F= E (delta L/Li) A


    3. The attempt at a solution
    I've found the area and tried using the equation above but did not get a correct answer. I may well have messed up the calculations because that equation confuses me a little and I seem to be algebraically challenged this fine morning.
    All my incorrect answers so far are:
    14.5e-8 cm
    7.470483757e-8 cm
    14.506204362e-7 cm
    7.470483757e-6 cm (the last three answers came from the equation above)

    Any help is greatly appreciated! Thank you!
     
  2. jcsd
  3. Oct 19, 2009 #2

    rock.freak667

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    [tex]\Delta L = \frac{FL}{AE}[/tex]


    what units are E in?
     
  4. Oct 19, 2009 #3
    I've been trying to find the equation in latex... :/ E is in N/m^2.
     
  5. Oct 19, 2009 #4

    rock.freak667

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    I was just checking to see what units the value of E you quoted were in.

    But try plugging the number back in and checking again, you aren't supposed to get such small changes in length.
     
  6. Oct 19, 2009 #5
    Okay I plugged everything into it and got an answer but I need to be sure it's right. I only have one more try. :/ Would the answer be 1.802481745?

    PS: I love your signature. Makes everything so much simpler. : )
     
  7. Oct 19, 2009 #6

    rock.freak667

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    If you mean 1.8025 cm, then I believe so as that looks better than 14.506204362x10-7 cm
     
  8. Oct 19, 2009 #7
    Where did that answer come from? And sorry about the long numbers. My homework website is extremely picky
     
  9. Oct 19, 2009 #8

    rock.freak667

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    1.802481745 what unit is this in?

    for the other number, I just quoted one of your above answers.
     
  10. Oct 19, 2009 #9
    Centimeters. The final answer is supposed to be in centimeters so I multiplied the answer from the equation by 100.

    Oh yeah I forgot about that one. :/ That was early this morning.
     
  11. Oct 19, 2009 #10

    rock.freak667

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    then 1.802481745cm should be it.
     
  12. Oct 19, 2009 #11
    That it is! Thank you very much for your help, sir.
     
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