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Young's modulus - calculating delta L

  1. Nov 7, 2009 #1
    1. Consider a steel guitar string of initial length L=1.00 meter and cross-sectional area A=0.500 square millimeters. The Young's modulus of the steel is Y=2.0 \times 10^{11} pascals. How far ( Delta L) would such a string stretch under a tension of 1500 newtons?
    Use two significant figures in your answer. Express your answer in millimeters.




    2. Y = kL/A
    k = YA/L




    3. k = YA/L = (2*10^11 N/m^2)*(.0005m^2) / 1m = 1*10^8 N/m

    deltaL = F/k = 1500N/(1*10^8 N/m) = 1.5*10^-5m = .015 mm

    I made a mistake with units somewhere but I can't spot it.
     
  2. jcsd
  3. Nov 7, 2009 #2
    Remember that when converting from square millimeters to square meters, you have to square the factor that you are changing by.

    Since 1mm = 0.001m, 1mm2 = 0.001m * 0.001m = 0.000001m2

    Your problem is that you are dividing by 0.0005m2 instead of 0.0000005m2, so your answer is exactly three orders of magnitude too small.
     
  4. Nov 7, 2009 #3
    Thanks!
     
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