Young's modulus - calculating delta L

1. Nov 7, 2009

Linus Pauling

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?

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. Nov 7, 2009

mibjkk

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.

3. Nov 7, 2009

Thanks!