A cord is 5.71e+1 meters long and 1.56 mm in diameter. When it supports a 1.41 kg load it stretches 3.50 cm. What is the Young's modulus of the cord's material?
length l = 5.71 x 10 m = 57.1 m
d = 1.56 mm = 1.56 x 10-3 m
r = 0.78 x 10-3m
m = 1.41 kg
Increase in length Δl = 3.5 x 10-2 m
Area of cross section A = p (0.78 x 10 -3)2 m2
=1.91 x 10-6 m2
Young's modulus Y = (F/A)/(Δl/l) = stress / strain = F l /A Δl
where F=mg=1.41 x 9.8 = 13.82
Y = (13.82 x 57.1)/(1.91 x 10-6 x 3.5 x -2) = 11.8 x 109 N/m2