find the youngs modulus in units of Pa ?

Question

For safty in climbing a mountaineer uses a nylon rope that is 22 m long and 1.5 cm in diameter. when supporting a 94 kg climber, the rope elongates 1.6 m. find youngs modulus ? answer in units of Pa ?

I used the equation:

Y= (F/A)/(delta L / L initial )

and i get .226768 but it seems to be wrong ?

Answer 1

Ok, let's go on :

Young modulus = (F / A) / (dL / L)

F = 94*9.8 = 921.2 Newtons

Area = (1.5/200)^2*pi

dl = 1.6 m

L = 22 m

Y = 921.2 / (1.5 /200)^2*pi / 1.6 / 22

Y = 12666.5 / 1.7*10^-4 = 7450*10^4 = 745*10^5

Y = 745 Pa

Hope that helps

Answer 2

GPa stands for Giga-Pascals Giga = Billion Pascals (Pa) = Newtons/square meter 1 GPa = 10^9 Pa -----NOT 1 Pa = 10^10 GPa!---- I gave thumbs down to saurabh p, because he had the wrong conversion factor listed.

Answer 3

I'll bet your mistake is in using the area of the rope in cm^2, the area has to be in m^2 = 3.1416 x (.0075m)^2, which is a very small number???