How much does a string stretch when under load?

[hm8]

Homework Statement

A 12 inch long string with a 0.5 mm diameter and is composed of a 10GPa modulus
material is fixed at one end and loaded by a 100 g mass at its other end. What is the length
of the string when it is under load? (Note that the length is necessarily greater than 12
inches.)

L_Initial = 12 in = .305 m
A = ∏r² = ∏(.00025)² = 1.96 * 10^-7 m^2
E = 10 N/m²
F= .1 * 9.8 = .98 N

Homework Equations

F=kx

k=(EA)/L

The Attempt at a Solution

Basically I'm just not sure which length to use for finding the spring constant k, the final or initial length?

So should be solving something like this for final length?

F=(EA/L_final)(L_final-L_Initial)

or this:

F=(EA/L_initial)(L_final-L_Initial)

 

[PhanthomJay]

F=(EA/L_initial)(L_final-L_Initial)

Use this one. But first correct your value for E you are way off in the number of zeroes after the '10'.