Hookes law equation for all gauges of copper wire

1. Apr 22, 2008

groom03

[SOLVED] Hookes law equation for all gauges of copper wire

1. The problem statement, all variables and given/known data
For my coursework i'm trying to find an equation using hookes law that works with all gauges of copper wire, i know that this means i will have to change the hookes law equation from F=ke to F=ake (a is not the area it's just a letter for the constant that i need to find)

2. Relevant equations
F=ke
F=ake
Youngs modulus

3. The attempt at a solution
i've tried working out the stiffness for several wire gauges and seeing if there was a pattern to them but my teacher said i should involve the youngs modulus equation.

Any help really appreciated

2. Apr 22, 2008

Hootenanny

Staff Emeritus
Hooke's law can be derived by collecting the constants of Young's modulus. Try doing the same, but this time you want two constants, not just one.

3. Apr 22, 2008

groom03

by substituting i can get E=kl/A

A is going to be known because i'd know the wire gauge and using rho=f/a i can work out the force but i still can figure out how i'd find k unless i'd already know it when working out

Am i getting close?

4. Apr 22, 2008

Hootenanny

Staff Emeritus
Young's modulus in it's entirety is defined thus,

$$E = \frac{\sigma}{\varepsilon}= \frac{F/A_0}{\Delta \ell/\ell_0} = \frac{F \ell_0} {A_0 \Delta \ell}$$

Where $F$ is the applied force, $A_0$ is the original area, $\Delta\ell$ is the extension, $\sigma$ is the stress and $\varepsilon$ is the strain.

Does that help?

5. Apr 22, 2008

groom03

scratch that i can also get the equation k=EL/A but now i'm totally stuck

i could substitute that k into the f=ke equation but i've been told that the youngs modulus was for a unit length so i would have to do something to....

6. Apr 22, 2008

Hootenanny

Staff Emeritus
What's wrong with,

$$F = \frac{A_0E\Delta\ell}{\ell_0} = A_0\cdot C\Delta\ell$$

7. Apr 22, 2008

groom03

i think i've figured out how you get to that

E=FL/Ae

EA=FL/e

EAe=FL

EAe/L=F

F=ACe (if C equals youngs mod/length)

Which rearranges to e=F/A/C

i think that's right... i hope

8. Apr 22, 2008

Hootenanny

Staff Emeritus
Yup, sounds good to me

9. Apr 23, 2008

YAAAAAAAAY