# Hookes law equation for all gauges of copper wire

groom03
[SOLVED] Hookes law equation for all gauges of copper wire

## Homework Statement

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)

F=ke
F=ake
Youngs modulus

## 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

Staff Emeritus
Gold Member
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.

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?

Staff Emeritus
Gold Member
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?

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...

Staff Emeritus
Gold Member
What's wrong with,

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

groom03
What's wrong with,

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

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

Staff Emeritus
Gold Member
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
Yup, sounds good to me

groom03
YAAAAAAAAY