Hookes law equation for all gauges of copper wire

In summary, the conversation discusses finding an equation using Hooke's law that works with all gauges of copper wire. This would involve changing the Hooke's law equation from F=ke to F=ake, where a is a constant that needs to be found. Young's modulus is suggested as a way to derive the equation, and the conversation delves into using the constants of Young's modulus to find the equation. Ultimately, it is determined that the equation can be written as F=A_0C\Delta\ell, where C represents the Young's modulus divided by length.
  • #1
groom03
27
0
[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)


Homework Equations


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
 
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  • #2
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
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
Young's modulus in it's entirety is defined thus,

[tex]E = \frac{\sigma}{\varepsilon}= \frac{F/A_0}{\Delta \ell/\ell_0} = \frac{F \ell_0} {A_0 \Delta \ell} [/tex]

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

Does that help?
 
  • #5
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
What's wrong with,

[tex]F = \frac{A_0E\Delta\ell}{\ell_0} = A_0\cdot C\Delta\ell[/tex]
 
  • #7
Hootenanny said:
What's wrong with,

[tex]F = \frac{A_0E\Delta\ell}{\ell_0} = A_0\cdot C\Delta\ell[/tex]


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
groom03 said:
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 :approve:
 
  • #9
YAAAAAAAAY

thanks for your help
 

1. What is Hooke's Law equation for all gauges of copper wire?

Hooke's Law states that the force applied to a spring or elastic material is directly proportional to the displacement of the material from its rest position. The equation is F = kx, where F is the force applied, k is the spring constant, and x is the displacement.

2. How does Hooke's Law apply to copper wire?

Hooke's Law can be applied to any elastic material, including copper wire. When a force is applied to a copper wire, it will stretch or compress in response. The amount of stretch or compression is directly proportional to the force applied, as described by the Hooke's Law equation.

3. What is the significance of the spring constant in Hooke's Law?

The spring constant, represented by the variable k in the equation, is a measure of the stiffness of the material. A higher spring constant means that the material is harder to stretch or compress, while a lower spring constant means it is easier to stretch or compress. In the case of copper wire, the gauge or thickness of the wire will affect the spring constant.

4. Does Hooke's Law apply to all gauges of copper wire?

Yes, Hooke's Law can be applied to all gauges of copper wire. However, the spring constant will vary depending on the gauge or thickness of the wire. Thicker wires will have a higher spring constant, meaning they require more force to stretch or compress compared to thinner wires.

5. How is Hooke's Law used in practical applications involving copper wire?

Hooke's Law is used in many practical applications involving copper wire, such as in electrical circuits and springs. By understanding the relationship between force and displacement, engineers can design circuits and devices that use copper wire in a safe and efficient manner.

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