How Is the Spring Constant Derived from Young's Modulus, Length, and Area?

[nickb145]

Homework Statement

Consider a metal bar of initial length L and cross-sectional area A. The Young's modulus of the material of the bar is Y. Find the "spring constant" k of such a bar for low values of tensile strain.


Express in terms of Y, L, and A.

Homework Equations

I know the hooks law equation and the modulus but i can't figure out the answer it wants me ot get

Maybe I'm doing it wrong but i am getting Y/(L*A)...

The Attempt at a Solution

 

[CWatters]

Spring constant = F/ΔL .....(1)

Youngs Mod. Y = F/ΔL * L/A ......(2)

Rearrange (2) to give an equation for F/ΔL

Substitute into 1

 

[nickb145]

im getting F=(Y*A)/L

 

[CWatters]

You are close but the answer isn't the force F = (Y*A)/L

The problem asks you to work out an equation for the spring constant k.