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.

Spring constant = YA / L

Explanation:

Let F be the force being applied on cross sectional area A of metal bar due to which an extension of ΔL is obtained in the wire of length L then

stress = F / A

strain = ΔL / L

Young's modulus = (F / A) / (ΔL / L)

Y = (F L / A ΔL)

(F / ΔL) = (YA / L)

Spring constant = (F / ΔL)

Spring constant = YA / L