Question

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.

Answer 1

Answer:

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