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

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Homework Help Overview

The discussion revolves around deriving the spring constant \( k \) for a metal bar based on its Young's modulus \( Y \), initial length \( L \), and cross-sectional area \( A \). Participants are exploring the relationship between these physical properties under low tensile strain conditions.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are attempting to relate the spring constant to Young's modulus and are discussing the equations involved, including Hooke's Law and the definition of Young's modulus. There are questions about the correct formulation and rearrangement of these equations.

Discussion Status

The discussion is ongoing, with some participants providing equations and others questioning the correctness of the derived expressions. There is an indication of productive exploration of the relationships between the variables, but no consensus has been reached on the final form of the spring constant.

Contextual Notes

Participants are working under the assumption of low tensile strain and are required to express the spring constant in terms of the given variables. There is a noted confusion regarding the correct application of the equations involved.

nickb145
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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

 
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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
 
im getting F=(Y*A)/L
 
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.
 

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