# Elasticity and Young's Modulus

1. Apr 22, 2012

### R2Zero

1. The problem statement, all variables and given/known data

Consider a metal bar of length L, cross-sectional area A, equilibrium atomic separation x, and Young's modulus E. When a tension force F is applied to the bar, it causes an extension ΔL. Calculate the atomic force constant k by deriving expressions for (a) the number of chains of atoms in any cross section, (b) the number of atoms in a single chain of length L, (c) the microscopic extension Δx between atoms, and (d) the tensile force f between atoms. (e) Write f= kΔx and show that k=Ex. (f) Calculate the value of k for a typical metal for which E = 1.2 GN/m$^{2}$ and x=0.16 nm.

2. Relevant equations

f=kΔx

k=Ex

stress = modulus x strain

F/A = E ΔL/L

ΔL= FL/(EA)

3. The attempt at a solution

Part f is probably the only part of the problem I feel confident about doing. As far parts a through e, I can't make heads or tails of how to derive the expressions involving atomic separation x. This problem seems to somewhat relate Hooke's law with elastic materials and a picture on my book describes the interatomic forces in the material as spring-like.

2. Sep 19, 2012

### afcartagenam

What is the difference between the modulus of elasticity in compresão and modulus of elasticity in tension?
Which Modulus of elasticity should employ a finite element model?