bar-extension-uses-e-a-over-l - Elasticity: Stress, Strain, and Material Response Step by Step

A uniform bar derives its stiffness from Young modulus, area, and length. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A bar force starts from an accepted Young source

The bar does not choose stiffness directly. It cites Young modulus, then combines area, length, and extension.

E=16\ \text{Pa}\qquad \Delta L=1\ \text{m}

Stiffness and force respond to area and extension

The table separates stiffness from force. Area changes stiffness; extension changes force after stiffness is set.

\begin{array}{c|c|c|c|c|c}E&A&L&\Delta L&k&F\\16\ \text{Pa}&2\ \text{m}^{2}&8\ \text{m}&1\ \text{m}&4\ \text{N/m}&4\ \text{N}\\16\ \text{Pa}&2\ \text{m}^{2}&8\ \text{m}&2\ \text{m}&4\ \text{N/m}&8\ \text{N}\\16\ \text{Pa}&4\ \text{m}^{2}&8\ \text{m}&1\ \text{m}&8\ \text{N/m}&8\ \text{N}\\\end{array}

A uniform bar uses E A over L before force is trusted

The bar stiffness is derived from the cited Young modulus source, then multiplied by the checked extension.

k=\frac{EA}{L}=\frac{16\ \text{Pa}\cdot2\ \text{m}^{2}}{8\ \text{m}}=4\ \text{N/m};\quad F=k\Delta L=4\ \text{N}