Properties of Matter — Elasticity & Fluid Statics (Medium)

Quick Recap — Elasticity & Fluid Statics

• Elasticity: stress $=\dfrac{F}{A}$, strain $=\dfrac{\Delta L}{L}$, Young's modulus $Y=\dfrac{FL}{A\,\Delta L}$; elongation $\Delta L=\dfrac{FL}{AY}$ (so $\Delta L\propto L$ and $\propto\dfrac{1}{r^2}$).
• Energy: elastic PE $=\tfrac12 F\,\Delta L=\tfrac12\times$stress$\times$strain$\times$volume. Thermal stress (clamped rod) $=Y\alpha\,\Delta T$.
• Bulk modulus: $B=-\dfrac{\Delta P}{\Delta V/V}$; compressibility $=\dfrac1B$; maximum self-supported length $=\dfrac{\sigma_{break}}{\rho g}$.
• Pressure: $P=P_0+\rho g h$ (depends only on depth). Pascal / hydraulics: $\dfrac{F_1}{A_1}=\dfrac{F_2}{A_2}$.
• Buoyancy: a floating body has $\dfrac{\text{submerged volume}}{\text{total}}=\dfrac{\rho_{body}}{\rho_{fluid}}$; apparent weight $=$ weight $-$ upthrust.

Worked mini-example. A steel wire ($Y=2\times10^{11}$ Pa, $L=2$ m, $A=1$ mm$^2$) under a $100$ N load stretches by $\Delta L=\dfrac{FL}{AY}=\dfrac{100\times2}{(10^{-6})(2\times10^{11})}=10^{-3}$ m $=1$ mm.