Mechanical Properties of Matter — Mechanics

Vedatom Physics Mechanics / Properties of Matter

◈ Simulations ▤ Full book

Reading matter right

Elastic means it comes back. Steel is more elastic than rubber — elasticity is measured by how hard a material fights to restore its shape (Y), not by how far it stretches.

Stress causes strain. Within Hooke's regime they're proportional; the modulus is the slope. Past the yield point the material remembers the abuse.

Surfaces cost energy. A liquid surface is stretched skin under tension — drops go spherical and narrow tubes pull water uphill to shrink it.

Viscosity is fluid friction. A falling ball stops accelerating when viscous drag balances its net weight — terminal velocity, growing as r².

walk the stress–strain curve · §03

full primer ↗

Mechanics · all fourteen modules inked · all lit

§01

Stress, strain & Young's modulus

Hang a load from a wire and the wire answers with an internal restoring force. Stress is that force per unit area, strain the fractional stretch, and Young's modulus their ratio — a number owned by the material, not the wire: ΔL = FLAY. Pick a material, hang the weights, and read the stretch.

Bench · a 2 m wire, 1 mm across, under load

hanging load F{{ wiF }} N

elongation ΔL = FLAY

{{ wi.dL }}

stress FA{{ wi.stress }}

strain ΔLL

{{ wi.strain }}

Young's modulus Y

{{ wi.Y }} GPa

energy density u = ½ × stress × strain

{{ wi.u }}→ {{ wi.U }} stored in the wire

§03

Walking the stress–strain curve

signature bench

Load a ductile metal steadily and its whole biography unrolls on one graph. Straight and honest up to the proportional limit, still springy to the elastic limit, then yield — beyond it the metal flows, keeps a permanent set when unloaded, hardens up to its ultimate strength, and finally necks down and fractures. Drag the strain and watch where you are.

Bench · one ductile specimen, loaded to destruction

applied strain{{ cv.strainLab }}

regime

Read the slope. The straight start is Young's modulus; a stiffer material rises more steeply. Brittle materials (glass, cast iron) fracture while still on the straight part — no yield, no warning.