Points to Ponder

When a wire hangs from a ceiling with a weight $F$ attached at the bottom, the ceiling pulls upward on the wire with a force equal to $F$ (Newton’s third law). At any cross-section $A$ inside the wire, the tension is only $F$ — not $2F$ — because the ceiling’s force acts on the top end, not on the interior. So tensile stress is $F/A$, not $2F/A$.

Hooke’s law ($\text{stress} \propto \text{strain}$) holds only in the initial straight-line portion of the stress-strain curve. Beyond the proportional limit, the relation becomes nonlinear and Hooke’s law no longer applies.

Young’s modulus and shear modulus are defined only for solids because solids alone have fixed lengths and definite shapes that can change under load. Liquids and gases do not have a fixed shape or length, so these moduli are meaningless for them.

Bulk modulus applies to solids, liquids, and gases because all three can change volume. It describes the response when the entire body is subjected to uniform pressure from all sides, so the shape stays the same and only the volume changes.

Metals typically have a higher Young’s modulus than alloys or elastomers. A high Young’s modulus means a large force is needed to produce a small change in length — the material is stiffer.

In everyday language, people often call a material “more elastic” if it stretches a lot. That is incorrect. In physics, a material is more elastic if it stretches less for the same load. …