Hooke's lawlaw
In 1660, Robert Hooke, experimenting with springs for clocks, formulated the rule: 'As the force, so the stretch' — Ut tensio, sic vis. He announced his discovery in 1678 in the form of an anagram ceiiinosssttuv, fearing plagiarism. After deciphering it later, the world learned the law of elasticity. Solids are networks of atoms linked by 'springs' of electromagnetic forces; for small displacements these bonds are linear, giving rise to a restoring force. A tuning fork, a string, a steel bridge in windy weather — all are examples of a harmonic oscillator generated by Hooke's law.
How it works
The scale in a grocery store: the spring inside stretches under the weight of the goods, and we read the mass on the dial. Keyboard keys return to their original position thanks to the elasticity of silicone domes. Ancient catapults worked on the same principle of elastic deformation of ropes.
💡 The word 'elasticity' doesn't quite capture the essence: elasticity is a property, while Hooke's law is a quantitative measure. Asphalt seems hard, but it also deforms elastically under car wheels — otherwise roads would crumble.
F = -k x
F — elastic force (vector, N), exerted by the deformed body; k — stiffness coefficient (positive constant, N/m), characterizing the elastic properties of a specific spring; x — displacement vector (from equilibrium, m). The minus sign shows that the force is directed opposite to the displacement.
\sigma = E \epsilon
σ — mechanical stress (Pa), force per unit cross-sectional area; E — Young's modulus (modulus of elasticity, Pa), a fundamental material characteristic (for steel E ≈ 2.1×10¹¹ Pa, for rubber E ~ 10⁶ Pa); ε — strain (dimensionless), ε = ΔL/L₀, where ΔL is the change in length, L₀ is the original length.