Hooke's Law
σ = Yε — stretch a steel bar, watch ΔL grow linearly with F. Live σ–ε point on the Hooke line.
Key Notes
For small deformations, the stress in a solid is DIRECTLY proportional to the strain: stress = E × strain. This is Hooke's law.
The proportionality constant E is the MODULUS OF ELASTICITY — material-specific, geometry-independent.
Stress = force per unit area (N/m² = Pa). Strain = fractional deformation (dimensionless).
Three types of stress/strain: tensile/compressive (longitudinal), volumetric (bulk), shear (tangential).
Each has its own modulus: Young's (Y) for longitudinal, Bulk (B) for volume, Shear (G) for shape.
Linear region: Hooke's law holds. Beyond the proportional limit, the curve deviates.
Spring force F = −kx is a special case of Hooke's law applied to a spring; k = stiffness.
Elastic deformations are REVERSIBLE — strain disappears when stress is removed. Beyond the elastic limit, deformation is permanent (plastic).
Formulas
Hooke's law (general)
σ = stress, ε = strain, E = modulus (Young's, bulk, or shear depending on the geometry).
Longitudinal (Young's)
Force per area causes a fractional length change.
Spring (1D Hookean)
k = elastic constant; restoring force opposes displacement.
Elastic potential energy
Per unit volume: ½·stress·strain.
Important Points
Hooke's law is LINEAR — valid only for small strains (typically < 0.1%).
The modulus depends on the MATERIAL but not on the shape or size of the sample.
Stress is intensive (Pa, like pressure). Strain is dimensionless.
Beyond elastic limit: no longer linear, plastic deformation begins, eventually fracture.
Real materials may show small NON-LINEARITY even in the elastic regime — Hooke's law is a first-order approximation.
Hooke's law extends to fluids (bulk modulus) and to torsion (shear modulus) — same idea, different geometry.
Hooke's Law notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.