Strain: longitudinal, shearing and volumetric
Stress, strain and Hooke's law · Physics
Study notes
A 3-m steel wire stretches by 1.5 mm under a load, and a 1-m³ block of the same steel shrinks by 2 cm³ under high pressure. Find (a) the longitudinal strain of the wire and (b) the volumetric strain of the block. Step 1: (a) Longitudinal strain = ΔL/L = 1.5 mm / 3000 mm = 0.0015/3 = 5 × 10⁻⁴. Step 2: (b) Volumetric strain = ΔV/V = 2 cm³ / 1,000,000 cm³ = 2 × 10⁻⁶ (magnitude). Step 3: Compare: the wire's strain is 250 times larger — stretching a long thin wire produces far more visible deformation than squeezing a compact block. Answer: (a) 5 × 10⁻⁴ (0.05%), (b) 2 × 10⁻⁶. Both are dimensionless, as strain always is.