Stress and Strain

Hooke's law describes how a particular spring or wire responds to force, but the spring constant k depends on the dimensions of the object — a thicker wire is stiffer than a thinner one of the same material. To compare the mechanical properties of materials rather than specific objects, we need quantities that are independent of the object's size and shape. That is where stress and strain come in.

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Tensile Stress

Tensile stress is the force per unit cross-sectional area experienced by a material under tension:

$\sigma = \frac{F}{A}$σ=AF​

where:

• σ (Greek letter sigma) is stress, measured in Pa (pascals) or N m⁻²
• F is the applied force in N
• A is the cross-sectional area in m²

Stress tells you how concentrated the force is. A 1000 N force applied to a wire of cross-sectional area 1.0 × 10⁻⁶ m² produces a stress of 1.0 × 10⁹ Pa (1 GPa) — the same force distributed over a 1 m² area produces a stress of only 1000 Pa.

Worked example: A steel wire has a diameter of 0.80 mm and supports a mass of 5.0 kg. What is the tensile stress in the wire?