A light elastic wire of cross-sectional area 2 mm² carries a load of 100 N. The load is attached suddenly from the natural unstretched position. Neglect the mass of the wire and assume linear elastic behaviour. If the maximum stress reached is N MPa, find N.
Physics · Properties of solid and fluid · Elastic Properties of Solids: Stress, Strain and Elastic Moduli
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Question

A light elastic wire of cross-sectional area 2 mm² carries a load of 100 N. The load is attached suddenly from the natural unstretched position. Neglect the mass of the wire and assume linear elastic behaviour. If the maximum stress reached is N MPa, find N.

Physics · Properties of solid and fluid · Elastic Properties of Solids: Stress, Strain and Elastic Moduli

G1 Physics · Accepted Answer

Static stress produced by the same load is σ(static) = W/A. Here, W = 100 N, A = 2 mm² = 2×10⁻⁶ m². Thus, σ(static) = 100/(2×10⁻⁶) = 5×10⁷ Pa = 50 MPa. For a load suddenly applied from zero extension, maximum extension = 2×static extension. Therefore maximum stress is also twice the static stress: σ(max) = 2σ(static) = 100 MPa. Hence, N = 100.