# How long will a steel wire with a length of 1.8 m and a diameter of 0.50 mm be lengthened

How long will a steel wire with a length of 1.8 m and a diameter of 0.50 mm be lengthened under the action of a load whose weight is 15N? Will the wire withstand a weight of 100N if its tensile strength is 1.2 GPa?

Data: l0 (length) = 1.8 m; d (diameter) = 0.5 mm2 (0.5 * 10 ^ -3 m); P1 (weight) = 15 N; P2 (weight) = 100 N.

Constants: E (Young’s modulus, steel) = 200 … 220 GPa = 210 * 10 ^ 9 Pa; [ϭ] (tensile strength) = 1.2 GPa.

1) Elongation: Δl / l0 = F / (E * S) = P1 / (E * 0.25 * Π * d ^ 2); Δl = P1 * l0 / (E * 0.25 * Π * d ^ 2) = 15 * 1.8 / (210 * 10 ^ 9 * 0.25 * 3.14 * (0.5 * 10 ^ -3 ) 2) = 6.55 * 10 ^ -4 m.

2) 1.2 GPa = [ϭ] ≥ ϭ = F / A = P ^ 2 / S = P2 / (0.25 * Π * d ^ 2) = 100 / (0.25 * 3.14 * (0 , 5 * 10 ^ -3) ^ 2 ≈ 0.51 GPa (withstand).

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