physics question, a wire under stress?
A steel wire of length 1.91m with circular cross section must stretch no more than 0.250cm when a tensile (stretching) force of 420N is applied to each end of the wire. What minimum diameter dmin is required for the wire? please explain steps!!
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Straightforward Young's modulus problem,
E = σ / ε = (F / A ₀)/(∆L/L₀)
E = 200 GPa ← see citation (make correction if you have another preferred value)
F = 420N
A₀= unknown
∆L = 0.0025m
L = 1.91m
200e9 N/m² = (420N / A₀) / (0.0025m/1.91m) = 320880N / A₀
A₀ = 320880N / 200e9 N/m² = 1.6e-6 m² = πd²/4
d = sqrt(4·1.6e-6m²/π) = 1.4e-3m = 0.14cm