The minimum diameter of the steel wire is 7.58 mm.
Stress applied to the steel wire
Young's modulus = stress/strain
strain = e/l = (7.32 x 10⁻³ m) / (19.3 m) = 3.79 x 10⁻⁴
stress = Young's modulus x strain
stress = 200 x 10⁹ N/m² x 3.79 x 10⁻⁴ = 7.59 x 10⁷ N/m²
Area of the wire
stress = Force/Area
Area = Force/stress
Area = mg/stress
Area = (350 x 9.8) / (7.59 x 10⁷)
Area = 4.519 x 10⁻⁵ m²
Minimum diameter of the wire
Area = πd²/₄
πd²/₄ = 4.519 x 10⁻⁵ m²
πd² = 4(4.519 x 10⁻⁵)
d² = (4 x 4.519 x 10⁻⁵)/π
d² = 5.75 x 10⁻⁵
d = √(5.75 x 10⁻⁵)
d = 7.58 x 10⁻³ m
d = 7.58 mm
Thus, the minimum diameter of the steel wire is 7.58 mm.
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