Determine the number N of steel wires with a diameter of d = 2 mm, of which the cable should be designed

Determine the number N of steel wires with a diameter of d = 2 mm, of which the cable should be designed for uniform lifting of a load with a mass of m = 2t, with a safety factor n = 3, if the tensile strength of steel = 4.0 × 10 * 8PA

Data: d (wire diameter) = 2 mm (2 * 10 ^ -3 m); m (cargo weight) = 2 t (2 * 10 ^ 3 kg); n (safety factor) = 3.

Constants: ϭ (tensile strength of steel) = 4 * 10 ^ 8 Pa; g (acceleration due to gravity) = 9.81 m / s2.

1) The highest operating voltage: ϭmax = ϭ / n = 4 * 10 ^ 8/3 = 1.33 * 10 ^ 8 Pa.

2) Number of wires: ϭmax = F / S = m * g / (N * Π * d ^ 2/4) = 4 * m * g / (N * Π * d ^ 2); N = 4 * m * g / (ϭmax * Π * d ^ 2) = 4 * 2 * 10 ^ 3 * 9.81 / (1.33 * 10 ^ 8 * 3.14 * (2 * 10 ^ -3 ) ^ 2) = 46.98 ≈ 47 wires.