Asbestos is a fibrous silicate mineral with remarkably high tensile strength. But it is no longer used because airborne asbestos particles can cause lung cancer. Grunerite, a type of asbestos, has a tensile strength of 15 x 102 kg/mm2 (thus, a strand of grunerite with a 1-mm2 cross-sectional area can hold up to 15 x 102 kg). The tensile strengths of aluminum and Steel No. 5137 are 25 x 104 Iblin2 and 5.0 x 104 Iblin2, respectively. Calculate the cross-sectional area (in mm2) of wires of aluminum and of Steel No. 5137 that have the same tensile strength as a fiber of grunerite with a cross-sectional area of
1.0 micro. mZ

Area of aluminum = 8.53 * 10⁻⁶ mm²

Area of steel = 4.27 * 10⁻⁶ mm²

Explanation:

1 in² = 645.16 mm²

1 lb = 0.453592 kg

Tensile strength of Grunerite = 1.5 * 10² kg/mm²

Tensile strength of aluminum = 2.5 * 10⁴ lb/in²

Tensile strength of aluminum = 2.5 * 10⁴ * (0.453592 kg/lb /645.16 mm²/in²)

Tensile strength of aluminum = 17.58 kg/mm²

Tensile strength of Steel No. 5137 = 5.0 * 10⁴ lb/in²

Tensile strength of Steel No. 5137 = 5.0 * 10⁴ * (0.453592 kg/lb /645.16 mm²/in²

Tensile strength of Steel No. 5137 = 35.15 kg/mm²

Area of Grunerite = 1.0 μm² = 10⁻⁶ mm²

Mass of Grunerite = area * tensile strength

mass of Grunerite = 10⁻⁶ mm² * 1.5 * 10² kg/mm² = 1.5 * 10⁻⁴ kg

Area of aluminum of same tensile strength as Grunerite = mass of Grunerite/ tensile strength of aluminum

Area of aluminum = 1.5 * 10⁻⁴ kg /  17.58 kg/mm²

Area of aluminum = 8.53 * 10⁻⁶ mm²

Area of Steel No. 5137 of same tensile strength as Grunerite = mass of Grunerite/ tensile strength of aluminum

Area of steel = 1.5 * 10⁻⁴ kg /  35.15 kg/mm² = 8.53 * 10⁻² mm²

Area of steel = 4.27 * 10⁻⁶ mm²