g Asbestos is a fibrous silicate mineral with remarkably high tensile strength. But is no longer used because airborne asbestos particles can cause lung cancer. Grunerite, a type of asbestos, has a tensile strength of 3.5 × 10ଶ kg mmଶ ⁄ (meaning a strand of grunerite with a 1-mmଶ cross-sectional area can hold up to 3.5 × 10ଶ kg). The tensile strength of aluminum and Steel No. 5137 are 2.4 × 10ସ lb inଶ ⁄ and 5.0 × 10ସ lb inଶ ⁄ respectively. Calculate the cross section areas in mmଶ 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 μmଶ

Aluminum cross sectional area = 1.99 * 10^-5 mm^2

Steel cross sectional area = 9.95* 10^-6 mm^2

Explanation:

Given data:

Tensile strength of Grunerite = 3.5 * 10^2 kg/mm^2 = 3.5 * 10^-4 kg/um^2

Tensile strength of Aluminum = 2.5 × 10^4 lb/in2 =  2.5 × 10^4 * 703.07 kg/m^2

Tensile strength of Steel number 5137 = 5.0 × 10^4 lb/in2 = 5.0 × 10^4*703.07 kg/m^2

Calculating the cross sectional area of the wires of aluminum and steel No5137

first we will determine the cross sectional area of the aluminum wire ( A ) by equating tensile strength of aluminum with the tensile strength

of Grunerite

(2.5 × 10^4 * 703.07)  * A = 3.5 * 10^-4 kg

Hence ; A = 1.99 * 10^-5 mm^2

Next we calculate the cross sectional area of steel

5.0 × 10^4*703.07 kg/m^2 * A" = 3.5 * 10^-4 kg

Hence ; A" = 9.95* 10^-6 mm^2

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