The Young\'s modulus of steel is 2.0 times10^11 N/m^2 and the tensile strength i

Question

The Young's modulus of steel is 2.0 times10^11 N/m^2 and the tensile strength is 8.0 times 10^8 N/m^2. The density of steel is 7.9 times 10^3 kg/m^3. (a) What is the maximum length of a steel cable that can hang vertically supported from one end of the cable? Assume the cable is supporting no other weight than its own and that the acceleration of gravity is the same all along the cable. [Note that the answer does NOT depend on the cross sectional area.] (b) What would the total elongation of the steel cable in part (a) be just before it breaks? You may assume for simplicity that the cable is elastic, i.e., it obeys Hooke's law, until the moment it breaks.

Explanation / Answer

Youngs modlulus Y of a material is given Y = FL/ADL

A = area

DL = change of length

L = original length

F = force

so here we apply

density D = mass/Volume

mass = DV = D * AL

Weight = mg = (7900 *9.81*AL)

W = force = 74499 AL

Stress = Force/area

8 e8 = 74499 AL/A

Length L = 8e8 /(74499)

L = 10738.3 m

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YOungs MOdulus = Stress/strain

strain = Stress/Y

strain = dL/L = 8e8/2e 11

change of lngth = 0.004 * 10738.3

change of length =dL = 43 m

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