# Answer to Question #25566 in Mechanics | Relativity for doug

Question #25566

a metal wire 1.3mm in diameter 2.1m long hangs vertical with 6.1kg object hanging from it. wire stretches 1.4mm. what is value of Young's modulus for the metal?

Expert's answer

Young's modulus E can be calculated by dividing the tensile stress by the tensile strain

E=sigma/epsilon = (F/S)/(delta L/L)

where F is is the force exerted on an object, S=pi*(d/2)^2 is cross-section area of wire delta L is the amount by which the length of the object changes. So,

E = (mg/S)/(delta L/L) = 6.1*9.8/(pi*(0.0013/2)^2)/(0.0014/2.1) = 67.5 * 10^9 Pa

E=sigma/epsilon = (F/S)/(delta L/L)

where F is is the force exerted on an object, S=pi*(d/2)^2 is cross-section area of wire delta L is the amount by which the length of the object changes. So,

E = (mg/S)/(delta L/L) = 6.1*9.8/(pi*(0.0013/2)^2)/(0.0014/2.1) = 67.5 * 10^9 Pa

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