Question

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?

Answer 1

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