A hanging wire made of an alloy of aluminum with diameter 0.11 cm is initially 2.2 m long. When a 34 kg mass is hung from it, the wire stretches an amount 1.24 cm. A mole of aluminum has a mass of 27 grams, and its density is 2.7 g/cm3. Based on these experimental measurements, what is Young's modulus for this alloy of aluminum?

Y = N/m2

As you've done before, from the mass of one mole and the density you can find the length of the interatomic bond (diameter of one atom). This is 2.55 10-10 m for aluminum. As shown in the textbook, the micro quantity ks, i (the stiffness of one interatomic bond) can be related to the macro property Y:

ks, i = N/m

Explanation:

Given that d = 0.11cm = 0.0011m, l = 2.2m, extension = 1.24cm = 0.0124m, mass = 34kg

force = 34 x 9.81 = 333.54N, Area = Pi x d²/4 = 3.142 x 0.0011^2/4 = 9.505x10^-7m²

Calculate the stress = Force/Area = 333.54N / 9.505x10^-7m²

= 350926661.4N/m²

calculate the strain = extension/original length

= 0.0124 / 2.2 = 0.00563

Young modulus of elasticity = Stress/Strain = 350926661.4N/m² /  0.00563

= 6.2332 x 10^10Pa

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