A hanging wire made of an alloy of nickel with diameter 0.19 cm is initially 2.8 m long. When a 59 kg mass is hung from it, the wire stretches an amount 0.286 cm. A mole of nickel has a mass of 59 grams, and its density is 8.90 g/cm3.

(a) Based on these experimental measurements, what is Young's modulus for this alloy of nickel?

Young's modulus for this alloy of nickel is 1.997*10^11 N/m^2

Explanation:

Young's modulus = stress/strain

Stress = Force (F) / Area (A)

F = mg = 59 kg * 9.8 m/s^2 = 578.2 N

A = πd^2/4 = 3.142 * (0.19/100) ^2/4 = 2.836*10^-6 m^2

Stress = 578.2/2.836*10^-6 = 2.039*10^8 N/m^2

Strain = extension/length = 2.86*10^-3 m/2.8 m = 1.021*10^-3

Young's modulus = 2.039*10^8/1.021*10^-3 = 1.997*10^11 N/m^2