Question

One mole of nickel (6.02 ✕ 1023 atoms) has a mass of 59 g, and its density is 8.9 g/cm3. You have a bar of nickel 2.46 m long, with a square cross section, 1.9 mm on a side. You hang the rod vertically and attach a 39 kg mass to the bottom, and you observe that the bar becomes 1.4 mm longer. Next you remove the 39 kg mass, place the rod horizontally, and strike one end with a hammer. How much time T will elapse before a microphone at the other end of the bar will detect a disturbance? (Assume a simple cubic lattice for nickel.)

Answer 1

density of nickel, rho = 8.9 g/cm^3 = 8900 kg/m^3

Length of the bar, L = 2.46 m

Cross sectional area, A = (1.9 x 10^-3)^2

A = 3.61 x 10^-6 m^2

Stress on bar when 39 kg mass is hanged = F/A = m*g/A

= (39 x 9.8) / (3.61*10^-6)

= 1.06 x 10^8 N/m^2

Srain = delta_L/L

= (1.4 x 10^-3) / 2.46

= 5.69 x 10^-4

Young's modulus of nickel, Y = Stress/Strain

= 1.06 x 10^8 / (5.69 x 10^-4)

= 1.86 x 10^11 N/m^2 or pa

speed of sound in solid bar, v = sqrt(Y/rho)

= sqrt(1.86 x 10^11 /8900)

= 4571 m/s

time taken for sound to travel along the length of the bar, T = L/v

= 2.46/4571

= 5.38 x 10^-4 s or 0.538 ms