One mole of nickel (6.02 10 23 atoms) has a mass of 59 g, and its density is 8.9

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 2.48 m long, with a square cross section, 2.4 mm on a side. You hang the rod vertically and attach a 45 kg mass to the bottom, and you observe that the bar becomes 0.9 mm longer. Next you remove the 45 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.)

Explanation / Answer

from the definition of density = mass/Volume and density of nickel, rho = 8.9 g/cm^3

= 8900 kg/m^3

Length of the bar, L = 2.48 m,   

Cross sectional area, A = (2.4*10^-3)^2 = 5.76 e -6 m^2

Sress on bar when 45 kg mass is hanged = F/A = m*g/A

= 45*9.8/(5.76 e -6 = 7.656 e 7 N/m^2

Strain = change of length/original length = delta_L/L

= 0.9e-3/2.48 = 362 e -4

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

= 7.656 e 7 /(3.62e -4 ) = 2.11*10^11 N/m^2 or pa

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

= sqrt(2.11 e 11/8900)

= 4.869 Km/s

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

T = 2.48/4869

T = 5.1 e -4 secs

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