You hang a heavy ball with a mass of 31 kg from a gold rod 2.6 m long by 2.1 mm

Question

You hang a heavy ball with a mass of 31 kg from a gold rod 2.6 m long by 2.1 mm by 3.0 mm. You measure the stretch of the rod, and find that the rod stretched 0.001597m.

Using these experimental data, what value of Young's modulus do you get?
Y =  N/m2

The atomic mass of gold is 197 g/mole, and the density of gold is 19.3 g/cm3.

Using this information along with the measured value of Young's modulus, calculate the speed of sound in gold.
v =  m/s

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 2.54 m long, with a square cross section, 2.4 mm on a side. You hang the rod vertically and attach a 41 kg mass to the bottom, and you observe that the bar becomes 0.8 mm longer. Next you remove the 41 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.)
s

Explanation / Answer

If Y is supposed to be the tensile elastic modulus (I have NO way of knowing),

Y = / = (mg/A)/(dL/L) = (131*9.8/(0.0026*0.0021)/(.001597/2.6) = 1.74011E10 Pa

b. We start by finding the bond length d, and also determine the Young's modulus Y, from which we can derive the bond stiffness k(b). See ref. 1 for a more detailed explanation of the method.
Bond length d is assumed equal to the atom's "diameter", which is actually just the cube root of its (cubic) volume.
d = (Volume/NAtoms)^(1/3)
= [59/8.9 (cm^3/mole) / 6.02E23 (atoms/mole)] ^ (1/3)
= 2.224E-8 cm/atom = 2.224E-10 m/atom
Young's modulus Y:
Y = F/(AL/L) = FL/(AL) = 9.8*41*2.54/(0.0024^2*0.08) = 2.21E9 Pa
Now we need to determine the number of atoms in the rod length N1 and cross section N2.
N1 = L/d

N2 = A/d^2
Elongation of each bond L(b) = L/N1 = dL/L
Force per bond F(b) = F/N2 = Fd^2/A
k(b) = F(b)/L(b) = (Fd^2/A)/(dL/L) = FL/(AL)*d^2/d = Yd
k(b) = 2.21E19*2.224E-10 = 0.491 N/m (answer)
Sound speed c = sqrt[Y(1-v)/(density(1+v)(1-2v))] where v is Poisson's ratio, ~0.3 for most metals.
t = L/c (answer)

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