We have a rod made of a certain metal. The rod’s length is L = 1.8 m and has a c

Question

We have a rod made of a certain metal. The rod’s length is L = 1.8 m and has a circular cross section with radius r = 3.2 mm. If we hang the rod vertically and hang a mass of m = 22 kg at its end we find that it is stretched by d = 1.5 mm.

Using the information given, estimate the Young’s modulus for this metal rod, in N/m.

If we know that this metal has a density of 11 g/cm^3, what would be the speed of sound in this metal in m/s?

We have a rod made of a certain metal. The rod’s length is L = 1.8 m and has a circular cross section with radius r = 3.2 mm. If we hang the rod vertically and hang a mass of m = 22 kg at its end we find that it is stretched by d = 1.5 mm.

Using the information given, estimate the Young’s modulus for this metal rod, in N/m.

If we know that this metal has a density of 11 g/cm^3, what would be the speed of sound in this metal in m/s?

Explanation / Answer

Young’s modulus for this metal rod E = stress / strain = (F/A)/(dL/L)

=> E = (22*9.8/(pi*(3.2*10^-3)^2))/( 1.5*10^-3 / 1.8) = 8.04*10^9 N/m^2

speed of sound = ( E / density)^0.5

=> speed = ( 8.04*10^9 / (11*10^3))^0.5 = 854.9 m/s   

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