We have a rod made of a certain metal. the rod’s length is l = 1.2 m and has a circular cross section with radius r= 3.8mm. 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 = 2.5 mm. (a) using the information given, estimate the young’s modulus for this metal rod, in n/m.
(b) if we know that this metal has a density of 12 g/cm^3, what would be the speed of sound in this metal in m/s?

         Y =  2.286 *)  N/m

         V =  436.46 m/s

Explanation:

Length, L= 1.2 m

Radius, R=3.8 mm=3.8*

mass, m = 22 kg

Extension, ΔL = 2.5 mm

(a)

Forces  P= mg =22*9.8 =215.6 N

               Stress  = P/A

                            = 215.6/[((r)²]

                Stress = ( 215.6 ) / [(3.14* (3.18*)²]

                Stress= 4.755 *  N/m²

    Strain in rod  =  ΔL/L = (2.5 *)/(1.2)

                           =(2.08 *)

     Now, Toung midulus  =Y= Stress/ Strain

                                          =(4.755 * )/(2.08 *)

                                          =(2.286 *)  N/m

(b)

                     Density of metal  = 12 g/

                                                   = 12*10³ kg/m

   Speed of sound in the metal=

v=

                               V=436.46 m/s