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taurus [48]
3 years ago
6

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 w

e 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?
Physics
1 answer:
navik [9.2K]3 years ago
8 0

Answer:

         Y =  2.286 *10^{9})  N/m

         V =  436.46 m/s

Explanation:

Length, L= 1.2 m

Radius, R=3.8 mm=3.8*10^{-3}

mass, m = 22 kg

Extension, ΔL = 2.5 mm

(a)

Forces  P= mg =22*9.8 =215.6 N

               Stress  = P/A

                            = 215.6/[(\pi(r)²]

                Stress = ( 215.6 ) / [(3.14* (3.18*10^{-3})²]

                Stress= 4.755 * 10^{6}  N/m²

    Strain in rod  =  ΔL/L = (2.5 *10^{-3})/(1.2)

                           =(2.08 *10^{-3})

     Now, Toung midulus  =Y= Stress/ Strain

                                          =(4.755 * 10^{6} )/(2.08 *10^{-3})

                                          =(2.286 *10^{9})  N/m

(b)

                     Density of metal  = 12 g/cm^{3}

                                                   = 12*10³ kg/m

   Speed of sound in the metal=

v=\sqrt{\frac{Y}{density} }  = \sqrt{\frac{2.286*10^{9} }{12*10^{3} } }

                               V=436.46 m/s

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