Question

A mass of 11.0 kg , fastened to the end of an aluminum wire with an unstretched length of 0.47 m , is whirled in a vertical circle with a constant angular speed of 118 rev/min . The cross-sectional area of the wire is 2.0×10⁻² cm2 .

Part A:

Calculate the elongation of the wire when the mass is at the lowest point of the path.

Express your answer using two significant figures.

Part B:

Calculate the elongation of the wire when the mass is at the highest point of its path.

Express your answer using two significant figures.

Answer 1

Calculate the elongation of the wire when the mass is at the highest point of its path.

Express your answer using two significant figures.

  angular velocity   ω   =   118 rev/s   =   118 * 2π   rad/s

                                       =   741.4      rad/s  

   Centrifugal force   F_c   =   m * r * ω²

                                       =   11 * 0.47 * 741.4²

                                       =   2841936.00N

   Net force   F   =   F_c + m * g

                           =   2841936.00+   11 * 9.8

                           =   2842043.8 N

   Young's modulus is defined as

   Y   =   F * L / A * ΔL

   Where ΔL is elongation produced and L = r = length of wire

   ΔL   =   F * L / A * Y

   =>   ΔL   =   2842043.8* 0.47/ 2.0 * 10^-6 * 2.0 * 10¹¹

                  =   3.3 * 10^-3   m

                  =   3.3   mm