Question

A circular steel wire 3.00 m long must stretch no more than 0.25 cm when a tensile force of 860 N is applied to each end of the wire. What minimum diameter is required for the wire? I just really need a clear explanation of how to figure out Young's Modulus of steel.  

Answer 1

length of the steel wire L = 3 m

stretched length ΔL = 0.25 cm = 0.0025 m

tensile force F = 860 N

Stress is directly proportional to strain.
     Stress α (strain )

     Stress = Y (strain )

here , Y =  youngs modulus ( or constant of proportionality)

   Stress = force / cross section area = F /A

   Strain = change in length / original length = ΔL /L

therefore ,

          (F/ A ) = Y . (ΔL /L )

Cross section Area of the wire is

            A = F L / Y . ΔL

here,

Young modulus of steel wire = 200x10⁹N/m²

substitute the given data in above equation we get

       A = (860 N)(3 m) / (200x10⁹N/m²)(0.0025 m)

          = 5.16*10^-6 m²

but,

Cross secton area A = πd² / 4

                           d² = 4A / π

diameter of the wire is

          d = √(4A / π)   

             = √[(4)(5.16*10^-6 m²) /(3.14)]

             = 2.5632*10^-3 m

(OR)

          d = 2.5632 mm