Question

Steel
Young's Modulus (Y)	20 X 1010 N/m2
Shear Modulus (S)	8.1 X 1010 N/m2
Bulk Modulus (B)	16 X 1010 N/m2

The table to the above represents various properties of steel. You have steel wire 4.4 meters in length that stretches 0.12 cm when subjected to a force of 300 N.

1)What is the diameter of the wire?

d₁ =__________ cm

3)What would the diameter of the wire be if you wanted the wire to stretch 0.06 cm less when subjected to this same force?

d₂ =______________ cm

Answer 1

1) let the diameter of the wire be 'd' m

now, stress = force/cross-sectional area = 300/(pi*d²/4) = 1200/(pi*d²)

now, as per Hooke's Law,

stress = young's moldulus*strain

strain = change in length/original length = 0.12/440 = 2.73*10^-4

thus,  1200/(pi*d²) = (20 X 10¹⁰)*(2.73*10^-4) = 2.45*10⁷

or, d² = 7*10^-6 m

or, d = 2.646*10^-3 m

or, diameter = 0.2646 cm

2) strain = 0.06/440 = 1.364*10^-4

thus, 1200/(pi*d²) = (20 X 10¹⁰)*(1.364*10^-4) = 2.73*10⁷

or, d² = 1.4*10^-5 m

or, d = 3.74*10^-3 m

or diameter = 0.374 cm