Suppose we hang a heavy ball with a mass 13 kg (so the weight is) from a steel wire 3.9 m long that is 3.1 mm in diameter (radius = 1.55*10-3 m). Steel is very stiff, and Young's modulus for steel is unusually large, 2 * 1011 N/m2. Calculate the stretch of the steel wire.

1.635*10^-3m

Explanation:

Young modulus is the ratio of the tensile stress of a material to its tensile strain.

Young modulus = Tensile stress/tensile strain

Tensile stress = Force/Area

Given force = 130N

Area = Πr² = Π * (1.55*10^-3) ²

Area = 4.87*10^-6m²

Tensile stress = 130/4.87*10^-6 = 8.39*10^7N/m²

Tensile strain = extension/original length

Tensile strain = e/3.9

Substituting in the young modulus formula given young modulus to be 2*10¹¹N/m²

2*10¹¹N/m² = 8.39*10^7/{e/3.9) }

2*10¹¹ = (8.39*10^7*3.9) / e

2*10¹¹e = 3.27*10^8

e = 3.27*10^8/2*10¹¹

e = 1.635*10^-3m

The stretch of the steel wire will be

1.635*10^-3m