A 19 cm long, 10 mm diameter string was found to stretch 3.5 mm under a force of 16 N. The string breaks at a force of 42 N. What is the stress in the string What is the strain in the string under a 13 N load? What is the modulus of elasticity of the string? (include units with answer) What is the ultimate strength D. (stress) of the string?

Stress = 165,521 Pa

Strain = 0.015

Modulus of Elasticity = 11,034,742.72 Pa

Ultimate Tensile Stress = 534,761 Pa

Explanation:

Stress @ Force = 13 N

F = kΔx ... Eq 1

Evaluate k @ F = 16 N and Δx = 0.0035m

k = 16 N / 0.0035 m = 4571.43 N/m

Stress = Force / Area ... Eq 2

Stress = 13 N * 4 / π (0.01²) = 165,521.1408 Pa

Strain @ Force = 13 N

Strain = Δx / original Length = (F / k) / original Length

Hence,

Strain = (13 N / 4571.43 N / m) / 0.19 m = 0.015

Modulus of Elasticity (E)

E = Stress / Strain

E = 165,521.1408 Pa / 0.015 = 11,034,742.72 Pa

Ultimate Tensile Stress

Max Stress that can be achieved by a material

Stress = Fmax/Area

Stress = 42 N * 4 / π (0.01²) = 534,761 Pa