a wire of length 5.0m and diameter 2.0mm exciteds by 0.25mm when a force of 50N was used to stretch it from it's end. calculate the stress , strain , young's modulus of the material of the wire (=3.142)

Answer 1

Given:
Length of wire (L) = 5.0 m
Diameter of wire (d) = 2.0 mm = 0.002 m
Change in length (ΔL) = 0.25 mm = 0.00025 m
Force applied (F) = 50 N
Young's modulus (Y) = ?

Radius of the wire (r) = d/2 = 0.001 m

Stress (σ) = Force/Area
Area = π r^2
Area = π *(0.001)^2
Area = 3.142 * 0.000001
Area = 0.000003142 m^2

Stress (σ) = 50 / 0.000003142
Stress (σ) = 15,893 Pa

Strain (ε) = Change in length / Original length
Strain (ε) = 0.00025 / 5.0
Strain (ε) = 0.00005

Young's modulus (Y) = Stress / Strain
Young's modulus (Y) = 15,893 / 0.00005
Young's modulus (Y) = 317,860,000 Pa

Therefore, the stress is 15,893 Pa, strain is 0.00005, and Young's modulus of the material of the wire is 317,860,000 Pa.