Question

Two exactly similar wire of steel and copper are stretched by equal force.if the total elongation is 10cm.find how much each wire is elongated given young's modules for steel =2×10^10 N/M^2 and Young's modules for copper 2×10^10N/M^2.​

Answer 1

The copper wire stretches 6.25 cm and the steel wire stretches 3.75 cm.

Step-by-step explanation:

Young's modulus is defined as:

E = stress / strain

E = (F / A) / (dL / L)

E = (F L) / (A dL)

Solving for dL:

dL = (F L) / (A E)

The wires have the same force, length, and cross-sectional area. So:

dL₁ + dL₂ = (FL/A) (1/E₁ + 1/E₂)

Given that dL₁ + dL₂ = 0.10 m, E₁ = 20×10¹⁰ N/m², and E₂ = 12×10¹⁰ N/m²:

0.10 = (FL/A) (1/(20×10¹⁰) + 1/(12×10¹⁰))

FL/A = 0.75×10¹⁰ N/m

Solving for dL₁ and dL₂:

dL₁ = (FL/A) / E₁

dL₁ = (0.75×10¹⁰ N/m) / (20×10¹⁰ N/m²)

dL₁ = 0.0375 m

dL₂ = (FL/A) / E₂

dL₂ = (0.75×10¹⁰ N/m) / (12×10¹⁰ N/m²)

dL₂ = 0.0625 m

The copper wire stretches 6.25 cm and the steel wire stretches 3.75 cm.