A wire of cross sectional area of (6x10-5m) and length 50cm stretches by 0.2mm under a load of 300N. Calculate the young modulus?

Masterofbooksdirected

2 years ago

To calculate the Young's modulus of the wire, you can use the formula:

Young's Modulus (Y) = (Stress) / (Strain)

Stress is the force applied (F) divided by the cross-sectional area (A) of the wire. Strain is the change in length (ΔL) divided by the original length (L) of the wire.

1. Calculate Stress (σ):
Stress (σ) = Force (F) / Cross-Sectional Area (A)
Stress (σ) = 3000 N / (6 × 10^-5 m^2)
Stress (σ) = 50,000,000 N/m² (or 50 MN/m²)

2. Calculate Strain (ε):
Strain (ε) = Change in Length (ΔL) / Original Length (L)
Given that the wire stretches by 0.2 mm, convert this to meters: ΔL = 0.2 mm = 0.2 × 10^-3 m
Original Length (L) = 50 cm = 0.5 m
Strain (ε) = (0.2 × 10^-3 m) / (0.5 m)
Strain (ε) = 0.0004

3. Now, calculate Young's Modulus (Y):
Young's Modulus (Y) = Stress (σ) / Strain (ε)
Young's Modulus (Y) = (50,000,000 N/m²) / 0.0004
Young's Modulus (Y) = 125,000,000,000 N/m²

So, the Young's Modulus of the wire is 125 Giga Pascals (GPa), which is a measure of its stiffness and ability to withstand stretching.