Calculate the stress, strain and young's modulus of a wire with a cross-sectional area of 3 x 10^-7 m^2 and a length of 0.6 m that is stretched to a distance of 1.2 x 10^-3 by a 120 N force.
stress=force/Area
To calculate the stress, strain, and Young's modulus of the wire, we need to use the following formulas:
1. Stress (σ) = Force (F) / Area (A)
2. Strain (ε) = Extension (ΔL) / Original Length (L₀)
3. Young's Modulus (Y) = Stress / Strain
Step 1: Calculate the stress (σ).
Using the formula for stress (σ = F / A), we can substitute the given values:
σ = 120 N / (3 x 10^-7 m^2)
σ ≈ 4 x 10^8 N/m^2
Step 2: Calculate the strain (ε).
Using the formula for strain (ε = ΔL / L₀), we can substitute the given values:
ε = (1.2 x 10^-3 m) / 0.6 m
ε = 2 x 10^-3
Step 3: Calculate Young's Modulus (Y).
Using the formula for Young's Modulus (Y = σ / ε), we can substitute the calculated values from steps 1 and 2:
Y = (4 x 10^8 N/m^2) / (2 x 10^-3)
Y = 2 x 10^11 N/m^2
Therefore, the stress of the wire is approximately 4 x 10^8 N/m^2, the strain is 2 x 10^-3, and the Young's modulus is approximately 2 x 10^11 N/m^2.