A steel rod with a length of 2 meters and a cross-sectional area of 0.002 m² is stretched by a force of 800 N. What is the strain in the rod?

To calculate the strain in the rod, we need to use the formula for stress and strain.

Stress (σ) is defined as the force (F) divided by the cross-sectional area (A). So, σ = F/A.

Strain (ε) is defined as the change in length (ΔL) divided by the original length (L). So, ε = ΔL/L.

First, we need to calculate the stress in the rod.

Given: Force (F) = 800 N Cross-sectional area (A) = 0.002 m²

So, Stress (σ) = F/A = 800 N / 0.002 m² = 400,000 N/m².

The stress in the rod is 400,000 N/m².

Next, we need to calculate the strain in the rod.

The strain is the ratio of the deformation (change in length) to the original length. In this case, we don't have the change in length. But we know that stress and strain are related by the material's modulus of elasticity (E) according to Hooke's law:

Stress = E * Strain or Strain = Stress / E

For steel, the modulus of elasticity (E) is typically around 200 GPa, or 200,000,000,000 N/m².

So, Strain (ε) = σ / E = 400,000 N/m² / 200,000,000,000 N/m² = 0.000002.

The strain in the rod is 0.000002 (or 2 x 10^-6), which is a unitless quantity as it's a ratio of lengths.