A wire is stretched by a force of 2000 N, and it experiences a strain of 0.02. If its Young's modulus is 1.6 x 10^11 N/m², what is its cross-sectional area?

Sure, let's solve this step by step.

1. First, we need to understand the relationship between stress, strain, and Young's modulus. The formula is Stress = Young's modulus * Strain.

2. In this case, we are given the strain and Young's modulus, and we need to find the stress. So, we rearrange the formula to find Stress = Young's modulus * Strain = 1.6 x 10^11 N/m² * 0.02 = 3.2 x 10^9 N/m².

3. Stress is also defined as the force divided by the cross-sectional area (Stress = Force/Area). We can rearrange this formula to find the area: Area = Force / Stress.

4. Substituting the given force and the calculated stress into this formula gives us the cross-sectional area: Area = 2000 N / 3.2 x 10^9 N/m² = 6.25 x 10^-7 m².

So, the cross-sectional area of the wire is 6.25 x 10^-7 m².