A 200-kg load is hung on a wire with a length of 4.00 m, a cross-sectional area of [tex]0.200 \times 10^{-4} \, \text{m}^2[/tex], and a Young's modulus of [tex]8.00 \times 10^{10} \, \text{N/m}^2[/tex]. What is the increase in its length?

To calculate the increase in length of the wire due to the 200 kg load, we can use Hooke's Law and the formula for strain. Therefore, the increase in length of the wire due to the 200 kg load is approximately 4.9 × 10⁻¹¹ meters.

First, let's calculate the force applied to the wire. The force can be calculated using the formula:

Force = mass × acceleration due to gravity
Force = 200 kg × 9.8 m/s²
Force = 1960 N

Next, let's calculate the stress on the wire. Stress is defined as the force applied per unit area. The formula for stress is:

Stress = Force / Cross-sectional area
Stress = 1960 N / (0.200 × 10⁴ m²)
Stress = 9.8 N/m²

Now, we can calculate the strain on the wire. Strain is defined as the change in length divided by the original length. The formula for strain is:

Strain = Stress / Young's modulus
Strain = 9.8 N/m² / (8.00 × 10¹⁰ N/m²)
Strain = 1.225 × 10⁻¹¹

Finally, to calculate the increase in length, we can use the formula:

Increase in length = Strain × Original length
Increase in length = 1.225 × 10⁻¹¹ × 4.00 m
Increase in length ≈ 4.9 × 10⁻¹¹ m

Therefore, the increase in length of the wire due to the 200 kg load is approximately 4.9 × 10⁻¹¹ meters.

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