Final answer:
To calculate the force applied to a metal wire, you can use Hooke's Law. Given the dimensions and Young's modulus of the wire, you can use the formula F = k * x to find the force needed to extend the wire by a certain amount.
Step-by-step explanation:
Hooke's Law states that the extension of a spring or wire is directly proportional to the force applied to it. In this case, the force applied to the wire extends it by 7.2 mm. We can use Hooke's Law to calculate the force applied to the wire.
The formula for Hooke's Law is F = k * x, where F is the force, k is the spring constant (or Young's modulus), and x is the extension of the wire.
Given that the length of the wire is 5.2 m and the diameter is 1.0 mm, we can calculate the cross-sectional area of the wire using the formula Area = π * (diameter/2)^2.
With the Young's modulus of the wire given as 360 GPa, we can convert it to N/m² by multiplying by 10^9.
Plugging in the values, we get F = (360 * 10^9 N/m²) * (π * (0.001 m/2)^2 * 0.0072 m).
Calculating this equation will give us the force applied to the wire.