Final answer:
The force a piano tuner applies to stretch a steel piano wire by 8.00 mm is 10,470 N.
Step-by-step explanation:
To calculate the force a piano tuner applies to stretch a steel piano wire by 8.00 mm, we can use Hooke's Law which states that the force applied to a spring or wire is directly proportional to the extension or compression of the material.
The formula for Hooke's Law is F = k * ΔL, where F is the force, k is the spring constant, and ΔL is the change in length.
In this case, since the wire is stretched, the force can be calculated as follows:
F = k * ΔL = (π * (d/2)^2 * E) * ΔL / L, where d is the diameter, E is the Young's modulus, and L is the original length of the wire.
By substituting the given values, we can calculate the force:
F = (π * (0.850 mm / 2)^2 * 200 GPa) * 8.00 mm / 1.35 m = 10,470 N