Question

Calculate the force a piano tuner applies to stretch a steel piano wire by 8.00 mm, if the wire is originally 1.35 m long and its diameter is 0.850 mm.

a) 5,284 N
b) 7,877 N
c) 10,470 N
d) 13,063 N

Answer 1

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