Question

A metal wire has length 5.2 m and diameter 1.0 mm. The metal has Young modulus 360 GPa. The wire is fixed at one end and a force is applied to the other end. The force extends the wire by 7.2 mm. The wire obeys Hooke’s law. What is the force applied to the wire?

Answer 1

The force applied to the wire is 99 N.

Step-by-step explanation:

To calculate the force applied to the wire, 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 spring.

In this case, the extension is 7.2 mm (or 0.0072 m) and the length of the wire is 5.2 m. The formula for Hooke's law is: F = k * ΔL, where F is the force, k is the spring constant (or Young's modulus), and ΔL is the change in length.

First, we need to find the spring constant (k) using the formula: k = (F / ΔL) * L, where F is the applied force and L is the length of the wire. Rearranging the formula, we have: F = (k / L) * ΔL.

Plugging in the values, F = (360 * 10^9 N/m^2 / 5.2 m) * 0.0072 m = 99 N.