Question

Consider a cylindrical titanium wire 3.0 mm in diameter and 2.5 x 10⁴ mm long. Calculate its elongation when a load of 500 N is applied. Assume that the deformation is totally elastic.

Answer 1

To calculate the elongation of the titanium wire, use Hooke's Law and the formula for elongation.

Step-by-step explanation:

To calculate the elongation of the titanium wire, we can use Hooke's Law, which states that the elongation of a material is directly proportional to the applied force and inversely proportional to the cross-sectional area and length of the material. The formula for elongation is:

ΔL = (F * L) / (A * Y)

Where ΔL is the elongation, F is the applied force, L is the length of the wire, A is the cross-sectional area of the wire, and Y is the Young's modulus of the material.

Given that the diameter of the wire is 3.0 mm, we can calculate the cross-sectional area using the formula for the area of a circle:

A = π * (d/2)^2

Substituting the known values into the equations, we can calculate the elongation of the wire when a load of 500 N is applied.