Question

A tensile stress is to be applied along the long axis of a cylindrical brass rod

that has a diameter of 10 mm (0.4 in.). Determine the magnitude of the load
required to produce a 25 X10⁻³ mm ( 10⁻⁴ in.) change in diameter if the
deformation is entirely elastic.

Answer 1

The magnitude of the load required to produce a 25 X10⁻³ mm is 7073 N.

Step-by-step explanation:

To determine the magnitude of the load required to produce a 25 x 10⁻³ mm change in diameter of a cylindrical brass rod, we can use the concept of tensile stress and the formula for stress.

The formula for stress is:

Stress = Force / Area

Since the deformation is entirely elastic, we can assume that the stress is within the proportional limit, so Hooke's Law can be applied:

Stress = Young's Modulus * Strain

Young's Modulus for brass can be found in reference tables and is typically around 90 x 10⁹ Pa.

By rearranging the formula, we can find the magnitude of the load:

Force = Stress * Area

Plugging in the values, we get:

Force = (90 x 10⁹ Pa) * (π * (0.005 m)²)

Force ≈ 7073 N