Question

A cylindrical rod with a radius of 0.3 in. and a length of 15 in. is subjected to a tensile load. If the rod is to experience neither plastic deformation nor an elongation of more than 0.018 in. when the applied load is 7,000 lb, which of the four metals or alloys listed below are possible candidates? Justify your choice(s).

Answer 1

Answer:

We estimate the material is bronze, which has a modulus E=120 GPa.

Explanation:

With the dimensions of the rod, the force applied and the maximum elongation, we can estimate E, the Young's modulus, which is a property of the material.

The Young's modulus measures the stiffness of a solid material, relating the force applied  per unit of area and the elongation per unit of length.

$E=\frac{F/A}{\epsilon/L} =\frac{F}{A}\cdot\frac{L}{\epsilon}= \frac{F}{\pi r^2}\cdot\frac{L}{\epsilon}=\frac{7000lb}{3.14*(0.3in)^2}\frac{15in}{0.018in}\\\\E= \frac{7000lb}{0.283in^2}\cdot 833.33=20,631,196.33psi=20.6 Mpsi$

Note: lb-force per square inch is equal to psi.

To estimate which material is, we have to look in a Young's modulus list of materials to look for one that has a E near 20.6 Mpsi (or 142 GPa).

The closest material is bronze, which has a modulus E=120 GPa.