Answer to Question #165113 in Mechanics | Relativity for Sage Topaz

Question

What is the minimum diameter of an Al wire able to support a 7.0 kg mass without exceeding its elastic limit?

Answer 1

Let's first find the minimum radius of the wire:

$$r=\sqrt{\dfrac{A}{\pi}}=\sqrt{\dfrac{F}{Stress_{max}\pi}}=\sqrt{\dfrac{mg}{Stress_{max}\pi}},$$ $$r=\sqrt{\dfrac{7.0\ kg\cdot9.8\ \dfrac{m}{s^2}}{\pi\cdot30\cdot10^6\ Pa}}=8.53\cdot10^{-4}\ m.$$

Finally, we can find the minimum diameter of an Al wire:

$$D=2r=2\cdot8.53\cdot10^{-4}\ m=1.71\cdot10^{-3}\ m.$$