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

Question #165113

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

1
Expert's answer
2021-02-22T10:24:21-0500

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


r=Aπ=FStressmaxπ=mgStressmaxπ,r=\sqrt{\dfrac{A}{\pi}}=\sqrt{\dfrac{F}{Stress_{max}\pi}}=\sqrt{\dfrac{mg}{Stress_{max}\pi}},r=7.0 kg9.8 ms2π30106 Pa=8.53104 m.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=28.53104 m=1.71103 m.D=2r=2\cdot8.53\cdot10^{-4}\ m=1.71\cdot10^{-3}\ m.

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