Answer to Question #241620 in Physics for Lil_Sage

Question

A MASS OF 4KG IS ATTACHED TO THE END OF A VERTICAL WIRE OF LENGTH 4M AND  A DIAMETER OF 4MM EXTENDS THE WIRE BY 2MM.COMPUTE THE YOUNG MODULUS OF THE WIRE.

Answer 1

Find load:

$$F=mg.$$

Find strain:

$$\epsilon=\frac{\Delta L}L.$$

Find stress:

$$\sigma=\frac FA=\frac{4mg}{\pi d^2}.$$

On the other hand, the stress is

$$E=\frac\sigma \epsilon=\frac{\sigma L}{\Delta L},\\\space\\ E=\frac{4mgL}{\pi d^2\Delta L}=\frac{4·4·9.8·4}{3.14·0.004^2·0.002}=6.24·10^9\text{ Pa}.$$