Question #241620

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.




1
Expert's answer
2021-09-24T09:25:05-0400

Find load:


F=mg.F=mg.

Find strain:


ϵ=ΔLL.\epsilon=\frac{\Delta L}L.

Find stress:


σ=FA=4mgπd2.\sigma=\frac FA=\frac{4mg}{\pi d^2}.

On the other hand, the stress is


E=σϵ=σLΔL, E=4mgLπd2ΔL=449.843.140.00420.002=6.24109 Pa.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}.


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