Answer to Question #291536 in Physics for Asna

Question #291536

How much load is needed to elongate a steel wire to 0.5 %of its original length ? The diameter of the wire is 2mm and youngest modulus of the material of the wire is 20×10^10 N/m^2

1
Expert's answer
2022-01-28T08:14:15-0500

Given:

ε=0.005\varepsilon=0.005

r=1mm=103mr=1\:\rm mm=10^{-3}\:\rm m

E=201010N/m2E=20*10^{10}\:\rm N/m^2


The Hooke's law says

σ=FA=εE\sigma=\frac{F}{A}=\varepsilon E

Hence, the load

F=εAE=πεr2EF=\varepsilon AE=\pi\varepsilon r^2E

F=3.140.005(103)2201010=3140NF=3.14*0.005*(10^{-3})^2*20*10^{10}=\rm 3140\: N


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