Question #174029

Young's modulus for steel is 2×10^11N/m^2. A weight of 100N hangs from a steel wire of length 3m and cross-sectional area 1.5×10^-6m^2. If the extension is 0.25mm, calculate the extension produced


1
Expert's answer
2021-03-24T19:42:58-0400

The extension is 0.25 mm as stated in the condition of the problem. Check whether this is a correct value.

The stress is


σ=FA=66.67106 N/m2.\sigma=\frac{F}{A}=66.67·10^6\text{ N/m}^2.


The strain is


ϵ=σE=Δll, Δl=lσE=1103 m.\epsilon=\frac{\sigma}{E}=\frac{\Delta l}{l},\\\space\\ \Delta l=l\frac{\sigma}{E}=1·10^{-3}\text{ m}.

Thus, the actual extension should be 1 mm


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