Find diameter of steel wire - stress

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The diameter of the steel wire, which is 18m long and elongates 9mm under a 380kg load, is calculated to be approximately 6.89mm. The stress experienced by the wire is determined to be 1.00x10^8 N/m^2. Given that the elastic limit is 3.00E8 N/m^2, the wire does not experience permanent deformation. The calculations and results presented are confirmed to be correct. It is recommended to ensure unit consistency and provide clear explanations for better understanding.
UrbanXrisis
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a) what is the diameter of a steel wire 18m long that elongates 9mm when a load of 380kg is hung on its end?
b) if the elastic limit is 3.00E8 N/m^2, does permanent deformtion occur?

a.
\Delta L=FL/YA
9E-3m=\frac{3724N*18m}{20E10N/m^2*A}
A=3.724E-5m^2
diameter=6.8859mm

b.
stress=F/A
stress=\frac{3724N}{3.724E-5m^2}
stress=1.00x10^8N/m^2
no deformation

is that all correct?
 
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Looks good to me!
 


Yes, your calculations and answers appear to be correct. However, it is always a good idea to double check your work and make sure all units are consistent. Additionally, it would be helpful to provide a clear explanation of the steps and equations used to arrive at your answers. This will ensure that others can follow your reasoning and understand your solution.
 

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