Find diameter of steel wire - stress

[UrbanXrisis]

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?

 

[HallsofIvy]

Looks good to me!

 

[thepatientmental]

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.