If the elastic limit of steel is 5.0×108 Pa,determine the minimum diameter a steel wire can have if it is tosupport a 60 kg circus performerwithout its elastic limit being exceeded.

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Usamah Prosser · Accepted Answer

elastic limit is the maximum strees that can be applied to thesubstance before it gets permenantly deformed E = maximum stress as we know stress =FA or E=FA for stress to be maximum area should be minimum hence here A is the minimum area of cross-section thesubstance and F is the maximum force applied on the subtance now in the given problem E=5×108 Pa=elstic limit of steelwire mass of the circus performer m = 60 kg downward force F acting on the steel wire = weight of the man= m.g =588N now let A be the minimumarea of cross-section ofthe steel wire then using E=FA or A=FE=117.6×10−8m2 now area A=r2=117.6×10−8 r=6.12×10−4m where r is the radius of the wire hence the diameter of the wire d=2.r=12.24×10−4m=1.224mm

If the elastic limit of steel is 5.0\times10^8 Pa,determine the minimum diameter a steel wire can have if it is tosupport a 60 kg circus performerwithout its elastic limit being exceeded.

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