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.

Haven 2021-04-23 Answered
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
Answered 2021-04-25 Author has 86 answers

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=117.6×108m2
now area A=r2=117.6×108
r=6.12×104m
where r is the radius of the wire
hence the diameter of the wire d=2.r=12.24×104m=1.224mm

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