# 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.

If the elastic limit of steel is $5.0×{10}^{8}$ 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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Usamah Prosser

elastic limit is the maximum strees that can be applied to thesubstance before it gets permenantly deformed
E = maximum stress
as we know
stress $=\frac{F}{A}$
or $E=\frac{F}{A}$
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
$E=5×{10}^{8}$ 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
$E=\frac{F}{A}$
or $A=\frac{F}{E}=117.6×{10}^{-8}{m}^{2}$
now area $A={r}^{2}=117.6×{10}^{-8}$
$r=6.12×{10}^{-4}m$
where r is the radius of the wire
hence the diameter of the wire $d=2.r=12.24×{10}^{-4}m=1.224mm$