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Mechanical Properties of Solids

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Question : 9 of 21
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A steel cable with a radius of 1.5 cm supports a chairlift at a ski area. If the maximum stress is not to exceed 108 N m−210^{8}\,\mathrm{N}\,\mathrm{m}^{-2} ,what is the maximum load, the cable can support?
Solution:  
Here, maximum stress =108 N m−2=10^{8}\,\mathrm{N}\,\mathrm{m}^{-2} ;
radius of the cable, r = 1.5 cm = 0.015 m.
Therefore, area of cross-section of the cable,
A=πr2=π×(0.0152)2A=\pi r^{2}=\pi\times(0.0152)^{2}
=2.25×10−4π m2=2.25\times10^{-4}\pi\,\mathrm{m}^{2}
The maximum load, the cable can support,
F = maximum stress × area of cross-section
=108×2.25×10−4π=10^{8}\times2.25\times10^{-4}\pi
=7.07×104 N=7.07\times10^{4}\,\mathrm{N}
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