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Question
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–2, what is the maximum load the cable can support?
Solution 1
Radius of the steel cable, r = 1.5 cm = 0.015 m
Maximum allowable stress = 108 N m–2
Maximum stress = `"Maximum Force"/"Area of cross section"`
∴Maximum force = Maximum stress × Area of cross-section
= 108 × π (0.015)2
= 7.065 × 104 N
Hence, the cable can support the maximum load of 7.065 × 104 N.
Solution 2
Maximum load = Maximum stress x Cross-sectional area
`= 10^8 Nm^(-2) xx 22/7 xx (1.5 xx 10^(-2) m)^2`
`= 7.07 xx 10^4 N`
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