A steel cable with a radius of 1.5 cm

cbse
properties-of-solids

#1

A steel cable with a radius of 1.5 cm supports a chair lift 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?


#2

Given, radius of steel cable ® =1.5 cm = 1.5 x ${{10}^{-2}}$ m
Maximum stress = ${{10}^{8}}$ N/${{m}^{2}}$ Area of cross-section of steel cable (A) = $\pi$${{r}^{2}}$
= 3.14x 2.25 x${{10}^{-4}}$ ${{m}^{2}}$

Maximum stress = Maximum force / Area of cross- section
or Maximum force = Maximum stress X Area of cross-section
= ${{10}^{8}}$ x (3.14X 2.25 x${{10}^{-4}}$ )N = 7.065X${{10}^{4}}$ N
= 7.1 x${{10}^{4}}$ N