An elevator cable is to have a maximum stress of `7 xx 10^(7) Nm^(-2)` to allow for appropriate safety factors. Its maximum upward acceleration is `1.5 ms^(-2)`. If the cable has to support the total weight of 2000 kg of a loaded elevator, the area cross-section of the cable should be

Options

A. `3.22 cm^(2)`
B. `2.38 cm^(2)`
C. `0.32 cm^(2)`
D. `8.23 cm^(2)`

Answer

a

Explanation

`T_("max") = m (g + a) = (2000) (9.8 + 1.5) = 22600 N`
Maximum stress `= (T_("max"))/("Area")`
`:.` Area `= (T_("max"))/("maximum stress") = (22600)/(7 xx 10^(7))`
`= 3.22 xx 10^(-4) m^(2) = 3.22 cm^(2)`