Question

A steel wire with cross-section $3c{m}^2$ has elastic limit $2.4\times {10}^{8}Pa$ . The maximum upwards acceleration that can be given to a $1200kg$ elevator supported by this cable, if the stress is not exceeding one-third of elastic limit, is $2n$. Then the value of $n$ is
​​​​​​​[Answer upto two decimal points] [ Take $g=10m/s^2$]

Answer 1

Given: Elastic limit stress $=2.4\times {10}^{8}Pa$
Now for maximum acceleration $a$,
$\Rightarrow m(g+a)=\left(\frac{1}{3}Stress\right)\times Area\Rightarrow m(g+a)=8\times {10}^7\times 3\times {10}^{-4}\Rightarrow 1200(10+a)=24\times {10}^3\Rightarrow 10+a=20\Rightarrow a=10m/s^2$