A uniform wire of cross-sectional area $A$ is suspended from the ceiling of an elevator. A block of

Question

A uniform wire of cross-sectional area $A$ is suspended from the ceiling of an elevator. A block of weight $W$ is attached to its free end. If the elevator is accelerating upwards with an acceleration of $g/2$, the longitudinal stress in the wire is

Professor PC Thomas Classes · Answer

When the elevator accelerates upwards with acceleration $a$, the effective acceleration due to gravity is $g_{eff} = g + a$. Here, $a = g/2$, so $g_{eff} = g + g/2 = 3g/2$. The tension in the wire is $T = m g_{eff} = m(3g/2) = \frac{3}{2}(mg) = \frac{3W}{2}$. The longitudinal stress is defined as the restoring force per unit area, which equals $\frac{T}{A} = \frac{3W}{2A}$.