$6-42$ A cylindrical tank with hemispherical ends is required to hold $150$ psi of pressurized air at room temperature. The pressure cycles from zero to maximum. The steel has $\backslash ($ S$\_\{$u t$\}=\backslash )500$ MPa $.$ Determine the infinite$-$life fatigue safety factor if the tank diameter is $0\mathrm{.}5$ m $,$ the wall thickness is $1$ mm $,$ and its length is $1$ m $.$