$1.(22$ points$)$ Consider the $2014-$T$6$ alloy which S$-$N fatigue behavior is shown in Figure $9\mathrm{.}27.$ A $10\mathrm{.}0$ mm diameter cylindrical rod fabricated from this alloy is subjected to a repeated tension compression loading along its axis. Determine the fatigue life if the maximum and mean loads are $30,000$ N and $7850$N$,$ respectively. Assume a factor of safety value of $2\mathrm{.}0$ and that the curve was generated for a mean stress corresponding to a mean load of $7850$ N$.($NOTE TO CHEGG SOLVER: PLEASE DO NOT USE CHATGPT$/$AI$,$ IT DOES NOT DO IT CORRECTLY$)$