PROBLEM $2(30$ points$)$

Consider an ideal steel part under fully reversed bending with ultimate strength of $1200$ MPa $.$

$($a$)$ Find the uncorrected mean strength.

$($b$)$ Find the uncorrected endurance limit$.$

$($c$)$ Sketch the $\backslash ($ S $\backslash )-\backslash ($ N $\backslash )$ diagram: label the ultimate strength, uncorrected mean strength, and uncorrected endurance limit on the $\backslash ($ y $\backslash )-$axis and label the number of cycles on the x $-$axis.

$($d$)$ What is the fatigue strength for $10300$ cycles?

$($e$)$ What is the number of cycles the part can endure before failure at stress of $850$ MPa $?$

$($f$)$ What is the number of cycles the part can endure before failure at stress of $100$ MPa $?$