An orthogonal cutting operation is performed using a rake angle of $15.$ Chip thickness before the cut $=$

$0\mathrm{.}012$ in and width of cut $=0\mathrm{.}220$ in$.$ The chip thickness ratio is measured after the cut to be $0\mathrm{.}55.$

Determine $($a$)$ the chip thickness after the cut $(5$ pts$.),($b$)$ shear angle $(5$ pts$.),($c$)$ friction angle $(5$ pts$.),$

$($d$)$ coefficient of friction $(5$ pts$.),$ and $($e$)$ shear strain $(5$ pts$.).$ SHOW ALL WORK PLEASE!!