In a turning operation, a cylindrical workpiece with an initial diameter of $150$ mm and a

length of $700$ mm is being machined with a spindle speed of $1000$ RPM and a feed rate of

$0\mathrm{.}35m\frac{m}{r}ev.$ The depth of cut is $3\mathrm{.}2$ mm and the cutting speed is $80\frac{m}{m}in.$ Chip thickness

before the cut is $0\mathrm{.}33$ mm and chip thickness after the cut is $0\mathrm{.}91$ mm $.$ Assume the rake

angle is $10.$ Cutting force measures $2100$ N and thrust force measures $1900$ N $.$

Determine: $($a$)$ the chip ratio, $($b$)$ the shear plane angle, $($c$)$ the shear strain, $($d$)$ the material

removal rate, and $($e$)$ the coefficient of friction.