$20\mathrm{.}21($A$)($USCS units$)$ A cast iron workpiece is turned on a lathe whose mechanical efficiency $=$

$0\mathrm{.}87.$ Cutting speed $=400f\frac{t}{m}in,$ feed $=0\mathrm{.}011i\frac{n}{r}ev,$ and depth of cut $=0\mathrm{.}120in.$ Cutting force $=$

$250$ lb $.$ Determine $($a$)$ the horsepower consumed by the turning operation; $($b$)$ horsepower that must

be generated by the lathe; $($c$)$ unit horsepower and specific energy for the work material in this

operation.