Problem $2(20$ points$)$

Several tool life tests were performed on a steel workpiece in a lathe, resulting in the following data: at a

cutting speed of $152\frac{m}{m}in,$ the tool life was found to be $121\mathrm{.}84$ mins ; then, when the cutting speed was

changed to $172\frac{m}{m}in,$ the tool life was found to be $74\mathrm{.}31$ mins.

$($a$)$ Determine the n and C values in the Taylor tool life equation.

$($b$)$ Based on the n and C values you found, what is the likely material of the cutting tool used in these

tests?

$($c$)$ Using your Taylor tool life equation, compute the tool life that corresponds to a cutting speed of $130$

$\frac{m}{m}in.$

$($d$)$ Using your Taylor tool life equation, compute the cutting speed needed for a tool life of $100$ mins.