Orthogonal machining of a steel work-piece is done with a $$HSS$$ tool of zero rake angle. The ratio of the cutting force and the thrust force on the tool is $$1:0.372.$$ The length of cut chip is $$4.71$$ $$mm$$ while the uncut chip length is $$10$$ $$mm.$$ What are the shear plane angle $$\phi $$ and friction angle $$\beta $$ in deg.? Use Merchant's theory.

Two different tools $$A$$ and $$B$$ having nose radius of $$0.6mm$$ and $$0.33mm$$ respectively are used to machine $$C-45$$ steel employing feed rate of $$0.2$$ $$mm/rev$$ and $$0.1mm/rev$$ respectively. The tool that gives better finish and the value of ideal surface roughness are

A $$60deg$$ symmetrical $$V$$ tool is used in shaping a work piece with a depth of cut of $$0.1$$$$mm$$ and feed of $$0.1mm/stroke$$. The theoretical peak to valley height, in $$mm,$$ of the surface produced is

The heat generated in metal cutting is dissipated in different proportions into environment, tool, chip and work-piece. The correct order of this proportion in decreasing magnitude is (no cutting fluid is use ($$d$$)