In a machining experiment, tool life was found to vary with the cutting speed in the following manner

What is percentage increase in tool life when the cutting speed is halved.

In a single point turning tool, the side rake angle and orthogonal rake angle are equal. $$\varphi $$ is the principle cutting edge angle and its range is $$0$$ to $$90.$$ The chip flows in the orthogonal plane. The value of $$\varphi $$ is closer to

Orthogonal turning is performed on a cylindrical work piece with shear strength of $$250Mpa.$$ The following conditions are used: cutting velocity is $$180m/min,$$ feed is $$0.2mm/rev,$$ depth of cut is $$3mm,$$ chip thickness ratio is $$0.5.$$ The orthogonal rake angle is $$7deg.$$ Apply Merchants theory for analysis,

The shear plane angle (in degrees) and the shear force respectively are

Orthogonal turning is performed on a cylindrical work piece with shear strength of $$250Mpa.$$ The following conditions are used: cutting velocity is $$180m/min,$$ feed is $$0.2mm/rev,$$ depth of cut is $$3mm,$$ chip thickness ratio is $$0.5.$$ The orthogonal rake angle is $$7deg.$$ Apply Merchants theory for analysis,

The cutting and frictional forces respectively are