Two cutting tools are being compared for a machining operation. The tool life equations are:
$$\eqalign{ & \,\,\,\,\,\,\,\,\,\,\,\,Carbi{\mathop{\rm de}\nolimits} \,\,tool:\,\,\,\,\,\,\,\,\,\,\,\,V{T^{1.6}} = 3000 \cr & \,\,\,\,\,\,\,\,\,\,\,\,HSS\,\,tool:\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,V{T^{0.6}} = 200 \cr} $$

Where $$V$$ is the cutting speed in $$m/min$$ and $$T$$ is the tool life in $$min.$$ The carbide tool will provide higher tool life if the cutting speed in $$m/min$$ exceeds

Details pertaining to an orthogonal metal cutting process are given below.

Chip thickness ratio $$0.4$$
Under formed thickness $$0.6mm$$
Rake angle $$ + {10^0}$$
Cutting speed $$2.5m/s$$
Mean thickness of primary shear zone $$25microns$$

The shear strain rate in $${s^{ - 1}}$$ during the process is

Following data refers to an automat and a center lathe, which are being compared to machine a batch of parts in a manufacturing shop

Automat will be economical if the batch size exceeds

In orthogonal turning of a bar of $$100$$ $$mm$$ diameter with a feed of $$0.25$$ $$min/rev,$$ depth of cut of $$4$$ $$mm$$ and cutting velocity of $$90$$ $$m/min,$$ it is observed that the main (tangential) cutting force is prependicular to the friction force acting at the chip-tool interface. The main (tangential) cutting force is $$1500$$ $$N.$$

The orthogonal rake angle of the cutting tool in degree is