The cutting tool are being tried for an operation. Tailors tool life equation for them are as follows
$$\eqalign{ & HSS\,\,tool\,:\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,V{T^{0.1}} = 200 \cr & Carbide\,\,tool\,:\,\,\,\,\,\,\,V{T^{0.35}} = 500 \cr} $$
Find out the break even speed above which the carbide tool will be economical.

The following data is available for machining a component on a turret or center lathe: find out the total number of components to be machined to justify the use of turret lathe

In an orthogonal cutting test on the following data were obtained
Uncut chip thickness $$=0.25mm,$$ Cutting speed: $$60m/min,$$ Tool rake angle: $$0$$ Chip thickness $$0.75mm,$$ Cutting force : $$900$$ $$N$$, Thrust force : $$450$$ $$N$$

Calculate the shear angle, total power in making the cut and coefficient of friction between the chip tool interface.

In a turning operation the tool life of the carbide tool was found to be $$20min$$ and $$100min,$$ at cutting speeds of $$120m/min$$ and $$80m/min$$ respectively. What will be the tool life of the tool under same condition but at a cutting speed of $$100m/min.$$