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.

During orthogonal turning of a steel rod by zero rake tool at feed $$0.25mm/rev$$ and depth of cut $$2.0mm,$$ the following observations were obtained. Tangential component of cutting force $$=1000N$$, Axial component of cutting force $$=500N,$$ chip thickness $$=1.0mm,$$ with the help of diagram determine the yield shear strength of work material under the given cutting conditions.

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 $$100m/min.$$