Two cutting tools with tool life equations given below are being compared:
$$\eqalign{ & Tool\,\,1:\,\,\,\,\,\,\,V{T^{0.1}} = 150 \cr & Tool\,\,2:\,\,\,\,\,\,\,V{T^{0.3}} = 300 \cr} $$
where $$V$$ is cutting speed in $$m/minute$$ and $$T$$ is tool life in minutes. The breakeven cutting speed beyond which Tool $$2$$ will have a higher tool life is _______________ $$m/minute$$.

The too life equation for $$HSS$$ tool is $$V{T^{0.14}}\,\,{f^{0.7}}\,\,{d^{0.4}} = $$ Constant. The tool life $$(T)$$ of $$30$$ $$min$$ is obtained using the following cutting conditions $$=45$$ $$m/min,$$ $$f=0.35mm,$$ $$d=2.0$$ $$mm.$$ If speed $$(V),$$ feed $$(f)$$ and depth of cut $$(D)$$ are increased individually by $$25\% ,$$ the tool life (in $$min$$) is

For a certain job, the cost of metal cutting is $$Rs.18C/V$$ and the cost of tooling is Rs.$$270C/(TV).$$ Where $$C$$ is a constant, $$V$$ is the cutting speed in $$m/min$$ and $$T$$ is the tool life in minutes. The Taylor's tool life equation is $$V{T^{0.25}} = 150.$$ The cutting speed (in $$m/min$$) for the minimum total cost is ___________

For an orthogonal cutting operation, tool material is $$HSS,$$ rake angle is $${22^ \circ },$$ chip thickness is $$0.8$$ $$mm,$$ speed is $$48$$ $$m/min$$ and feed is $$0.4$$ $$mm/rev$$. The shear plane angle (in degrees) is