The Merchant circle diagram showing various forces associated with a cutting process using a wedge shaped tool is given in the Figure

The coefficient of friction can be estimated from the ratio

In a machining operation with turning tool, the tool life $$(T)$$ is related to cutting speed $$v$$ $$(m/s),$$ feed $$f(mm)$$ and depth of cut $$d(mm)$$ as $$$T = C\,v{\,^{ - 2.5}}\,{f^{ - 0.9}}\,{d^{ - 0.15}}$$$
where, $$C$$ is a constant. The suggested values for the cutting parameters are: $$V=1.5$$ $$m/s,$$ $$f=0.25$$ $$mm$$ and $$d=3$$ $$mm$$ for normal rough turning. If the operation is performed at twice the cutting speed and the other parameters remain unchanged, the corresponding percentage change in tool life is ______________.

A $$60$$ $$mm$$ wide block of low carbon steel is face milled at a cutting speed of $$120$$ $$m/min,$$ feed of $$0.1$$ $$mm$$/tooth and axial depth of cut of $$4$$ $$mm.$$ A schematic representation of the face milling process is shown below. The diameter of the cutter is $$120$$ $$mm$$ and it has $$12$$ cutting edges. The material removal rate (in $$m{m^3}/s)$$ is __________

A cylindrical bar of $$100$$ $$mm$$ diameter is orthogonally straight turned with cutting velocity, feed and depth of cut of $$120$$ $$m/min$$, $$0.25$$ $$mm/rev$$ and $$4$$ $$mm,$$ respectively. The specific cutting energy of the work material is $$1 \times {10^9}\,\,J/{m^3}.$$ Neglect the contribution of feed force towards cutting power. The main or tangential cutting force (in $$N$$) is __________________