If under a condition of plain turning the life of the cutting tool decreases by $$50\% $$ due to increase in the cutting velocity by $$20\% $$, then what is the $$\% $$ increase in tool life due to reduction in the cutting velocity by $$20%$$ from its original value.

A single point cutting tool made of $$HSS$$ has the value of constant $$'C'$$ $$80,$$ and $$n=0.2$$ in the basic tool life equation. If the tool cost per regrind is Rs $$2$$ and the vmachine hour rate is Rs. $$30,$$ determine the most economical cutting speed (tool cost includes the cost of time spent on changing.

A mild steel block of width $$40$$ $$mm$$ is being milled using a straight slab cutter $$70mm$$ diameter with $$30$$teeth. If the cutter rotates at $$40$$$$rpm$$ and the depth of cut is $$2mm,$$ determine the value of maximum uncut chip thickness when the table feed is $$20mm/min$$

In an orthogonal cutting operation on a work piece of width $$2.5mm,$$ the uncut chip thickness was $$0.25$$ $$mm$$ and the tool rake angle was $$0$$(zero) degrees. It was observed that the chip thickness was $$1.25mm.$$ The cutting force was measured to be $$900N$$ and the thrust force was found to be $$450N.$$ Find the mean shear strength of the work piece material and if the coefficient of friction between the chip and the tool was $$0.5,$$ what is the machining constant.