$50$ Points$)$ A turning cutting tool with a major cutting$-$edge angle of $90\backslash$deg and a minorcutting edge angle of $10\backslash$deg and rake angle of $10\backslash$deg is used on a $1$ kW lathe to turn a $50$ mmdiameter cast iron bar. Shear strength of cast iron may be assumed to be constantduring the cutting and equal to $410$ ksi and the maximum surface cutting speed that thetool can tolerate without overheating is $600$ m$/$min$.$ The friction coefficient betweenthe tool and machined chip is $0\mathrm{.}8.$The rod diameter is to be reduced over an axial length of $100$ mm within $1$ min.A$)$ What will be the width of cut or feed in this cutting operation? $(2)$B$)$ Assuming that the rod is machined at the maximum cutting velocity and minimumpower is required for the feed operation, what is the cutting force's magnitude? $(5)$C$)$ What will be the shear angle for this operation? State all the assumptions that youused to compute the shear angle? $(5)$D$)$ Compute the magnitude of shear force and normal force on the shear plane? $(5)$E$)$ Compute the magnitude of normal force and frictional force at chip$/$tool interface?$(5)$F$)$ Compute the normal force and resultant force being applied on the tool? $(5)$G$)$ Determine the depth of cut possible for the computed shear force and shearstrength? $(5)$H$)$ Compute the cutting ratio and chip velocity for this operation? $(5)$I$)$ Determine the power dissipated due to shear deformation and power dissipated dueto frictional sliding at the chip$/$tool interface? $(5)$J$)$ What is the minimum Ra $($in mm$)$ achievable for this cut? $(8)$