In a pipe flange facing operation carried out on a lathe, the depth of cut is $12$ mm$,$ he inside and outside diameters of the flange are $250$ mm and $500$ mm$,$ respectively. The specific cutting energy of the work material is $2\mathrm{.}6$ GJ$/$m$3,$ the maximum rotational frequency of the lathe spindle is $6$ s$1,$ and the maximum feed that can be applied is $0\mathrm{.}25$ mm$.$ The major cutting edge angle of the tool is $6$ degrees. Find:

a$.$ The maximum power required for machining when the machine is operating at maximum capacity

b$.$ Thecuttingforce

c$.$ The machining time