In machining tests it was found that for a particular material, the

following relation applied:

$2+-{}_{n_e}=\frac{}{2}$

Also, when the rake angle ${}_{n_{}}$ was $20$ degrees, the coefficient of friction

was $1\mathrm{.}2.$

a$.$ What would the chip thickness be if in a turning operation the feed

was $0\mathrm{.}15$ mm and the major cutting$-$edge angle was $60$ degrees?

b$.$ If the cutting force is limited to $3$ kN and the specific cutting energy

of the work material is $2G\frac{J}{m^3}$ what maximum depth of cut can

be taken?