$13\mathrm{.}12$ A cold heading operation is performed to produce the head on a steel nail. The strength copfficient for this steelis $600$ MPa $,$ and the strain hrerdening exponent is $0\mathrm{.}22.$ Coefficient of friction at the die$-$work interface is $0\mathrm{.}14.$ The wire stock out of which the nail is made is $5\mathrm{.}00$ mm in diameter. The head is to have a diameter of $9\mathrm{.}5$ mm and a thictrness of $1\mathrm{.}6$ mm $.$ The final length of the nailis $120$ mm $.($a$)$ What length of stook mustproject out of the die in order to provide sufficient volume of material for this upsetting operation? $($b$)$ Compute the maximum force that the punch must apply to form the head in this open$-$die operation, ram presaure, $($e$)$ ram force, and $($f$)$ power if the ram speed $=20i\frac{n}{m}in.$