Q$6.$ In upsetting a cylindrical workpiece, the average die$-$pressure formula under dry friction is given by Eq$.(5\mathrm{.}72)$ on Page $275$ in the textbook. This equation can be expanded and truncated to give Eq$.(5\mathrm{.}72$a$).$

$($a$)$ Derive the equation.

P$\_($av$)=$Y$(1+(2\backslash$mu R$)/(3$h$))$

$($b$)$ Write the formula for force F required for this operation. Use the average pressure given by Eq$.(5\mathrm{.}72$a$).$