$3\mathrm{.}1$ A cylindrical part is upset$-$forged in an open die. The starting diameter $=55mm$ and height $=60mm.$ Height after forging $=40mm.$ Coefficient of friction at the die$-$work interface $=0\mathrm{.}26.$ Yield strength of the low$-$carbon steel $=105$MPa; its strength coefficient $=550$MPa and strain$-$hardening exponent $=0\mathrm{.}26.$ Determine the force in the operation

$3\mathrm{.}1\mathrm{.}1$ just as the yield point is reached $($yield at strain $=0\mathrm{.}002),$

$3\mathrm{.}1\mathrm{.}2$ at a height of $50mm,$ and

$3\mathrm{.}1\mathrm{.}3$ at a height of $40mm.$ Use of a spreadsheet calculator is recommended.