Problem $1$: A $300-$mm$-$wide strip with a thickness of $30$ mm is fed through a rolling mill with two powered rolls,

each of radius $=350$ mm$.$ The work thickness is to be reduced to $25$ mm$.$ The work material has a flow curve

defined by K $=300$ MPa and n $=0\mathrm{.}22,$ and the coefficient of friction between the rolls is assumed to be $0\mathrm{.}14.$

$($i$)$ Demonstrate that the thickness of the plate can be reduced in one step $($considering friction$).$

$($ii$)$ Calculate the average rolling force of the rolling operation.