Question $3.$

$3\mathrm{.}1$ A shaft, $250$ mm in diameter, is revolving in a bearing and exerting a force of $75$ kN on the bearing. The coefficient of friction between the shaft and the bearing is $0,02$ and the shaft rotates at $\backslash (350\backslash$mathrm$\{$r$\}/\backslash$mathrm$\{$min$\}\backslash ).$ Calculate the power lost due to friction.

$3\mathrm{.}2$ When a work piece, $75$ mm in diameter, is machined on a lathe, the cutting force applied to the cutting tool is $2500$ N $.$ Assume that $\backslash (15\backslash$mathrm$\{$~N$\}.\backslash$mathrm$\{$m$\}\backslash )$ of torque is lost due to friction in the bearings of the lathe spindle. Calculate the following:

$3\mathrm{.}2\mathrm{.}1$ The torque needed at the driving pulley of the lathe.

$3\mathrm{.}2\mathrm{.}2$ The driving force at the driving pulley of the lathe if it has an effective diameter of $250$ mm $.$

$3\mathrm{.}2\mathrm{.}3$ The power needed at the driving pulley of the lathe if it rotates at $\backslash (275\backslash$mathrm$\{$r$\}/\backslash$mathrm$\{$min$\}\backslash ).$

$3\mathrm{.}3$ The ram of a shaper has a mass of $200$ kg and is moving in slides. The coefficient of friction between the ram and the slides may be taken as $0,08.$ Calculate the following:

$3\mathrm{.}3\mathrm{.}1$ The horizontal force needed to move the ram.

$3\mathrm{.}3\mathrm{.}2$ The coefficient of friction if the force, which is moving the ram, reduced by $\backslash (25\backslash \%\backslash ).$