A machine slide weighing $3000$ N is elevated by a double start acme threaded screw at the rate of $\backslash (840\backslash$mathrm$\{$~mm$\}/\backslash$mathrm$\{$min$\}\backslash ).$ If the coefficient of friction be $0\mathrm{.}12,$ calculate the power to drive the slide. The end of the screw is carried on a thrust collar of $32$ mm inside diameter and $58$ mm outside diameter. The pitch of the screw thread is $6$ mm and outside diameter of the screw is $40$ mm $.$ If the screw is of steel, is it strong enough to sustain the load? Draw a neat sketch of the system.

$[$Ans$.0\mathrm{.}165$ kW $]$