A double$-$threaded Acme power screw is used to raise a $2500-$lb load. The outer diameter of the screw is $1\mathrm{.}25$ in$.$ and the mean collar diameter is $2\mathrm{.}0$ in$.$ The coefficients of friction are $0\mathrm{.}20$ for the thread and $0\mathrm{.}25$ for the collar. Determine the following:

$($a$)$ Required torque for raising and lowering the load. Ans. Tr $=1000$ in$-$lb$,$ Tl $=837$ in$.-$lb$.$

$($b$)$ Geometrical dimensions of the screw. Ans. l $=0\mathrm{.}4$ in$.,$ dp $=1\mathrm{.}14$ in$.,$ $=3\mathrm{.}19,$ $=14\mathrm{.}4.$

$($c$)$ Efficiency in raising the load. Ans. e $=15\mathrm{.}9\%\%.$

$($d$)$ Load corresponding to the efficiency if the efficiency in raising the load is $18\%.$ Ans. W $=2840$lb