C$$mo resolver...

Problems:

A screw jack uses a power screw with square thread to lift a weight $W.$ The single$-$threaded screw has a nominal diameter of $1\mathrm{.}25$ inch and $4$ threads per inch. A plain thrust collar with a diameter of $dc=1\mathrm{.}5$ in is used. The friction coefficients for the running threads and the collar are estimated as $f=0\mathrm{.}12$ and $f_c=0\mathrm{.}09,$ respectively. A force $200$ lb is applied on the handle with an arm distance of $a=2\mathrm{.}5in.$ Determine:

a$)$ The maximum weight $W$ that can be lifted.

b$)$ The lifting speed if the handle is rotated at $0\mathrm{.}5re\frac{v}{s}.$

c$)$ The efficiency of the power screw.