A screw jack as shown in Figure uses a single square$-$thread screw to raise a load of $50$ kN$.$ The screw has a major diameter of $36$ mm and a pitch of $6$ mm$.$ The thrust collar mean diameter is $80$ mm$.$ Running friction coefficients are estimated to be $0\mathrm{.}12$ for the screw and $0\mathrm{.}09$ for the collar: a$)$ Determine the thread depth and helix angle. b$)$ Estimate the starting torque for raising and lowering the load. Is it self$-$locking? c$)$ Estimate the efficiency of the jack for raising the load. d$)$ Estimate the power required to drive the screw at a constant speed of one revolution per second. e$)$ Estimate the handle length $($a$)$ required to raise the load if the average human hand force is $200$ Newton. Comment on your result. f$)$ Find different stresses applied to the screw thread.