Question $3[10$ marks$]$

a$)$ A lead screw is being used on a lathe machine to advance the carriage of the lathe in time with the rotation of the spindle. The screw has an effective diameter of $45$ mm and a lead $5$ mm $.$ the screw must exert an axial thrust of $1\mathrm{.}0$ KN for driving the carriage. An effort of $50$ N is required to create the movement. Calculate the operating efficiency of the lead screw.

$[5$ marks$]$

b$)$ A jackscrew is used to raise and lower a $100-kg$ block as shown in below figure. The screw has a pitch $P=10mm,$ mean radius $r=8mm,$ and is single$-$threaded. The coefficient of static friction between the screw and the supporting thread of the base is $=0\mathrm{.}30.$ Determine the operating efficiency of the screw.

$[5$ marks$]$H