Q$3.(30$ marks$)$

The weight $W=6kN$ in Figure Q $3$ can be raised by rotating the square$-$threaded screw of the automobile jack, causing joints A and C to move towards each other. The lead of the thread is $L=4mm,$ the mean diameter is $d=8mm,$ and the coefficient of static friction is $=0\mathrm{.}2.$

$($a$)$ Determine the force $P$ required to raise the load when $=30.$

$[12]$

$($b$)$ Is the jack self$-$locking?

$[3]$