The jack shown is designed to lift small unit$-$body cars. The screw is threaded into the collar pivoted at $B,$ and the shaft turns in a ball thrust bearing at $A.$ The thread has a mean diameter of $10$ mm and a lead $($advancement per revolution$)$ of $2$ mm $.$ The coefficient of friction for the threads is $0\mathrm{.}20.$ Determine the force $P$ normal to the handle at $D$ required to

$($a$)$ raise a mass of $500$ kg from the position shown, and

$($b$)$ lower the load from the same position. Neglect friction in the pivot and bearing at A$.(1$

: The square$-$threaded screw use in jack for lifting cars