$3.$ An ACME thread $\backslash (\backslash$left$(2\backslash$alpha$=29^\{\backslash$circ$\}\backslash$right$)\backslash )$ power screw carries a load of $2\mathrm{.}5$ KN $.$ The screw is single threaded that has a $6$ mm pitch, $30$ mm pitch diameter $\backslash$& mean diameter, $80$ mm collar diameter and the friction coefficient is $0\mathrm{.}05.$

$($a$)$ Determine if the screw is self$-$locked in the absence of collar friction.

$($b$)$ Find the torque and mechanical advantage if the load is lifted in the absence of collar friction.

$($c$)$ Net torque required to lift the load if collar friction is present.