Please use shigleys mechanical design book to answer.

$5-$Screw Design for Swivel Hook

The steel crane hook as shown in the following figure is rated at P$=3$kN$.$

The ball$-$thrust bearing allows rotation of the hook for positioning the load. The lower race of the bearing

and a third $($bottom$)$ ring have matching spherical surfaces to allow self$-$alignment of the hook with the

bearing load. Usually, bearing size selected for a given load and service has internationally standardized

dimensions.

Both the threaded portion of the shank or bolt and the nut are made of M$12$ xx$1\mathrm{.}75$ class $5\mathrm{.}8$ rolled coarse

threads. A stress concentration factor of K$\_($t$)=3\mathrm{.}5$ and a safety factor of n$=5$ are used for threads.

h$.$ Determine the necessary nut length L$\_($n$).$