Example $5\mathrm{.}3$ A $3$ kN crate is supported by the rope and pulley arrangement shown in Figure

$5\mathrm{.}8($a$).$ Determine the magnitude and the direction of the minimum force $F$ that should be exerted

at the free end of the rope.

$($a$)$

Figure $5\mathrm{.}8$ Example $5\mathrm{.}3.$