Figure $2$: Crane with mass.

Question $2.$ The structure shown in Fig. $2$ is a crane, it is supported at $\backslash ($ A $\backslash )$ with a fixed base i$.$e fixed support. Given that the force in the crane's cable $\backslash ($ B C $\backslash )$ is $\backslash (\backslash$mathbf$\{$F$\}=105\mathrm{.}0\backslash$mathrm$\{$kN$\}\backslash ).$

The crane has two arms as well, of particular interest is the shorter crane arm which is $4$ m $-$long as shown. The weight of the crane arms can be neglected.

The counterweight $($labelled $\backslash ($ D $\backslash ))$ has a mass of $\backslash ($ m $\backslash )$ and it acts at $0\mathrm{.}5$ m from the end of the shorter crane arm. Take note of the coordinate system and all the dimensions and parameters. Thus, attempt the following:

$($a$)$ Determine the mass $\backslash ($ m $\backslash )$ of the counterweight such that the support moments in any component direction $($at $\backslash ($ A $\backslash ))$ vanish.

$($b$)$ Using your answer in $($a$),$ compute all the other support reactions at $\backslash ($ A $\backslash ).$