Problem $2(50\%)$

A retangular door weighted $W=500N$ is hinged at one vertical side $($ z $-$axis$).$ A couple $F=+200$i and $F=-200i$ is applied at D and C$.$ To achieve equilibrium, a rope under a tension $T$ is connected to A and B $.$

$($a$)$ Draw a free body diagram of the door, the two ropes and supports at A$.(10\%)$

$($b$)$ Find the angle $$ between the rope and the door edge BC$.(5\%)$

$($c$)$ Write down the vector $W$ and its moment about the hinge. $(5\%)$

$($d$)$ Find the vector moment due to the couple and its component about the hinge. $(10\%)$

$($e$)$ Find the vectors force $T$ with both magnitude and direction. $(10\%)$

$($f$)$ Find the vectors force and moment supported by the hinge. $(10\%)$