$(1)$

$P=650N$

${\displaystyle \underset{?}{\overset{?}{}}}{F}_y=0=C_y-800$

$C_4=800N$

$(2)$

$C=\sqrt[\phantom{2}]{(C_x{)}^2+(y_y{)}^2}=\sqrt[\phantom{2}]{(1540{)}^2+(800{)}^2}$

$C=1753\mathrm{.}17N$

${\displaystyle \underset{?}{\overset{?}{}}}{m}_C=0=F_{AB}(125)-650(300)$

$F_{AB}=1560N$

${\displaystyle \underset{?}{\overset{?}{}}}{F}_x=0=Cx-F_{AB}=>0=Cx-1560$

$Cx=1560N$

$(3)J=\frac{c{l}_2}{A_{\text{p}\text{i}\text{n}}}$

$40=\frac{1753\mathrm{.}17}{2(\frac{}{4})d_e^2}$

$d^2=27\mathrm{.}9$

$d=5\mathrm{.}28mm$

#$9$

$(1)C_E=\sqrt[\phantom{2}]{{300}^2+{125}^2}=325mm$

$(2){}_b=\frac{C}{A_b}=\frac{C}{dxt}=\frac{1690(N)}{(6{10}^{-3})(9{10}^{-3})}$

${\displaystyle \underset{?}{\overset{?}{}}}{F}_3=0=\frac{125}{325}C-P$

$C=\frac{325}{125}=2\mathrm{.}6(600)$

$C=1690W$