P$4\mathrm{.}15$ Gripper $\backslash ($ C $\backslash )$ of the industrial robot is accidentally subjected to a $60$ lb side load directed perpendicular to $\backslash ($ B C $\backslash )($Figure P$4\mathrm{.}15).$ The lengths of the robot's links are $\backslash ($ A B$=22\backslash )$ in$.$ and $\backslash ($ B C$=18\backslash$mathrm$\{$in$\}\backslash ).$ By using the moment components method, determine the moment of this force about the center of joint $\backslash ($ A $\backslash ).$

Figure $\backslash (\backslash$mathbf$\{$P $4.15\}\backslash )$

$\backslash (\backslash$qquad $\backslash )$

Details

An illustration shows a robotic arm, with a fixed end A $,$ a pivot B at the center of the arm, and a gripper C at the free end. The origin of the x y coordinate plane is at end A$.$ A force of $60$ pounds acts upward from the right on the gripper C$.$ The portion B C of the arm is at an angle of $40$ degrees relative to the portion $\backslash ($ A B $\backslash ).$ The portion $\backslash ($ A B $\backslash )$ is at an angle of $15$ degrees relative to the horizontal.