Cables AB and AC can sustain a maximum tension of 600 N....

Cables AB and AC can sustain a maximum tension of 600 N. Determine the maximum weight of the lamp that can be supported in the position shown, if the force in the pole is given as $F_{AO} = 400$ N. The force in the pole acts along the axis of the pole. Use Cartesian Vector Notation (CVN). Show Free body diagrams and all calculations.

A weight $W$ is supported by attaching it to a vertical uniform metal pole by a thin cord passing over a pulley having negligible mass and friction. The cord is attached to the pole 40.0 cm below the top and pulls horizontally on it ($\textbf{Fig. P11.78}$). The pole is pivoted about a hinge at its base, is 1.75 m tall, and weighs 55.0 N. A thin wire connects the top of the pole to a vertical wall. The nail that holds this wire to the wall will pull out if an $outward$ force greater than 22.0 N acts on it. (a) What is the greatest weight $W$ that can be supported this way without pulling out the nail? (b) What is the $magnitude$ of the force that the hinge exerts on the pole? Figure E11.78 (CAN'T COPY THE FIGURE)

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