Consider the system shown in $($Figure $1).$

Figure$1$ of $1$

An assembly consisting of a curved rod and a cable is shown in the x y z space. The curved rod $\text{'}$A$\text{'}$ C has the shape of a $60$ degree arc of a circle with a radius of $5$ feet and the center at the origin. Point C is located at a distance of $5$ feet from the origin on the positive z axis. Point $\text{'}$A$\text{'}$ is located in the first quadrant of the y z plane. Point B is located in the first quadrant of the x y plane, $7$ feet from the positive x axis and $6$ feet from the positive y axis. A force is applied to the rod at point $\text{'}$A$\text{'}$ and is directed along the cable $\text{'}$A$\text{'}$ B toward point B$.$

Part A

Determine the smallest force F

that must be applied along the rope in order to cause the curved rod, which has a radius of $5$ ft

$,$ to fail at the support C

$.$ This requires a moment of M

$=90$ lb$$ft

to be developed at C

$.$

Express your answer to three significant figures and include the appropriate units.