Note: This problem is optional and not graded. It is not part of the homework set and does not carry any points. It involves

polar coordinate systems.

The hollow tube is pivoted about a horizontal axis through point $O$ and is made to rotate in the vertical plane with a constant

counterclockwise angular velocity ${}^{}=5ra\frac{d}{sec}.$ If a $3-$lbs particle is sliding in the tube toward $O$ with a velocity of $1\mathrm{.}7$

$f\frac{t}{sec}$ relative to the tube when the position $=40$ is passed, calculate the magnitude $N$ of the normal force exerted by the