(Solved): The hollow tube is pivoted about a horizontal axis through point \( O \) and is made to rotate in ...

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 \( \dot{\theta}=3.7 \mathrm{rad} / \mathrm{sec} \). If a \( 0.17 \)-Ib particle is sliding in the tube toward \( O \) with a velocity of \( 4.2 \mathrm{ft} / \mathrm{sec} \) relative to the tube when the position \( \theta=28^{\circ} \) is passed, calculate the magnitude \( N \) of the normal force exerted by the wall of the tube on the particle at this instant.