Problem #$5$:

Determine the maximum constant speed at which the pilot can travel around the vertical curve having a radius of curvature $=800m,$ so that he experiences a maximum acceleration $a_n=8g=78\mathrm{.}5\frac{m}{s^2}.$ If he has a mass of $70$ kg $,$ determine the normal force he exerts on the seat of the airplane when the plane is traveling at this speed and is at its lowest point.

Problem #$6$:

A $0\mathrm{.}5-kg$ block B slides without friction inside a slot cut in arm OA which rotates in a vertical plane. The rod has a constant angular acceleration of $10ra\frac{d}{s^2}.$ Knowing that when $=45$ and $r=0\mathrm{.}8m$ the velocity of the block is zero, determine at this instant:

$($a$)$ the force exerted on the block by the arm

$($b$)$ the relative acceleration of the block with respect to the arm.