Consider Example 4.A.9 from the course lecture book. This problem deals with the NASA near-weightless training aircraft exercises for simulating the weightless environment for astronauts. (Due to the experiences of those in training, these training aircraft are nicknamed “Vomit Comets”.)

Shown below is the dynamic analysis of a passenger on this aircraft for predicting the apparent “weight” of the passenger of mass “m” as the aircraft passes the  maximum point of its path during this maneuver. At this point, the mg of the passenger is cancelled out by the influence of the mass times the centripetal component of acceleration when the radius of curvature of the path is less than v²/g. When this occurs, both the passenger is in a state of “free fall”, reducing the normal force on the passenger by the aircraft to zero. This state of weightlessness by the passenger can exist over a range of positions if the path taken by the aircraft is the parabolic-shaped trajectory of freefall.

The following video is provided by Zero Gravity Corporation of passengers riding on the Vomit Comet aircraft when the aircraft is near the maximum point of its path.