Ignoring air resistance, the normal force acting on a person with mass m in an amusement park ride must equal what?

In the context of a person on an amusement park ride, particularly one that involves acceleration such as a roller coaster or a similar ride, the normal force is the reaction force exerted by the surface of the ride on the person. This force adjusts based on the acceleration experienced by the person.

When considering vertical circular motion or scenarios with acceleration, the normal force does not simply equal the weight of the person, which is represented by mg, the gravitational force acting on them. Instead, when the ride experiences additional acceleration, the normal force must account for both the gravitational force and the net acceleration of the person in the ride.

If the only forces acting on the person were the weight (mg) and the normal force, we would be in a state of equilibrium, leading to the normal force equaling mg. However, in an accelerating frame, the net force experienced by the person alters. For example, if the ride is accelerating upward, the normal force must be greater than mg to provide the net upward acceleration (ma), leading to the condition where the normal force is equal to mg + ma. If the ride were accelerating downwards, the normal force would be less than mg.

Thus, in the context of acceleration, the correct answer reflects that the