Roller Coaster on a Banked Turn (front view)
The physics that applies to this curve is related to the experience of centripetal force that the curve entails. Before the car enters the curve, the Fn (normal force) is equal and opposite to the force of weight on the rider. As the car enters the curve, the force needed to keep the rider in the curve grows greater in the horizontal direction, and therefore the Fn moves to point towards the center of the curve (it being a vector between weight and the centripetal force). The force horizontally is the greatest at the largest angle of the curve, and grows less as the rider leaves the curve. The horizontal component of the normal force provides the required centripetal force that keeps the rider in the circular path, while the vertical component opposes the weight and keeps the person from accelerating down.
In a roller-coaster, the idea of a banked turn, is to a) give the rider a more comfortable way of feeling the Fn that stops the persons body from entering straight-line motion once entering the curve, and b) to make the the rider feel more "g's". The forces that cannot be seen in the animation (because they are either in a view that is not possible to see, or that they are relatively insubstantial) are: the force of air friction on the rider, and the force of friction between the car and the rider.
by Eavan C.
