First, it should be mentioned that there is no such force called centripetal force, it is just Newton’s second laws being applied differently, we just call this scenario as such to help classify the what is happening. Centripetal force is the feeling of a body being propelled forward but is halted by an obstruction, then continues on a path and is pushes against it. Same thing happens in a car when you make a turn.  You are traveling the same velocity as the car, but when it turns you are still moving forward. You are then halted by either the door or seat belt, which stops you. When this happens you get the feeling of being pushed against the surface or to the outer edge of the car. This same concept is applied to coasters as the coaster enters a loops and banked turns.

In a loop, designers aim to make the rider feel somewhat weightless when in the cart, but still have enough velocity to push the riders against the seat to prevent the feeling of falling out. You wouldn’t want to scare all your costumers with the fear of falling out of their seat during a ride. To do this, they make it so that the normal force between the coaster and the track is equal. This gives the feeling of weightlessness as your body is flying upwards and gravity tries to pull you down but nothing happens as the forces are equal. They make it so that there is enough force on you to be pushed against the seat to prevent a complete feeling of falling, but still weightless. This is also used on the tops of hills to give the same feeling.

Another use of this is on banked turns. Banked turns use this idea to allow the coaster to turn gently without creating the feeling of  being flung out due to the high speeds. This can be seen on roads where ice and rain are frequent. As a car reaches a sharp turn, ice and water will cause cars to slide off the road due to the lack of friction and the car wanting to continue forward. By banking the road slightly, the car will press against the road from centripetal forces rather than against nothing, which would lead to sliding off the road. Banked turns create less stress for the rider and the coaster as it is easier to turn than on a horizontal turn.