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Roller Coasters and Math



          In this diagram, as the ball is moving up the hill its gradually gaining potential energy. Once it goes over the top, gravity allows it to gain velocity and it begins a free-fall. As it rounds the curve, centripetal acceleration allows it to gain even more velocity. Once it reaches the first loop, acceleration stress slows it down. However, when it reaches the top of the loop, centrifugal force (the force that drives a moving body away from the center of rotation) adds to the cars kinetic energy, allowing it to make it back to the station where friction brings it to a stop. Without all of the angles being exactly as they are, or all of these forces acting on it, the car would not be able to make it back to the station.