This Demonstration illustrates the concept of conservation of energy using a model of a frictionless roller coaster. The height and velocity of the ball dynamically change so that the total of the initial potential and kinetic energy in the system equals the total of the final potential and kinetic energy in the system.
You can change the initial height, initial velocity, mass of the ball, and the radius of the loop. To watch an animation of the ball as it rolls along the roller coaster, open the "time" control and click on the "play" button.
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