For a non-idealized roller coaster system, not all of the energy is conserved.  Friction is the main cause of energy leaks in the system and the reason why mechanical energy is not fully conserved for a real roller coaster.  This is because friction is a nonconservative force.  Nonconservative forces are forces that cause a change in total mechanical energy.  Friction opposes motion by working in the opposite direction.  The friction between the train and its tracks as well as between the train and the air take energy out of the system, slowing the train and creating both heat and sound.  This effect is most noticeable at the end of the ride as all remaining kinetic energy is taken out of the system though brakes.  Because of the energy leaks due to friction, each successive hill or loop on a roller coaster must be shorter than all the hills or loops previous to it, otherwise the train will not have enough energy to make it all the way over.



Centripetal Acceleration


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