Energy cannot be created or destroyed, but it can be converted from one form to another. For the idealized roller coaster, all energy is conserved through conservative forces, such as gravity. As the train accelerates down the lift hill, potential energy is converted into kinetic energy. When the train ascends another hill, the kinetic energy is converted into potential energy again. This is conservation of mechanical energy, and it continues throughout the entire ride. The total mechanical energy for the train is shown by the equation:
Where E is the total mechanical energy, K is kinetic energy, and U is potential energy. From this, the equation for conservation of total mechanical energy can be derived:
Ei
= Ef
or
Ki
+ Ui = Kf + Uf
Where Ei
is total initial mechanical energy and Ef is total final
mechanical energy. This shows that the
total initial mechanical energy equals the total final mechanical energy for
the system. It is because of this
phenomenon that a roller coaster is called a “coaster.” After the initial input of energy to carry
the train up the lift hill, the roller coaster simply coasts through the rest
of the ride.
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Physics