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**Conservation of Energy**

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:

## E = K + U

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:

E_{i}_{
}= E_{f}

or

K_{i}_{
}+ U_{i}_{ }= K_{f}_{ }+ U_{f}

Where E_{i}
is total initial mechanical energy and E_{f} 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.

**Friction**

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**Back to Roller Coaster
Physics**