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Potential and Kinetic Energy
The Law of Conservation of Energy states that the total energy of an isolated system is constant despite it's internal changes. This means that the total energy at the beginning of the roller coaster ride should be equivilent to the energy at the end.
At the beginning of the ride, all of the coasters energy is potential energy, or Ep. An object potential energy can be found using the equation Ep=MxHxG.
At the bottem of the first hill, all of the coasters energy is kinetic, or Ek. AN object's kinetic energy can be founf by using this equation: Ek= (1/2)MxVxV
As the law of convervation of energy states, the energy of the coaster stays the same. Thus, at any point, both potential and kinetic energy must be taken into consideration in order to find the total energy. The equation for is is Et=Ep+Ek, or (MxGxH)+(1/2MxVxV)=MxGxH)+(1/2MxVxV). Thus, to find the total energy of an object you need to know it's mass, height and velocity.
In the picture above, the black star represents the place where the coaster has only potential energy. The orange star is where the coaster only has kinetic energy, and the red is where it has a combination of both.
