Do you think that mechanical energy will actually be conserved in the loop-the-loop
motion on the first car of the Viper roller coaster? Why or why not?
What data would you need to show that at least some of the forces on the roller coaster cars are non-conservative? Explain.
If the motion is performed in the absence of friction, then the mechanical energy (kinetic and potential energy) remains constant. This means that if you evaluate the sum of the potential and kinetic energies at some moment during the motion, it will be equal to the sum of the potential and kinetic energies at any other moment during the same motion.
Since the mechanical energy in a closed system is conserved, this means that the kinetic energy is converted to potential energy at some point along the motion path, and the potential energy is converted into kinetic energy at some other point along the path.
Hence, the evaluation of mechanical energy in the loop-the-loop motion does not depend on the path, but it depends on velocity of object and location of object with respect to a reference point of the path.