<P> where U is potential energy, m is mass, g is acceleration due to gravity and h is height above the ground . Two trains of identical mass at different heights will therefore have different potential energies: the train at a greater height will have more potential energy than a train at a lower height . This means that the potential energy for the roller coaster system is greatest at the highest point on the track, or the top of the lift hill . As the roller coaster train begins its descent from the lift hill, the stored potential energy converts to kinetic energy, or energy of motion . The faster the train moves, the more kinetic energy the train gains, as shown by the equation for kinetic energy: </P> <P> K = 1 2 m v 2 (\ displaystyle K = (\ frac (1) (2)) mv ^ (2)) </P> <P> where K is kinetic energy, m is mass, and v is velocity . Because the mass of a roller coaster car remains constant, if the speed is increased, the kinetic energy must also increase . This means that the kinetic energy for the roller coaster system is greatest at the bottom of the largest downhill slope on the track, typically at the bottom of the lift hill . When the train begins to climb the next hill on the track, the train's kinetic energy is converted back into potential energy, decreasing the train's velocity . This process of converting kinetic energy to potential energy and back to kinetic energy continues with each hill . The energy is never destroyed, but is lost to friction between the car and track . Brakes bring the ride to a complete stop . </P> <P> When going around a roller coaster's vertical loop, the inertia that produces a thrilling acceleration force also keeps passengers in their seats . As the car approaches a loop, the direction of a passenger's inertial velocity points straight ahead at the same angle as the track leading up to the loop . As the car enters the loop, the track guides the car up, moving the passenger up as well . This change in direction creates a feeling of extra gravity as the passenger is pushed down into the seat . </P>

When does a roller coaster have the most kinetic energy