The law of conservation of energy maintains that the total mechanical energy of a roller coaster is constant throughout its ride, as potential energy is converted to kinetic energy while descending, and kinetic to potential while ascending.
When analyzing the potential and kinetic energy on a roller coaster, we apply the principles of the law of conservation of energy, which states that in a closed system, the total energy remains constant. If we denote the initial position at the top of the first rise with subscript 1, and the final position with subscript 2, we express this law as PE1 + KE1 = PE2 + KE2, where PE is potential energy and KE is kinetic energy.
At the top of the first rise, the roller coaster has maximum gravitational potential energy due to its height, and minimum kinetic energy since it's moving slowly. As the coaster descends, its potential energy is converted to kinetic energy, increasing its speed. At the bottom, the kinetic energy is at its maximum, and as it ascends the next rise, kinetic energy is transformed back into potential energy, slowing the coaster down.
This exchange is ongoing throughout the ride, with energy continuously converting from potential to kinetic and vice versa, but the total mechanical energy remains constant, presuming no loss to friction or other forces.