Final answer:
In Physics, each successive hill on a roller coaster is shorter due to gradual energy loss through air resistance and mechanical friction, ensuring sufficient energy for the coaster to complete its course without stopping.
Step-by-step explanation:
The subject of the question is Physics, specifically dealing with the concepts of gravitational potential energy (GPE) and kinetic energy (KE) in the context of roller coasters. This Physics problem is at a High School level, examining energy conversion and the effects of friction in mechanical systems like roller coasters.
When a roller coaster is hauled to the top of the first peak, it accumulates a significant amount of gravitational potential energy. This energy is converted to kinetic energy as the coaster descends, reaching maximum speed at the lowest points of the ride. The reason subsequent hills are shorter is that some energy is lost to factors like air resistance and mechanical friction - albeit relatively small - and thus not all the potential energy can be converted back to kinetic energy. Hence, each successive hill must be shorter to ensure the roller coaster has enough energy to continue without stopping.
According to the law of conservation of energy, in a closed system - with no external work being done and no non-conservative forces like friction - the total mechanical energy remains constant. However, as a roller coaster progresses along its track, energy is gradually lost to the environment, necessitating shorter hills to compensate for these small losses and to maintain the motion of the coaster.