ENERGY
Roller coasters are based on some pretty simple physics, and for most of their route rely on just one form of fuel: gravity. As a roller coaster begins its ride, it is hauled up an incline by an ordinary chain drive. This introduces potential energy into the system. At the top of the incline that energy is released simply by pushing the train forward and allowing it to roll downhill. People sometimes ask why roller coaster designers always put the biggest hill at the beginning of the course, but this is the only way to build up enough speed for the whole ride. On any roller coaster, every hill will always be smaller than the one before it, since energy declines the farther you go.
During this first climb, the coaster gains a form of energy called potential energy. Energy that is "stored" based on raising an object through some distance. The higher the lift, the greater the potential energy gained. The potential energy PE depends on the mass of the object, m, how high the mass is, h, and the earth's gravity, g, which is a constant value.
When we allow the coaster to fall under gravity, ideally all the potential energy released during the fall (drop) is converted to kinetic energy which builds up the train's speed and momentum.When the coaster begins to move down the first slope, its potential energy changes into kinetic energy. Kinetic energy has to do with how fast the coaster goes. The faster the speed (velocity), the greater the kinetic energy. The kinetic energy depends on the mass of the coaster, m, and the speed that the coaster is moving at, v.
You can't see either type of energy. You can see only how high the coaster is and how fast it travels. Still, the idea of energy can be useful for the following reason: The total of the two types of energy stays the same for the whole trip.
In accordance with the principle of conservation of energy some of the kinetic energy acquired by each drop in height is re-converted back to potential energy as the train ascends the subsequent hill.
When the coaster descends, the potential energy decreases. Since the total energy must stay the same, that means that the kinetic energy must increase so the coaster moves faster.
When the coaster climbs, its potential energy increases. To keep the total energy the same, the kinetic energy must decrease so the coaster slows down.
Exactly why is a ride on a "good" coaster so scary? One reason is height. Another reason is speed. You plummet down the hills. You don't move quite so swiftly up the hills, however. Your speed changes during the ride. Why? One explanation involves energy. The coaster has no energy to start with. In order to get up that first big hill, called the lift, the coaster has to be dragged by a motor-driven chain. We provide energy (from an electric motor or engine) to raise the mass of the train from ground level to the top of the rollercoaster lift hill thus increasing its potential energy.
Pulled by gravity alone, roller coasters can attain speeds as high as 80 miles per hour, which is 25 miles per hour faster than you should travel in a Chevy Chevette, let alone in a sort of Flexible Flyer on rails.
In this imperfect world energy losses from deformation of the wheel tires, friction in the wheel bearings, air drag and headwinds take their toll robbing the train of some of its kinetic energy causing it to run slower than the theoretical maximum speed.
A well designed coaster will always have some left over kinetic energy even under the most unfavorable conditions so this is converted to thermal energy by trim brakes and the station brake-run at the end of the ride. Incidentally these final brakes often forcefully remind us of Newton's third law of motion -- "to every action there is an equal and opposite reaction"!