Why are all the hills in a roller coaster loop shorter in height than the first hill where it starts is first fall?
In most roller coasters, the hills decrease in height as the train moves along the track. This is necessary because the total energy reservoir built up in the lift hill is gradually lost to friction between the train and the track, as well as between the train and the air.
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Because of friction between the coaster cars and the track, along with air resistance as the cars move forward at high speed, the amount of mechanical energy available decreases throughout the ride. This is why the first hill must be always be tallest.
The total energy never goes up, only down, due to frictional losses, and so the maximum hill the cars can climb gets smaller and smaller. Putting a bigger hill later on will only make the roller coaster cars roll back down the way it came.
In most roller coasters, the hills decrease in height as the train moves along the track. This is necessary because the total energy reservoir built up in the lift hill is gradually lost to friction between the train and the track, as well as between the train and the air.
Energy conservationRollercoasters constantly shift between tapping into potential and kinetic energy. The kinetic energy gained when the train travels down the first hill – or fires out of the launch – gets it up the next, smaller hill.
Each gain in height corresponds to the loss of speed as kinetic energy (due to speed) is transformed into potential energy (due to height). Each loss in height corresponds to a gain of speed as potential energy (due to height) is transformed into kinetic energy (due to speed).
I the height of the second hill is higher than the first one, then it needs additional energy to climb the second hill. The coaster keeps on losing energy from air resistance and rolling friction between the rails and the coaster wheels and will eventually come to rest.
Basic mathematical subjects such as calculus help determine the height needed to allow the car to get up the next hill, the maximum speed, and the angles of ascent and descent. These calculations also help make sure that the roller coaster is safe. No doubt about it--math keeps you on track.
This places some limits on the design. For example, the coaster car can't go through a loop or over a hill that is taller than the initial hill because going higher would require more energy than it has available. If the track is too long, friction might eventually cause the coaster car to come to a complete stop.
Almost all roller coaster designers build a track that brings you back down. At the top of the first and tallest hill, your potential energy is at its highest it will ever be on this ride. As you begin to descend, your potential energy decreases until it's all gone at the bottom of the hill.
The higher the hill, the greater the potential or stored energy of the roller coaster car. When the car reaches the bottom of the hill, the potential energy has been completely converted into kinetic energy which is the energy of motion.