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Roller Coasters Research Paper

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The history of the roller coaster can be dated back as early as the 16th century. Reading about the origin of the roller coasters sparked my great interest in their construction. I came across interesting facts such as how roller coasters originated in Russia . They were once called the “Russian Mountains” and were composed of lumber with a sheet of thick ice covering the surface (“Roller Coaster History”). Their infrastructure captivated my attention and I found myself pondering on how they managed to construct their calculations and mathematically figure out the force needed for the roller coaster to continuously move. Therefore, I have constructed a roller coaster through the use of polynomial and trigonometric functions by taking into account …show more content…

Newton’s Second Law states that force times mass equals acceleration(fm=a). This law explains that when an unbalanced force is exerted on an object, the object will then accelerate in the direction of the force ("Newton's Second Law"). Therefore the greater force, the greater the acceleration. The pulley system that serves as a chain will be the unbalanced force since it is what changes the roller coasters motion and has the strength to pull it upwards. By conducting research on the total mass of roller coasters including their passengers, I came up with calculations that include the following:

Total Mass Calculations
Values (kg)
Mass of rider
100
Mass of empty coaster cart
550
Total Mass per Train
4500

The roller coaster will consist of a six cars per train. One car will be able to hold a total of 200 kg between two passengers totaling a maximum mass of 750 kg per car (1002+550=750). A fully loaded coaster train will have a maximum mass of 4500 kg. These calculations allow us to calculate and ensure the force that is needed for the motor in order to enable it to pull the train up its first hill.
The angle of the lift will be 45 degrees, therefore the train will be pushed up vertically for the distance of 44.063 meters, (49.063-5=44.063). The total incline length will equal:
44.063sin(45)= 62.3144921988058123

Calculations
Values
Lift Incline Angle
45
Lift Height (m)
49.063
Station Height (m)
5
Vertical Distance (m)

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