# Amusement Park Physics

explanatory Essay
1043 words
1043 words

Missing formulas

A new era in theme parks and roller coaster design began in 1955 when Disneyland ushered in the new era of amusement park design. Disneyland broke the mold in roller coaster design by straying from the typical norm of wooden roller coasters; thus, the steel tubular roller coaster was born. Disneyland’s Matterhorn was a steel tubular roller coaster with loops and corkscrews, which had never been seen before with the wooden coasters. In addition to the new steel tube roller coaster, the new coaster design also proved to be the most stable, allowing for wilder designs. The first successful inverted roller coaster opened up in 1992, and now it is not uncommon to find passengers of various roller coasters with their feet dangling above or below them as they circumnavigate the track. In 1997 Six Flags Magic Mountain opened a roller coaster, that just a few year previous would have been considered impossible. The Scream Machine is 415 feet tall and takes willing riders on an adrenaline rush using speeds of 100 miles per hour. Technology working with the laws of physics continues to push the limits of imagination and design.

Many people do not realize exactly how a roller coaster works. What you may not realize when you are cruising down the track at over 60 miles per hour, is that the roller coaster does not have a motor or engine. At the beginning of the ride the car is pulled to the top of the first hill where it comes to a momentary halt. At this point its potential energy is at a maximum and the kinetic energy is at a minimum. As the car falls down the hill it is losing potential energy and is gaining kinetic energy. It is this kinetic energy that keeps the car going throughout the remainder of the ride. The conversion of potential energy to kinetic energy is what drives the roller coaster, and all of the kinetic energy you need for the ride is present once the coaster descends the first hill. Once the car is in motion, different types of wheels keep the ride running smooth. Various running wheels help guide the coaster around the track. Friction wheels control lateral motion. A final set of wheels keeps the coaster on the track even if the coaster is inverted. Compressed air brakes are used to stop the coaster as it comes to an end.

#### In this essay, the author

• Explains that disneyland broke the mold in roller coaster design by straying from the typical norm of wooden coasters.
• Explains that roller coasters have no motor or engine, and the conversion of potential energy to kinetic energy is what drives them.
• Explains that at this point the curve y(x) for the roller coaster track must be specified, and its derivative can be substituted into this formula. this is seen to be a differential equation whose solution is some function x(t).
• Explains that potential energy is the energy that an object possesses by virtue of its location.
• Explains that m is the mass of the object, g is acceleration due to gravity (the gravitational constant), namely 9.81m/s2, and h is its height.
• Explains how a roller coaster ride can be analyzed by using the fact that as the train drops in elevation its potential energy is converted into kinetic energy.
• Explains how the notation y(x) and v (v) has been written to emphasize the fact that the elevation drop and hence the velocity both depend on the horizontal coordinate x
• Explains that potential energy can be converted into other forms of energy, such as kinetic energy. kinetic energy is the energy that an object has by virtue of its motion.
• Explains that if the velocity of an object is doubled, its kinetic energy is quadrupled. kinetic energy can also be converted into other forms of energy.