Have you ever ridden on a rollercoaster and felt your heart drop as you were going downhill? Have you asked yourself how getting these feelings were possible? The answer is math. You may ask what math has to do with rollercoasters. Math is the reason for everything and anything that has to do with rollercoasters. Without math, it would be impossible to even be able to create one. To build a rollercoaster you need to be able to use numbers when talking about the costs, taking measurements, calculating the sizes, weighing, measuring the safety, looking at statistics, and calculating the force, speed, and motion. Trigonometry, algebra, geometry and calculus all take a huge role helping out in forming these models.

Roller coasters first originated in the 16th and 17th centuries by the Russians. They would create sleds made of ice or wood and slide down slopes. The French were amused with this pass time that they actually took the idea back with them home. On HowStuffWorks.com it states, “The most widespread account is that a few entrepreneurial Frenchmen imported the ice slide idea to France.” This was the first time that people were amused with any thought or idea of sliding down some kind of slope and feeling a rush that someday would turn out to be one of the favorite pastimes to present day. It was not until years later when La Marcus Thompson, an inventor and designer created the first roller coaster in Coney Island, New York City. In Wired.com it states, “…hurtled passengers down an undulating 600-foot-long track at speeds of up to a blistering 6 mph would hardly be recognizable to riders of modern-day roller coasters.” The coaster was a 50 foot platform and the passengers would sit sideways. This was the beginning of the rollercoaster.

How does math come into play then? Math is needed to build a roller coaster because everything has to be precise. The first drop is one of the most important because it will determine the speed for the rest of the ride. The...

...RollerCoasters
The main energy transfers that happens as a “car” travels along the track from the start of the ride to the end.
1. The main energy transfers are between gravitational potential energy (GPE) and kinetic energy (KE), and the eventual decrease of mechanical energy as it transforms into thermal energy. Rollercoasters often start as a chain and motor exercises a force on the car to lift it up to the top of a very tall hill. At this height, GPE is at its highest, as we can see through the formula:
GPE = mass x gravitational field strength x height (for all physics in relation to Earth, take g to be 10 m/s2 or 10 N/kg)
We can see through this formula that as the height increases, so does the GPE, which will then be converted into KE, or kinetic energy. This is the energy that takes place as the “car” is falling down the hill. This is calculated through the formula:
KE = 0.5 x mass x speed
This means that the kinetic energy increases as the speed increases, and vice versa. Therefore, this means the higher the kinetic energy, the faster the “car”. We can actually be extremely specific in terms of this relationship. We know that as the mass doubles, the KE doubles, but as the speed doubles, the KE quadruples. This becomes important when analysing this formula:
KE = GPE/0.5mv2 = mgh
2. A rollercoaster ride is a thrilling experience which involves a wealth of...

...RollerCoaster
For many people, there is only one reason to go to an amusement park: the rollercoaster. Some people call it the "scream machine," with good reason. The history of this ride reflects a constant search for greater and more death-defying thrills.
How does a rollercoaster work?
What you may not realize as you're cruising down the track at 60 miles an hour is that thecoaster has no engine. The car is pulled to the top of the first hill at the beginning of the ride, but after that the coaster must complete the ride on its own. You aren't being propelled around the track by a motor or pulled by a hitch. The conversion of potential energy to kinetic energy is what drives the rollercoaster, and all of the kinetic energy you need for the ride is present once the coaster descends the first hill..
Once you're underway, different types of wheels help keep the ride smooth. Running wheels guide the coaster on the track. Friction wheels control lateral motion (movement to either side of the track). A final set of wheels keeps the coaster on the track even if it's inverted. Compressed air brakes stop the car as the ride ends.
Wooden or steel coaster: Does it make a difference?
Rollercoasters can be wooden or steel, and can be...

...Samantha Robinson
Math105
Math and RollerCoasters
It’s not something that most people think about when they’re standing in line for an hour waiting for two minutes of thrill, but math has a lot to do with building a rollercoaster. The engineer needs to know how long and how high the ride needs to be before it can begin to be put together. These measurements have to be precise because the first drop has to give it enough speed to carry it through all the features of the ride. They would also have to take into consideration whether it will be made out of wood or steel because a wood coaster can not be as high as a steel one. The weight of the cars plays a part in the structure since it can’t be too heavy or this will interfere with the speed. It will also cause it to fall down the steep sloop it travels to get to the first drop. To name a few, geometry, algebra and trigonometry are used when a rollercoaster is being designed.
There are various types of rides and they all have to be built differently.
The corkscrew is shaped like a twisted spiral. Geometry definitely plays a big part in the creation of this ride because the track rails have to be equal so the wheels can stay in sync.
When a launch coaster is being put together the engineer needs to calculate the amount of stress that can be put on the launching...

...The RollerCoaster Question
a)
E1=E2
Eg+Ek= Eg1+Ek1
mgh+1/2mv2= mgh1+1/2mv21
(1250)(9.8)(10)+1/2(1250)(v)2=(1250)(9.8)(65)+1/2(1250)(2.5)2
v= 32.9 m/s
Therefore you need 200003.9 watts of power to raise the cars to the top of the 1st hill with the speed of 32.9 m/s
Therefore you need 200003.9 watts of power to raise the cars to the top of the 1st hill with the speed of 32.9 m/s
Energy= 800156 J
P= E/T
= 800156J/40s
= 200003.9 W
b)
E1-Wf =E2
The expected speed of the cars is 8.5 m/s. Friction did 608000 J of work on the cars from the top of the hill to the braking zone.
The expected speed of the cars is 8.5 m/s. Friction did 608000 J of work on the cars from the top of the hill to the braking zone.
Eg+Ek-Wf= Eg1+Ek1
mgh+1/2mv2-Wf= mgh1+1/2mv21
Wf= mgh+1/2mv2- mgh1-1/2mv21
= (9.8)(65)+1/2(2.5)2-(9.8)(12)-1/2(8.5)2
= 608000 J
c)
Wf=Ff x d
The average Frictional Force was 844.4 N.
The average Frictional Force was 844.4 N.
Ff = Wf/d
=608000J/720m
= 844.4 N
Assumptions
* Acceleration of gravity is 9.8 m/s2
* Moving in direction of Force ( cos=0)
* Sitting in middle cart.
* Start 10 m off the ground “loading area”
* Air resistance isn’t a huge factor
Physics
* The rollercoaster is always moving (Kinetic Energy)
* Gravitational Potential Energy is constant
* Friction of Roller...

... The cars subsequently gain kinetic energy. Kinetic energy - the energy of motion - is dependent upon the mass of the object and the speed of the object. The train of coaster cars speeds up as they lose height. Thus, their original potential energy (due to their large height) is transformed into kinetic energy (revealed by their high speeds). As the ride continues, the train of cars are continuously losing and gaining height. 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)
http://www.physicsclassroom.com/mmedia/energy/ce.cfm (7/10)
A rollercoaster moves in the same way a marble would roll down a slanted surface. The marble rolls because it has Gravitational Potential Energy. Potential Energy is gathered by an object as it moves upwards, or away from, the earth. With a rollercoaster, this is acheived by pulling the train up a lift hill to the coaster's highest point. As it moves higher, it has more potential to fall to earth, increasing its Kinetic Energy. Kinetic Energy is gathered as an object falls. There's a transfer of Potential Energy to Kinetic Energy as the rollercoaster train leaves the top of the lift hill and enters the first drop....

...Individuals love to go to the amusement parks and try out the rides that are available. The most common and thrilling ride is the rollercoaster. An amusement park is not an amusement park if it does not contain a rollercoaster. What makes these rollercoasters so fun that every amuse parks has one. A lot of people would say it is their extreme high speeds that makes it very exciting. That is a valid answer, but it is the wrong answer. The speed has nothing to do with the excitement. It is more than likely that most people travel faster on their ride along the highway on the way to the amusement park than they would in a rollercoaster. Basically the thrill all comes from the acceleration and the feeling of weightlessness that they produce. Rollercoasters thrill people because of their ability to accelerate them downward one moment and upwards the next; leftwards one moment and rightwards the next. How does this thrill machine work? There are two ways that this question will be answered. First, through the basic principles and then through a more advanced explanation.
Rollercoaster rides involve a great deal of physics. The ride often begins with a chain and motor which exerts a force on the train of cars to lift the train to the top of a tall hill. Once the cars are lifted to the top of the hill,...

...works based on free-fall) and the rollercoaster.
The Physics of RollerCoasters
How does a RollerCoaster work? Rollercoasters have no engines (although many still tend to think they do) and are thus not propelled around the track by a motor. The transfer of potential energy to kinetic energy is what steers the rollercoaster, and all of the kinetic energy required for the ride is present once the coaster goes down the first ‘hill’. Laws of Gravitation Gravitational energy takes place due to the gravitational force by which matter attracts other matter. As the coaster is pulled up the first ‘peak’ of the coaster, the gravitational energy increases. When the coaster Montezum RollerCoaster reaches the backside of the hill, the gravitational force is what causes it to accelerate. A great part of the roller coaster's gravitational energy is converted to kinetic energy on the backside of the first ‘peak’. As the coaster goes up the second ‘peak’, its kinetic energy is converted back into gravitational energy. Since the roller coaster's kinetic energy at the end of its first ‘peak’ is less than its gravitational energy at the beginning of this same ‘peak’, the second ‘crest’ is shorter than the first. If the...

...“A rollercoaster is considered any elevated track with curves and rises, carrying passengers in open, rolling cars for entertainment” (5). Today’s rollercoasters appear to be tons of tubular metal intertwined around itself, but regardless of how big, fast, or gravity defying they are, they all use the same natural force – gravity. The more twisting, turning, flipping, and the faster a rollercoaster goes, the more the coaster depends on the law of physics, not mechanics, to keep it moving. There is no onboard motor on rollercoasters but they can still reach speeds that exceed the limits of a car on the parkway, while completing a curve, twist, rise, or plunge.
History of RollerCoasters
Modern day rollercoasters are based off of the fails and successes of those created over the years and though they are more complex today, rollercoasters wouldn’t exist today if it weren’t for the ones of past generations. Originating in Russia, rollercoasters were as basic as they come – a simple ramp. Russia had the climate for sledding, but with flat plains and high altitudes it wasn’t necessarily possible. To solve this problem they built frozen slides where inclines didn’t naturally exist. This worked well for the Russians but other countries...

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