Roller Coaster Research Paper

Physics Make-Up Assignment: Amusement Park Physics

Everyone is aware of a roller coaster’s adrenaline causing effects, but not everyone is aware of the physics behind the mechanics of these rides. Roller coasters run on potential and kinetic energy. The purpose of the roller coaster’s initial ascent is to build up the potential energy, the energy stored up in an object, so when eventually there are drops in the ride the potential energy will be released as kinetic energy, the energy that propels one downwards. There are other forces that are at work including gravity, which is why most rides start with a very high initial ascent. Because of this ascent, the force of gravity will pull down at a greater distance. Roller coasters such as the

Diamondback, Wildcat, and Falcon’s Fury demonstrate different forces at work.
Starting with the Wildcat, this rollercoaster is relatively mild in the fact that there are not huge turns or loops. This roller coaster goes up and down intermittently on the course of a minute ride. This ride combines potential and kinetic energy to send riders up and down sporadically. As the Wildcat goes up the hill on its initial ascent it uses potential energy and its equation is:
PE=mgh
Potential energy being shown as PE, m is mass, and g is gravity, and h is the height of the coaster.

The initial hill, or lift hill, is the tallest in the entire ride and is most likely at the beginning of the ride. The higher the life, the greater amount of potential energy is gained. Since mass and gravity is constant for the ride, if the height is increases the potential energy will increase.. Because of this the potential energy is greatest at the peak of the rollercoaster. As the rollercoaster begins to go downwards from the ascent the velocity increases. This descent cause the coaster to gain kinetic energy and the faster the coaster moves the more kinetic energy it gains shown by the

equation:
K=1/2mv2
The K is kinetic energy, the m is mass, and the v is velocity. Because, again, the mass is constant, so if the velocity is increased the kinetic energy will also increase. This means that the kinetic energy is greatest when the Wildcat reaches the end of the descent. In the case of the Wildcat, there are multiple descents and ascents. So, as the kinetic energy is the most at the end of the descent, and it starts decreasing again as the coaster starts moving up the hill and gaining potential energy. This phenomenon is called the law of conservation of energy meaning that energy cannot be created or destroyed, but it can be converted from one form to another. As mentioned before as a roller coaster descends it turns potential energy to kinetic energy and visa versa. Seen by the equation:
E=K+P
E is the total energy, K is kinetic, and P is potential. This equation shows that the total equals the combined of kinetic and potential.
Next, is the Diamondback which is a little more hardcore and you feel like you are getting whiplash from going around a loop backwards and forwards at a speed of 45 mph. The ride consists of one giant loop that the roller coaster car going around and around in. This circular motion is achieved through centripetal acceleration. Centripetal acceleration points toward the center of the circular path of a rollercoaster, but if you are a passenger you will stay in your seat and not fly out of the rollercoaster because of inertia. Inertia is the resistance to the change in the direction so quickly. The equation for centripetal acceleration is:
ar = v2 / r
A is centripetal acceleration, v is velocity, and r is the radius of the circle. The higher the roller coaster velocity, the greater the acceleration. This also means that if the radius is smaller the faster the centripetal acceleration will be. In the Diamondback, the loop is clothoid. Meaning, since the radius is reduced at the top of the loop the centripetal acceleration increases to keep the ride moving fast around the loop.
Lastly, the Falcon’s Fury is a ride that rises the passengers straight up and then releases the passengers straight down. Galileo first discovered the concept of free-fall by proving it when he dropped two masses at the same time and recorded the free fall rate is the same. Free fall rides are made up of three parts: the rise to the top, the stall at the top, and the plunge to the bottom. Force is applied to rise the passengers to the top. Then, all that energy is released when gravity pulls it to the ground. Again, using the potential and kinetic energy equations.
PE=mgh
K=1/2mv2
E=K+P
Mass cancels out and then it's up to gravity and velocity to drive the rollercoaster upwards and pull it downwards.
As for my rollercoaster ideas, I would create a park called Urgent Care and it would feature rides that symbolized the human body malfunctioning. For my first three rides I would have the Erectile Dysfunction, Vertigo, and Childbirth.
Erectile Dysfunction would be a rollercoaster that has a very high ascent then shoots straight down and then has a smaller ascent then again shoots back down. The physics behind it would be potential and kinetic energy. As the coaster rises up, the potential energy will increase. Then at the peak, it would have the most potential energy and as it is being pulled down by gravity the kinetic energy will increase until it is at its most at the bottom of the ride.

The first hill is a height of 80 meters, and as it goes down the velocity is 39.6 m/s. Since the first hill is the highest it will be able to use the energy throughout the ride. The rollercoaster then follows the path of a projectile in free fall and has a curve at the bottom that leads gently into the next part of the path.The coaster will be able to make the second hill, but it will not have the optimum velocity and won't be able to rise back up, giving the impression of erectile dysfunction.
My next rollercoaster is called Vertigo, a free fall drop roller coaster.

It rises up and goes down intermittently before going all the way up and shooting back down, giving the rider the feeling of vertigo. Vertigo is the sensation of whirling and loss of balance, associated particularly with looking down from a great height. This ride will use potential and kinetic energy, with mass canceling out and gravity and velocity driving the rollercoaster. The ride will have a height of 330 meters, a mass of 890 kilograms, and gravity will be 9.8 m/s. Meaning the potential energy will be 2,878,260. With this information we can determine the velocity. The mass is again 890, and then the kinetic energy is equal to the potential energy so 2,878,260. The velocity comes out to be 80.4

m/s.
My last ride is called Child Birth, which is a dark tunnel with a clothoid loop that leads out into the sunlight and splashes into water. Much like when you are born going from darkness to light. To calculate the centripetal acceleration we need the radius of the loop as well as velocity. The radius of my loop is 22 meters and the velocity is 40 m/s so the centripetal acceleration is 880 m/s. The water will slow the ride down at the end using friction against the bottom of the cart.
All in all, physics is in everything and everywhere.
Resources:

Amusement Park Physics. Retrieved from