Potential Energy and Potential Energy and Kinetic EnergyKinetic Energy

Sang Yun LeeSang Yun Lee

In Woo SongIn Woo Song

Song Kwang SeokSong Kwang Seok

Potential and Kinetic Energy in a Roller Potential and Kinetic Energy in a Roller CoasterCoaster

The ride often begins with a chain and motor exerting a force on The ride often begins with a chain and motor exerting a force on the train to lift it to the top of a very tall hill. the train to lift it to the top of a very tall hill.

At the top of the hill, the train possess a potential energy. At the top of the hill, the train possess a potential energy.

Potential energy is dependent upon the mass of the object and the Potential energy is dependent upon the mass of the object and the height of the object. height of the object. ( Work = mgh2 - mgh1 )

As it descends the first drop, it loses much of this potential As it descends the first drop, it loses much of this potential

energy. Instead, it subsequently gains kinetic energy. energy. Instead, it subsequently gains kinetic energy.

Kinetic energy is dependent upon the mass of the object and the Kinetic energy is dependent upon the mass of the object and the speed of the object. speed of the object. ( Work = 1/2mv2

2 – 1/2mv12 )

Thus, its original potential energy is transformed into kinetic Thus, its original potential energy is transformed into kinetic energy. energy.

As the ride continues, the train is continuously losing and gaining As the ride continues, the train is continuously losing and gaining height. Whenever it gains a height, there is a loss of speed as height. Whenever it gains a height, there is a loss of speed as kinetic energy is transformed into potential energy. Whenever it kinetic energy is transformed into potential energy. Whenever it loses a height, there is a gain of speed as potential energy is loses a height, there is a gain of speed as potential energy is transformed into kinetic energy. transformed into kinetic energy.

Mechanical Energy in a Roller Mechanical Energy in a Roller

CoasterCoaster

As potential and kinetic energy are As potential and kinetic energy are happening at the same time, mechanical happening at the same time, mechanical energy is applied.energy is applied.

( Work = (1/2mv2

2 – 1/2mv12) + (mgh2 - mgh1) )

From a Real Roller From a Real Roller Coaster…Coaster…

Incredible HulkIncredible Hulk

Universal's Islands of Universal's Islands of AdventureAdventure

Orlando, FloridaOrlando, Florida

I rode this one when I I rode this one when I went to Orlando this went to Orlando this spring break. So..I want to spring break. So..I want to investigate further…investigate further…

It is brought up to 110 It is brought up to 110 feet(33.5m), and the first feet(33.5m), and the first drop is 105 feet(32m).drop is 105 feet(32m).

Its mass is 300kg and can Its mass is 300kg and can hold 32 riders per train. If hold 32 riders per train. If I assume the average I assume the average mass of a normal person mass of a normal person as 55kg, the total mass is as 55kg, the total mass is 2060kg.2060kg.

What Is the Velocity of the Train?What Is the Velocity of the Train? If I just simply stretch the rail in 1 dimension, the rail looks like If I just simply stretch the rail in 1 dimension, the rail looks like

this…this…

m = 2060kg, h = 32mm = 2060kg, h = 32m

W = 2060*9.8*32 = 646016NmW = 2060*9.8*32 = 646016Nm

This amount of energy that is put into the roller coaster This amount of energy that is put into the roller coaster car remains with the car throughout its trip down the car remains with the car throughout its trip down the track. I want to find the velocity of roller coaster at 25m.track. I want to find the velocity of roller coaster at 25m.

646016 = mgh + 1/2mv646016 = mgh + 1/2mv22, at h = 25m, at h = 25m

646016 = 2060*9.8*25 + ½*2060*v646016 = 2060*9.8*25 + ½*2060*v22

646016 = 504700 + 1030*v646016 = 504700 + 1030*v22

141316 = 1030*v141316 = 1030*v22 137.2 = v137.2 = v22

v = 11.7m/sv = 11.7m/s

In the picture, the roller coaster reaches In the picture, the roller coaster reaches 25m at four different positions (blue dots).25m at four different positions (blue dots).

Therefore, the roller coaster has the same Therefore, the roller coaster has the same velocity, 11.7m/s at any 25m.velocity, 11.7m/s at any 25m.

The Origin of Roller CoasterThe Origin of Roller Coaster

The origin of the Roller Coaster dates back to the Russian Ice The origin of the Roller Coaster dates back to the Russian Ice Slides built in the 17th century in Russia. The structures Slides built in the 17th century in Russia. The structures were built out of lumber with a sheet of ice several inches were built out of lumber with a sheet of ice several inches thick covering the surface. Riders climbed the stairs thick covering the surface. Riders climbed the stairs attached to the back of the slide, sped down the 50 degree attached to the back of the slide, sped down the 50 degree drop and ascend the stairs of the slide that laid parallel to drop and ascend the stairs of the slide that laid parallel to the first one. the first one.

The History of Roller The History of Roller CoasterCoaster

It is known that by 1817 two coasters were built in France It is known that by 1817 two coasters were built in France called the Russes a Belleville and Promenades Aeriennes, called the Russes a Belleville and Promenades Aeriennes, both of which featured cars that locked to the track in some both of which featured cars that locked to the track in some manner. Bellville's ride was the first coaster to lock the cars manner. Bellville's ride was the first coaster to lock the cars by having the axles slide into a groove cut in the track. by having the axles slide into a groove cut in the track.

First Looping Roller CoasterFirst Looping Roller Coaster

The French Centrifugal Railway, the The French Centrifugal Railway, the world's first looping roller coaster with a world's first looping roller coaster with a 13-foot diameter loop was imported to 13-foot diameter loop was imported to France from England. France from England.

Today’s Roller CoastersToday’s Roller Coasters

Physics and Roller CoastersPhysics and Roller Coasters Roller Coaster designer must use knowledge of Roller Coaster designer must use knowledge of

kinematics to build a roller coaster.kinematics to build a roller coaster.

What kind of physics are there in roller coasters?What kind of physics are there in roller coasters? - Pretty much all! Potential, kinetic, and - Pretty much all! Potential, kinetic, and

mechanical energy, gravitation, free fall, mechanical energy, gravitation, free fall, projectile motion, centripetal acceleration, projectile motion, centripetal acceleration, friction, centrifugal acceleration, and so on. friction, centrifugal acceleration, and so on.

Based on my basic knowledge of physics, I want Based on my basic knowledge of physics, I want to concentrate on potential and kinetic energy, to concentrate on potential and kinetic energy, which are the most important terms to consider which are the most important terms to consider in building a roller coaster.in building a roller coaster.

ConclusionConclusion At the same height, a roller coaster has the same At the same height, a roller coaster has the same

velocity wherever its position is.velocity wherever its position is.

However, it is not that simple thing to think about However, it is not that simple thing to think about its velocity at certain points only based on the its velocity at certain points only based on the knowledge of potential and kinetic energy. The knowledge of potential and kinetic energy. The reason is that there are also friction, brake, and reason is that there are also friction, brake, and acceleration to consider its velocity. acceleration to consider its velocity.

Roller coasters can not be exited without the Roller coasters can not be exited without the knowledge of physics.knowledge of physics.

As far as the safety and recreation of passengers As far as the safety and recreation of passengers are concerned, physics is the most fundamental and are concerned, physics is the most fundamental and important notion in building roller coasters as well.important notion in building roller coasters as well.