#### Transcript Roller Coaster - Pennsylvania State University

```Potential Energy and
Kinetic Energy
Sang Yun Lee
In Woo Song
Song Kwang Seok
Potential and Kinetic Energy in a Roller Coaster
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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.
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At the top of the hill, the train possess a potential energy.
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Potential energy is dependent upon the mass of the object and the
height of the object. ( Work = mgh2 - mgh1 )
As it descends the first drop, it loses much of this potential energy.
Instead, it subsequently gains kinetic energy.
Kinetic energy is dependent upon the mass of the object and the speed
of the object. ( Work = 1/2mv22 – 1/2mv12 )
Thus, its original potential energy is transformed into kinetic energy.
As the ride continues, the train is continuously losing and gaining height.
Whenever it gains a height, there is a loss of speed as kinetic energy is
transformed into potential energy. Whenever it loses a height, there is
a gain of speed as potential energy is transformed into kinetic energy.
Mechanical Energy in a Roller Coaster
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As potential and kinetic energy are happening
at the same time, mechanical energy is applied.
( Work = (1/2mv22 – 1/2mv12) + (mgh2 - mgh1) )
From a Real Roller Coaster…
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Incredible Hulk
Orlando, Florida
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I rode this one when I
went to Orlando this
spring break. So..I want to
investigate further…
It is brought up to 110
feet(33.5m), and the first
drop is 105 feet(32m).
Its mass is 300kg and can
hold 32 riders per train. If
I assume the average mass
of a normal person as 55kg,
the total mass is 2060kg.
What Is the Velocity of the Train?
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If I just simply stretch the rail in 1 dimension, the rail looks like this…
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m = 2060kg, h = 32m
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W = 2060*9.8*32 = 646016Nm
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This amount of energy that is put into the roller coaster car
remains with the car throughout its trip down the track. I want
to find the velocity of roller coaster at 25m.
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646016 = mgh + 1/2mv2, at h = 25m
646016 = 2060*9.8*25 + ½*2060*v2
646016 = 504700 + 1030*v2
141316 = 1030*v2
137.2 = v2
v = 11.7m/s
In the picture, the roller coaster reaches
25m at four different positions (blue dots).
Therefore, the roller coaster has the same
velocity, 11.7m/s at any 25m.
The Origin of Roller Coaster
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The origin of the Roller Coaster dates back to the Russian Ice
Slides built in the 17th century in Russia. The structures were
built out of lumber with a sheet of ice several inches thick
covering the surface. Riders climbed the stairs attached to the
back of the slide, sped down the 50 degree drop and ascend the
stairs of the slide that laid parallel to the first one.
The History of Roller Coaster
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It is known that by 1817 two coasters were built in France called
the Russes a Belleville and Promenades Aeriennes, both of which
featured cars that locked to the track in some manner.
Bellville's ride was the first coaster to lock the cars by having
the axles slide into a groove cut in the track.
First Looping Roller Coaster
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The French Centrifugal Railway, the world's
first looping roller coaster with a 13-foot
diameter loop was imported to France from
England.
Today’s Roller Coasters
Physics and Roller Coasters
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Roller Coaster designer must use knowledge of
kinematics to build a roller coaster.
What kind of physics are there in roller coasters?
- Pretty much all! Potential, kinetic, and mechanical
energy, gravitation, free fall, projectile motion,
centripetal acceleration, friction, centrifugal
acceleration, and so on.
Based on my basic knowledge of physics, I want to
concentrate on potential and kinetic energy, which
are the most important terms to consider in building a
roller coaster.
Conclusion
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At the same height, a roller coaster has the same
velocity wherever its position is.
However, it is not that simple thing to think about its
velocity at certain points only based on the knowledge
of potential and kinetic energy. The reason is that
there are also friction, brake, and acceleration to
consider its velocity.
Roller coasters can not be exited without the
knowledge of physics.
As far as the safety and recreation of passengers are
concerned, physics is the most fundamental and
important notion in building roller coasters as well.
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