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The Math Behind Roller Coasters

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Jenna Burlew

on 18 December 2013

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Transcript of The Math Behind Roller Coasters

The Math Behind Roller Coasters
Energy cannot be destroyed, it is merely converted constantly from potential to kinetic energy and vice versa.
History of Roller Coasters
Created in Russia in the 1600s
Started off simply as people using wooden sleds down steep ice slopes
A Frenchman tried to apply this idea in Southern France, but the warm climate simply made it impossible
Lead to the creation waxed wooden slides and sleds with wooden wheels as the new form of coaster
Tracks were made to prevent accidents
Clothoid Loop
Used today instead of circular loops
Circular loops require more energy and greater entry speeds.
If the radius is reduced at the top, the centripetal force is increased. A large radius is kept at the bottom of the loop however to decrease the number of forces acting on the passengers
This keeps the train from losing too much speed and not being able to complete the loop
Jenna and Pat
Kinetic Energy

First introduced in the US at the end of 19th century
1898: First circular loop roller coaster was made, however the forces from the coaster
broke all the passengers' necks.
Safety now became
World's first steel coaster was "The Matter Horn" in Disneyland in 1959
American Roller Coasters
Potential Energy
At the top of the coaster all energy is potential.
The higher the first hill, the more potential energy is built up and can be used for the rest of the ride
It is the amount of energy stored.
g=acceleration due to gravity (9.81 m/s)
h=height from the ground
Some Examples of Kinetic v. Potential Energy
At the coaster crests the hill it has a lot of potential energy stored and ready for use
As it travels down the hill, the potential energy is converted to kinetic energy until it is all kinetic energy at the bottom fo the hill
Also known as the energy of motion.
Has an indirect relationship with potential energy
In 2.5 seconds
0mph to 120mph
Centripetal Force
The force that draws one to the middle of a circle, yet to the passengers it feels as though they are being pushed to the outer edge
This feeling is produced by our bodies own inertia as we want to continue in a straight line but we're being pulled in another direction entirely.
Luckily we as passengers are strapped in, so we don't go flying
Let's Make our own Roller Coaster!
Full transcript