speed increases as slope decreases (-), speed decreases as slope increases (+)

**Equation**

y=AcosB(x-C)+D

can be sin as well

A: amplitude

B: width

C: left/right

D: up/down

piecewise functions because most roller coasters are not a perfect cos/sin equations

contains loops, straight paths, hills, twists, turns

Loops

Centripetal Force

Newton's Laws of Motion

Centrifugal Force

**The Mathematics of Roller Coasters**

**Varshaa Thorali, Jenna Kim, Kevin Lin, Kevin Liu**

The Ride!

Bibliography

Per 4

Slope & Speed

Galileo Galilei

**Velocity**

Velocity is speed with direction and on a roller coaster, the velocity changes each time the direction is changed

The coaster must also have a minimum velocity or critical velocity at the top of the loop to make it through the loop.

THE Physics of it

The initial ascent is to give the roller coaster a reservoir of potential energy. Throughout the ride, the ride will only have the certain amount of potential energy given from the beginning and all it does is convert potential energy into kinetic energy.

The gravity and height of the cars is what gives the roller coaster potential energy to change into kinetic energy

Experiment with a simple roller coaster “Roller Coaster simulator”

Marble could take any path until it reaches the same height it starts from assuming no friction

With friction, it will keep rolling until it reaches the stop height

Acceleration

Climbs

forced into seat

Peaks

(airtime)

lighter weight

Drops

weightlessness

Velocity Does Not Matter

Loops

heaviest at bottom, weightless at top

rapidly changing forces

Banking

reduced lateral G force

Equations

About the Wheels

The wheels also determine a lot of things for the roller coaster. Some wheels guide the coaster, other wheels control sideways movement, and the final set of wheels keep the coaster on the track even when inverted.

"Amusement Park Physics." Amusement Park Physics. Web. <http://www.physicsclassroom.com/class/circles/u6l2b.cfm>

Berkowitz, Bonnie, and Laura Stanton, Published: July 1, 2013. "Why Roller Coasters Make Us Scream." Washington Post. The Washington Post. Web. <http://www.washingtonpost.com/wp-srv/special/health/why-roller-coasters-make-us-scream/>

"Calculus Behind Roller Coasters." Prezi.com. Web. <http://prezi.com/shtrkmrdbwex/calculus-behind-roller-coasters/>

"Design of a Thrilling Roller Coaster - Introduction to the Project." Homepage. Web. <http://www.maa.org/publications/periodicals/loci/joma/design-of-a-thrilling-roller-coaster-introduction-to-the-project>

Hollis, Elwyn, Department Of Mathematics, Armstrong Atlantic State University, and Ga 31419 Savannah. Mathematica(l) Roller Coasters. Web. <http://www.math.armstrong.edu/faculty/hollis/vita/Coasters.pdf>

"Math Apprentice - Real World Math." Math Apprentice - Real World Math. Web. <http://www.mathplayground.com/MathApprentice/roller_coaster_engineer.html>

"Roller Coasters." Roller Coasters. Web. <http://www.datagenetics.com/blog/march42014/index.html?utm_medium=App.net&utm_source=PourOver>

"The Physics of a Coaster." The Physics of a Coaster. Web. <http://www.coasterforce.com/coasters/technical-info/physics-of-a-coaster>

Wayne, Tony. Roller Coaster Physics Part 1A. Web. <http://vip.vast.org/BOOK/PDFFILES/PART1A.PDF>