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The Mathematics of Roller Coasters
Transcript of The Mathematics of Roller Coasters
speed increases as slope decreases (-), speed decreases as slope increases (+)
can be sin as well
piecewise functions because most roller coasters are not a perfect cos/sin equations
contains loops, straight paths, hills, twists, turns
Newton's Laws of Motion
The Mathematics of Roller Coasters
Varshaa Thorali, Jenna Kim, Kevin Lin, Kevin Liu
Slope & Speed
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
forced into seat
Velocity Does Not Matter
heaviest at bottom, weightless at top
rapidly changing forces
reduced lateral G force
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.
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