Roller Coaster Physics: Finding Final Velocity

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To determine the final velocity of a roller coaster on a slope, the conservation of energy principle is key, where kinetic energy (KE) and potential energy (PE) remain constant. The equation v² + 2gh can be used, where v is speed and h is height, indicating that speed depends primarily on the height difference rather than the slope angle. While the angle affects the time taken to reach the bottom, it does not influence the final speed directly. To account for factors like air resistance and rolling friction, real-world experiments or data from existing roller coasters should be consulted, as designers consider these energy losses in their calculations. Understanding these principles is crucial for effective roller coaster design.
cookieworks
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believe it or not, this is a totally serious question. I am currently trying to design a roller coaster. Given that it is at a slope, what equation(s) would i use to find final velocity knowing gravitational acceleration, slope, and distance of my slope? ex: my slope is 45 degrees in a downward direction at a distance of approximately 21 feet (15 feet up, 15 feet over). what equation would i use and how would i implicate all of the variables into it?

P.S. you are dealing with someone who is here because all of his teachers failed him. sorry if i spelled anything wrong.
 
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hi cookieworks! welcome to pf! :smile:
cookieworks said:
… what equation(s) would i use to find final velocity knowing gravitational acceleration, slope, and distance of my slope?

conservation of energy …

KE + PE = constant …

https://www.physicsforums.com/library.php?do=view_item&itemid=132" = constant

v2 + 2gh = constant (v is speed, is height)

the speed v depends on the difference in height, h, and not on the angle of the slope at all

(of course, this ignores things like wind resistance, friction in the bearings, etc)
 
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but with the distance added in there on an incline, wouldn't the time vary, changing the velocity at the bottom of the hill?
 
how would i add in resistance as well assuming that i am only dealing with air friction?
 
speed does not depend on time, or on angle of slope, only on height …

all the angle does is change the time it takes you to get there
cookieworks said:
how would i add in resistance as well assuming that i am only dealing with air friction?

do experiments with actual cars loaded with people or dummies (or find out from existing roller-coasters)
 
The roller coaster designers are aware of the energy losses in coaster (rolling resistance and aerodynamic drag). The rolling resistance factor varies with temperature, mostly due to the lubricants involved. Some coasters will use speed adjusting devices like spinning tires to correct the speed of the cars mid-track.
 

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