Roller Coaster Physics: Finding Final Velocity

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SUMMARY

The discussion focuses on calculating the final velocity of a roller coaster using principles of physics, specifically conservation of energy. The key equation presented is KE + PE = constant, which simplifies to v² + 2gh = constant, where v represents speed and h represents height. It is established that the final speed is determined solely by the height difference, not the slope angle, while factors such as air resistance and rolling resistance are acknowledged as influencing overall performance. Practical advice includes conducting experiments with weighted cars to account for energy losses due to friction and drag.

PREREQUISITES
  • Understanding of basic physics concepts, particularly conservation of energy
  • Familiarity with kinetic energy (KE) and potential energy (PE) equations
  • Knowledge of gravitational acceleration (approximately 9.81 m/s²)
  • Awareness of factors affecting roller coaster dynamics, such as air resistance and rolling resistance
NEXT STEPS
  • Research the effects of air resistance on roller coaster speed and design
  • Explore advanced roller coaster design techniques, including speed adjusting devices
  • Study real-world data from existing roller coasters to analyze energy losses
  • Learn about the physics of inclined planes and their impact on motion
USEFUL FOR

Roller coaster designers, physics students, engineers, and anyone interested in the mechanics of motion and energy conservation in amusement park rides.

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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welcome to pf!

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)
 
Last edited by a moderator:
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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