Roller Coaster Physics: Finding Final Velocity

In summary, the equations used to find the final velocity of a roller coaster depend on the principle of conservation of energy. The speed of the coaster depends on the difference in height and is not affected by the angle of the slope. Factors such as wind resistance and friction in the bearings can be accounted for through experiments or by consulting existing roller coasters.
  • #1
cookieworks
3
0
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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  • #2
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)
 
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  • #3
but with the distance added in there on an incline, wouldn't the time vary, changing the velocity at the bottom of the hill?
 
  • #4
how would i add in resistance as well assuming that i am only dealing with air friction?
 
  • #5
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)
 
  • #6
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.
 

1. What is the formula for finding the final velocity of a roller coaster?

The formula for finding the final velocity of a roller coaster is Vf = √(Vi^2 + 2as), where Vf is the final velocity, Vi is the initial velocity, a is the acceleration, and s is the distance traveled.

2. How is acceleration involved in calculating the final velocity of a roller coaster?

Acceleration plays a crucial role in calculating the final velocity of a roller coaster. It is the rate at which the roller coaster's velocity changes. The steeper the slope of the track, the higher the acceleration, resulting in a faster final velocity.

3. Can the final velocity of a roller coaster be negative?

Yes, the final velocity of a roller coaster can be negative. This means that the roller coaster is moving in the opposite direction from its initial direction. It could be due to external forces such as friction or air resistance acting on the roller coaster.

4. How does the height of a roller coaster affect its final velocity?

The height of a roller coaster plays a significant role in determining its final velocity. The higher the roller coaster's starting point, the more potential energy it has. As the roller coaster moves down the track, this potential energy is converted into kinetic energy, resulting in a higher final velocity.

5. What other factors besides acceleration and distance can affect the final velocity of a roller coaster?

Other factors that can affect the final velocity of a roller coaster include the mass of the roller coaster, the design of the track, and external forces such as air resistance and friction. Additionally, the use of special features like loops and corkscrews can also impact the final velocity by changing the acceleration and distance of the ride.

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