Finding the Angle of a Banked Curve for Roller Coaster Design

In summary, the conversation is about designing a roller coaster and using physics to calculate the angle of a banked curve. The formula "Tan theta=v^2/rg" is mentioned but the person is unsure of its derivation. They ask for another formula that does not include friction. Another person suggests a link that explains the forces at work on a banked curve, and the formula "Velocity max=square root (rg tan theta)" is mentioned as a rearranged version of the original formula. The person expresses gratitude for the help.
  • #1
newme
4
0
Hey I am doing a assignment on Roller coaster physics and i am to design a Roller coaster taking all the aspects of physics.

I am stuck at my banked curve i don't know what formula to use to find the angle of the curve.
I have seen this formula in the forums
Tan theta=v^2/rg

but the thing is i don't know how that formula was derived so i can't useit in my assigment unless i know how it was made.

So if someone know how to make that formula or another forumula i can use please could you post it. Thanks

ahh you and i for got to say that you can ignore friction.
 
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  • #2
Welcome to PF, Newme. I can't help you with any math stuff; I'm more of a 'hands on' guy. (No one would get on my rides in Rollercoaster Tycoon. :frown:)
You are definitely in the right place to get the answers, though. Just hang tight and the experts will show up like rock bass on a dead minnow.
 
  • #3
  • #4
thanks

Thanks for that!
Ok so know with this formula
Velocity max=sqaure root (rg tan theta)
can be rearanged to tan theta=v^2/rg
thanks for the help on that
 

1. What is a frictionless banked curve?

A frictionless banked curve is a curved surface that is designed to allow objects to move along it without experiencing any resistance or friction. This type of curve is commonly used in roller coasters, race tracks, and other applications where high speeds are involved.

2. How does a frictionless banked curve work?

A frictionless banked curve works by utilizing the force of gravity to keep an object moving along its surface without any friction. The curve is angled in such a way that the centripetal force created by the object's motion is balanced by the normal force of the curve, allowing the object to maintain a constant speed and direction.

3. What are the benefits of using a frictionless banked curve?

Using a frictionless banked curve allows for higher speeds and smoother motion compared to a flat surface. This is because the frictionless surface reduces the amount of energy lost due to friction, allowing objects to maintain their velocity and direction more easily.

4. What factors affect the design of a frictionless banked curve?

The design of a frictionless banked curve is affected by several factors, including the speed of the object, the mass of the object, and the angle of the curve. The radius of the curve and the coefficient of friction between the object and the surface also play a role in the design.

5. Are there any limitations to using a frictionless banked curve?

While a frictionless banked curve can greatly reduce the amount of energy lost due to friction, it is not completely free of friction. Other factors such as air resistance and imperfections in the surface can still affect the motion of objects. Additionally, the design of the curve must be carefully calculated to ensure the object maintains a safe and stable path.

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