How Fast Can a Car Travel on a 22° Icy Banked Curve with a 170m Radius?

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Homework Help Overview

The problem involves determining the maximum speed at which a car can travel on a banked curve with a specific radius and angle, under icy conditions where friction is negligible. The subject area includes concepts of centripetal acceleration and forces acting on an object in circular motion.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the forces acting on the car, including gravitational force and normal force, and how these relate to centripetal acceleration. There are attempts to apply trigonometric functions to resolve forces and questions about the significance of certain forces in the context of the free body diagram (FBD).

Discussion Status

The discussion is active, with participants questioning each other's reasoning and clarifying concepts related to forces and acceleration. Some guidance has been offered regarding the interpretation of forces in the FBD and their relation to Newton's second law, but no consensus has been reached on the specific calculations or methods to apply.

Contextual Notes

Participants note that the mass of the car is not provided, and there is discussion about how this might affect the calculations, particularly regarding the cancellation of mass in the equations. The context of icy conditions and negligible friction is also emphasized as a critical factor in the problem.

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A curve of radius 170 m is banked at an angle of 22°. At what speed can it be negotiated under icy conditions where friction is negligible?

Can someone explain how to get the answer for this question? Thanks
 
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it concerns centripetal acceleration. did you try it at all? you need to at least show some of your work or thought processes.
 
Ok
I drew out the FBD

Fg going down
Fny going up
Fnx going to the right
Fn going at a 68 degree angle to the horizontal

Using the trig functions, I got: (not to significant figures)
Fg = 9.8 [N]
Fn = 9.8 [N]
Fnx = 3.96 [N]
Fn = 10.57 [N]

Ac = (Vc^2)/(r)
Fc = MAc = (MVc^2)/(r)
 
this is for your "1 kg" car, right?

which of these Forces is center-pointing?
 
Fnx is center pointing

The mass is not given
Apparently the masses should cancel out with the formulas but I don't really know which ones to choose
 
What does Fc mean? That is to say, in your last equation, what is the meaning of Fc by itself, making no reference to the rest of the equalities on that line?

Hint: how does Fc relate to your FBD?
 
robphy said:
What does Fc mean? That is to say, in your last equation, what is the meaning of Fc by itself, making no reference to the rest of the equalities on that line?

Hint: how does Fc relate to your FBD?

Its going towards the center
 
Why does one draw a FBD in the first place?
How does it help you correctly apply Newton-II? In fact, what is the precise statement of Newton-II?
 
robphy said:
Why does one draw a FBD in the first place?
How does it help you correctly apply Newton-II? In fact, what is the precise statement of Newton-II?

Netforce(X/Y) = MA
 

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