Banked Curves - Question

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In summary, the conversation is about determining the speed at which a curve with a radius of 170 m and a banked angle of 22° can be negotiated under icy conditions with negligible friction. The individual is trying to solve the problem using centripetal acceleration and drawing a free body diagram. They also discuss the meaning of Fc, the role of the mass in the equations, and the importance of a FBD in correctly applying Newton's Second Law.
  • #1
Xylitol
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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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  • #2
it concerns centripetal acceleration. did you try it at all? you need to at least show some of your work or thought processes.
 
  • #3
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)
 
  • #4
this is for your "1 kg" car, right?

which of these Forces is center-pointing?
 
  • #5
Fnx is center pointing

The mass is not given
Apparently the masses should cancel out with teh formulas but I don't really know which ones to choose
 
  • #6
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?
 
  • #7
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
 
  • #8
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?
 
  • #9
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
 

1. What is a banked curve?

A banked curve is a curve in a road or racetrack that is higher on one side than the other. This allows vehicles to safely travel at higher speeds without sliding or losing control.

2. How does a banked curve work?

A banked curve works by using the force of gravity to keep a vehicle moving in a circular path. The higher side of the curve provides a centripetal force that keeps the vehicle moving towards the center of the curve, preventing it from sliding outwards.

3. What factors affect the banking angle of a curve?

The banking angle of a curve is affected by the speed of the vehicle, the radius of the curve, and the coefficient of friction between the tires and the road surface. A higher speed or tighter curve radius will require a steeper banking angle to keep the vehicle safe.

4. Why are banked curves important in racing?

Banked curves are important in racing because they allow vehicles to maintain higher speeds while turning, giving them a competitive advantage. Without banked curves, racetracks would need to have many more sharp turns, resulting in slower overall speeds and less excitement for spectators.

5. Are banked curves only used in road and racetrack design?

No, banked curves can also be found in roller coasters, water slides, and other amusement park rides. They are designed to provide thrills and excitement for riders, while also ensuring their safety.

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