Banked Highway Curve: Calculating Maximum Safe Speed

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In summary, the conversation discusses a problem involving a curved highway with a banked surface, and a car's ability to take the curve without skidding. The necessary equations and factors are mentioned, including the car's mass, the radius of curvature, and the friction coefficient. The conversation ends with the person thanking for the help, but stating that the question has been cancelled.
  • #1
bikerkid
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Hey, I'm really having problems with this question and I don't really know what to do. I'm hoping someone can help me. Thanks in advance.

Homework Statement


A highway curves to the left with radius of curvature R = 35 m. The highway's surface is banked at 19 degrees so that the cars can take this curve at higher speeds.
Consider a car of mass 907 kg whose tires have static fiction coefficient of .72 against the pavement.
The acceleration of gravity is 9.8 m/s^2.

How fast can the car take this curve without skidding to the outside of the curve? Answer in units of m/s.


Homework Equations


(mv^2)/r = Fn Sin(angle)
mg = Fn Cos (angle)
(v^2)/rg = Tan (angle)
Ac = g tan (angle)
 
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  • #2
Please show some effort and work.

Consider friction also. Ffriction = [itex]\mu[/itex]Fn

To keep the car on the road, the weight component pointing down the curve and the friction must be equal to the inertial force of the car mv2/r.

On a bank/ramp, the weight can be resolved into normal and parallel forces with respect to the plane of the road.

http://hyperphysics.phy-astr.gsu.edu/hbase/mechanics/carbank.html
 
  • #3
Alright, thanks. I already knew that stuff.

The question was killed anyway, so I don't have to do it. Thanks for your help.
 

1. What is a banked highway curve?

A banked highway curve is a curved section of a highway that is designed with a higher outer edge than inner edge, allowing vehicles to safely navigate the curve at higher speeds.

2. Why are highway curves banked?

Highway curves are banked to counteract the centrifugal force that pulls a vehicle towards the outside of the curve. The higher outer edge of the curve helps to balance this force and keep the vehicle on the road.

3. How do engineers determine the banking angle of a highway curve?

The banking angle of a highway curve is determined based on the curve's radius, speed limit, and the type of vehicle it is designed for. Engineers use mathematical equations and simulations to determine the optimal banking angle for a safe and comfortable driving experience.

4. What are the benefits of a banked highway curve?

Banked highway curves can improve safety and efficiency on the road. They allow for smoother and faster navigation of curves, reducing the risk of accidents and traffic congestion. Banked curves also reduce the strain on vehicles and drivers, resulting in a more comfortable and enjoyable driving experience.

5. Are all highway curves banked?

No, not all highway curves are banked. Banked curves are typically only found on highways with high-speed limits and significant curves. Local roads and residential areas usually have flat curves, as they do not require the same level of speed and efficiency as highways.

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