Minimum coefficient of friction to keep cars from sliding off the road

In this case, the main forces are the friction force, the normal force, and the centripetal force. Using the equations Fk=ukFn and F=mv^2/R, we can set up a system of equations to solve for the minimum coefficient of friction (uk) needed to prevent the cars from sliding off the road. After some algebraic manipulation, we can find that uk=0.13. In summary, the minimum coefficient of friction needed for cars to take the turn without sliding off the road is 0.13.
  • #1
rockchalk1312
38
0
A banked circular highway curve is designed for traffic moving at 61 km/h. The radius of the curve is 201 m. Traffic is moving along the highway at 44 km/h on a rainy day. What is the minimum coefficient of friction between tires and road that will allow cars to take the turn without sliding off the road? (Assume the cars do not have negative lift.)


Fk=ukFn
Fs, max=usFn
F=mv^2/R


Honestly no idea at how to attempt it. Although I did find that θ needed to be:
tanθ=v^2/gR
tanθ=12.2^2/(9.8)(201)
θ=4.32°

Thank you for any help!
 
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  • #2


As always, the first step is to draw a diagram showing all the forces acting on the car.
 

1. What is the minimum coefficient of friction needed to keep cars from sliding off the road?

The minimum coefficient of friction needed to keep cars from sliding off the road varies depending on factors such as the weight and speed of the car, as well as the road conditions. However, in general, a coefficient of friction of 0.7 or higher is considered sufficient to prevent cars from sliding off the road.

2. How do road conditions affect the minimum coefficient of friction needed to keep cars from sliding off the road?

Road conditions, such as wet or icy surfaces, can significantly decrease the coefficient of friction between the tires of a car and the road, making it more likely for the car to slide off the road. This is why it is important for drivers to adjust their speed and driving behavior according to the road conditions to maintain control of their vehicle.

3. Can the weight and speed of a car affect the minimum coefficient of friction needed to keep it from sliding off the road?

Yes, the weight and speed of a car can greatly impact the minimum coefficient of friction needed to prevent sliding. Heavier cars require a higher coefficient of friction to maintain control, while faster speeds can also decrease the coefficient of friction, making it easier for a car to slide off the road.

4. What are some ways to increase the coefficient of friction to prevent cars from sliding off the road?

Some ways to increase the coefficient of friction and prevent cars from sliding off the road include using tires with good tread and proper air pressure, driving at a safe speed for the road conditions, and avoiding sudden or sharp turns. Additionally, using sand or salt on icy roads can increase the coefficient of friction and improve traction for vehicles.

5. Are there any other factors that can affect the minimum coefficient of friction needed to keep cars from sliding off the road?

Yes, there are other factors that can affect the minimum coefficient of friction needed to prevent cars from sliding off the road. These include the type of tires on the car, the suspension system, and the overall condition of the vehicle. It is important for drivers to regularly maintain their vehicles to ensure optimal safety on the road.

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