Car travelling around a banked corner with friction

In summary, the problem involves finding the slowest speed a car can travel along a curve with a radius of 74.0m banked at an angle of 23 degrees and a coefficient of static friction of 0.09. Using the relevant equations, the minimum speed was found to be 19.70 m/s. The force of friction in this case is pointed upwards, preventing the car from sliding outwards.
  • #1
ineedhelp1234
6
0
The problem:
A car is traveling along a curve having a radius of 74.0m, banked at an angle of theta = 23 deg. The coefficient of static friction is 0.09. What is the slowest speed the car can negotiate the curve?


Relevant equations:
Fc = Fnet
Fc = mv^2/r
Fnet = [(tan(theta) + u)/(1-utan(theta))]mg


The attempt at a solution
v^2 = (74)[(tan23 + 0.09)/(1-0.09tan23)](9.8)
v = (387.92)^0.5
v= 19.70 m/s


This answer isn't being accepted by the online program we use in class and I can't figure out what I'm doing wrong. Any help would be much appreciate
 
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  • #2
Seems rather unusual for the question to be asking for the slowest speed.
 
  • #3
I think it means the slowest the car will be able to travel without sliding into the centre - it'll have to be moving fast enough to offset the other forces. That's how I took it at least. Part 2 of the question asks for the fastest speed, I figured I'd just try to figure out part 1 first:)
 
  • #4
Okay so i just realized that the speed I had found, 19.7 m/s, is for the fastest speed.

Now I have no idea how to solve for the slowest speed
 
  • #5
You calculated the maximum velocity. You should have calculated the minimum.

[tex]v_{min}=\sqrt{\frac{rg(sin\theta -\mu cos\theta)}{cos\theta +\mu sin\theta}}[/tex]
 
  • #6
To find your the slowest speed, your force of friction will be pointed the other direction. Redraw your forces. Think of any object (toy car) rolling on a notebook at a certain angle. If it is going really slow, it will start to 'slide' downwards right? It does not have enough speed to keep it at a constant radius. Since it's sliding downward force of friction is pointing up, away from the center.

Solve the same way you did with the maximum speed, where you had force of friction pointing downward (thus keeping the object from flying outwards).
 
  • #7
The equation worked, which is great, and the explanation was really helpful - I was just going to ask where the equation came from when i saw it - so thank you all!
 

Related to Car travelling around a banked corner with friction

1. What is a banked corner?

A banked corner is a curved section of road or track that is angled slightly higher on the outer edge, allowing vehicles to travel around the corner more easily.

2. How does friction affect a car travelling around a banked corner?

Friction is the force that opposes motion between two surfaces in contact. In the case of a car travelling around a banked corner, friction helps to keep the car from sliding off the track and allows it to maintain its speed and direction.

3. What factors determine the amount of friction experienced by a car on a banked corner?

The amount of friction experienced by a car on a banked corner depends on the weight of the car, the coefficient of friction between the tires and the surface of the track, and the angle of the banked corner.

4. Can a car travel at a constant speed around a banked corner?

Yes, a car can travel at a constant speed around a banked corner if the angle of the banked corner and the speed of the car are appropriately matched. This allows the centripetal force to balance out the centrifugal force, keeping the car moving in a circular path at a constant speed.

5. How does the speed of the car affect the amount of friction on a banked corner?

The speed of the car affects the amount of friction on a banked corner because it determines the amount of centrifugal force acting on the car. The higher the speed, the greater the centrifugal force, which requires a larger amount of friction to keep the car on the track.

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