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Car driving around a banked curve (with friction)

  • Thread starter TA1068
  • Start date
13
0
1. Homework Statement
A concrete highway curve of radius 80.0 m is banked at a 13.0 degree angle.

What is the maximum speed with which a 1400 kg rubber-tired car can take this curve without sliding? (Take the static coefficient of friction of rubber on concrete to be 1.0.)


2. Homework Equations
[tex] F_r = \frac{mv^2}{r}[/tex]

[tex]F_f = \mu N[/tex]


3. The Attempt at a Solution
I have a few pieces here, but I'm not completely sure how to put them together.

There's a rotational force pulling towards the center of the circle:
[tex] F_r = \frac{mv^2}{r}[/tex]
Where mass and radius are given.

Also, there is a frictional coefficient:
[tex]F_f = \mu N[/tex]
Where [tex]\mu[/tex] is 1.0 and N is mgcos[tex]\theta[/tex] (at least I believe it is... or is it just mg?) where m, g, [tex]\mu[/tex], and [tex]\theta[/tex] are given.

I had a relatively easy time understanding problems in which there was no friction, but I can't quite figure this out. Anyone have any advice to push me in the right direction? :)
 

Answers and Replies

85
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You already noted that the centripedal force is towards the center of the circle, so all you need to know now is which forces have a component pointing horizontally towards the center. I suggest that you draw a free body diagram with all the forces. This will help you see which contribute (and what components) to the centripetal force.
 
335
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carbank.gif
 
13
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Awesome... Thank you very much! It all makes sense now. I kept treating centripetal force as a force in itself instead of a net force. Thanks again!
 

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