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Old Apr 29th 2009, 01:35 PM   #1
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Join Date: Jan 2009
Posts: 26
Exclamation Circular motion "mu"

I dont have a particular question but there was a question on a quiz that totally stumped me, I am writing the test on this unit tomorrow so any help is appreciated.

the question was like.
A car is traveling in a circle with radius of 17 metres, is .38, what is the maximum speed the car could travel and maintain its course.

I figured it was something to do with friction force being = to centripetal force, but I dont have any formula's with other than ff = N.

And you dont know N or ff. I assume you have to find centripetal acceleration first?

is it ff=fc
mu N= (mv^2)/r
mu ma = (mv^2)/r
mu a= v^2/r
mu v^2/r = v^2/r
0.38 v^2/17 = v^2/17

Or something like that ??

Thank you.

Last edited by brentwoodbc; Apr 29th 2009 at 01:43 PM.
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Old Apr 29th 2009, 04:30 PM   #2
Join Date: Jul 2008
Posts: 33


The friction force $\displaystyle F_{f} = \mu \cdot N $ in this case.
For the car to maintain its course we need to have:

$\displaystyle F_{c}=m\cdot \frac{v^{2}}{r} = \mu \cdot mg $ , if the car is driving on a flat road $\displaystyle N = mg $.

Now you solve for the speed v. (Notice that the masses m cancel out).

$\displaystyle v = \sqrt{r\cdot \mu \cdot g} $
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