What is the Coefficient of Static Friction for a Car on a Circular Track?

[vijay123]

hey guys, jus wunna see how u solve this question.

-a car traveling on a flat(unbanked) circular track accelerates uniformly from rest with a tangetial acceleration of 1.70m/s(squared). the car makes it one fourth of the way around the circle before it skids off the track. cetermine the coefficient of static friction between the car and the track from this data.

 

[Andrew Mason]

hey guys, jus wunna see how u solve this question.

-a car traveling on a flat(unbanked) circular track accelerates uniformly from rest with a tangetial acceleration of 1.70m/s(squared). the car makes it one fourth of the way around the circle before it skids off the track. cetermine the coefficient of static friction between the car and the track from this data.

You will have to show us what you have done so far to analyse the problem.

What is the condition for the car leaving the track?

AM

 

[vijay123]

thats what the question says...i don't understand your question.
i think the condition is that centripetal force is exerted in one side and static friction is at the other side...now i think that the centripetal force outdid the static frcition.so we know that tangential acceleration is 1.7 and we also know that the displacement of theta is pie divided 4 radians...since the displacemn is 45degrees.

 

[lightgrav]

Do you know how the static friction Force depends on the coefficient?

What "formula" do you know for the "centripetal force"? What causes it?

What's different about the later part (car NOT travel in circle) and earlier?

 

[vijay123]

fine..i ll state down everythn...
static friction is equal to mu*mg.
centripetal froce is equal to mv(sqaured) divided by radius.
now they have given us tangetial acceration...i knoiw that tangentail acceleration is equal to radius * angular acceleration.
herfore...(omega)sqaured=2*angular acceleration*displacement...were omega is angular velocity, and displacement is theta which is 45degress or pie/4 rad. therofre...ifrom the info, we could find omega in terms of radius.now mv(squared)/r is simply m*(omega)(sqaured)*radius. hence if we would equate the equation on static friction to this equation...we would get an answer...i got an answer with was nearly half of the actual ans.
my ans was 0.24 but the actual one is 0.57(approx there). yea...so i wunted to see were i went wrong...(this is a 9th grade problem...which i am in)(chapter is on rotation motion)

 

[lightgrav]

You did all the Physics right ...
but 1/4 of the way around a circular track is 90 degrees ... pi/2 .

 

[vijay123]

ooooooooo...my god!
how silly of me...thanks a lot for correcting me on that...lol...to about an hour pondering were i have gone wrong...lol...thanks a lot...really been a pleasure meeting you

 

[vijay123]

but..my answers is again a bit off...according to my calculations, the coffeicinet of frcition is 0.545 but the actual ans. is 0.57...(think dat made any difference?)

 

[lightgrav]

Well, I can't check your calculations because you never told me the radius.
did you round off the angular accel? did you round off pi?

Wait ... the car also has tangential acceleration, as well as centripetal a.

You have to find the magnitude of the TOTAL acceleration (Pythagoras).

 

[vijay123]

k thx...i ll try that way...
the question does not state the radius anyway...i think they get canceled way if you do the final calculations...thx for the advice

 

[vijay123]

yay...i got the answer...thx a lot lightgrav...your da man!

 

[Andrew Mason]

yay...i got the answer...thx a lot lightgrav...your da man!

Since the condition for leaving the track is: centripetal force = static friction force.

mv^2/R = m(at)^2/R = \mu mg

(1) \mu = a^2t^2/gR

So we need to find t^2/R.

\theta = \pi/2 = \int \omega dt = \int \alpha t dt = \frac{1}{2}\alpha t^2

Since a = \alpha R:

\frac{1}{2}\alpha t^2 = \frac{at^2}{2R} = \pi/2

So:

t^2/R = \pi/a

Substituting into (1):

\mu = a\pi/g

\mu = 1.7*3.14/9.8 = .545

AM

 

[vijay123]

hey mason...but the answer is 0.571...i too got that ans. but not with calculus...but actually, you would have to find the magnitude of acceleration and not radial accelerations...thats wut ma calculations show me...but the correct ans. is 0.571.

 

[vijay123]

but thanks for the calculus method..it makes more sense...

 

[arunbg]

You have to find the magnitude of the TOTAL acceleration (Pythagoras).

I don't think you need to take the NET acceleration,
rather you need to use the fact that at the instant of slipping, max static frictional force ( which provides for rotation ) equals centripetal force, and the tangential acceleration has to be used separately as AM pointed out .
And as far as I can see AM's solution is absolutely correct ( as it usually is :) )

Arun
__________________________________________________________

Two things are infinite: the universe and human stupidity; and I'm not sure about the the universe.
Albert Einstein

 

[vijay123]

that what my previous calculation did but my answer was just like mason's one. but when i flipped through the ans. book, it gave another. so i tried to find the magnitude of roational and tangential acceleration and then equated it to the force of friction. i got the correct ans.
i know it doesn't make sense but i don't have another way of doing it.
any suggestions. ans. is 0.57

 

[Doc Al]

I don't think you need to take the NET acceleration,
rather you need to use the fact that at the instant of slipping, max static frictional force ( which provides for rotation ) equals centripetal force, and the tangential acceleration has to be used separately as AM pointed out .

Yes, you do need to consider NET acceleration. Realize that the static friction provides the total force, not just the centripetal component.

 

[vijay123]

..

thanks a lot for that confirmation doc al.
i seem to get the concept now.

 

[Andrew Mason]

Yes, you do need to consider NET acceleration. Realize that the static friction provides the total force, not just the centripetal component.

So where does it say that this is not a rocket powered car?

If you assume the car accelerates due to tire friction, the expression for \mu is:

\mu = \sqrt{a^2\pi^2 + a^2}/g = .571

AM

 

[vijay123]

lol...i understand you too...if the car did not have wheels, then your ans. would have been true.
but too bad, this is not that roket space car in sci fi.

 

[arunbg]

Of course , Doc thanks for the correction .
What was I thinking !( rams head against wall )
I just proved my sig, the latter part that is :D

_______________________________________________

Two things are infinite: the universe and human stupidity; and I'm not sure about the universe.
Albert Einstein

 

[Doc Al]

So where does it say that this is not a rocket powered car?

Good point! May as well have those rockets provide the centripetal force as well.

 

[vijay123]

haha..i like you guys

 

[Andrew Mason]

lol...i understand you too...if the car did not have wheels, then your ans. would have been true.
but too bad, this is not that roket space car in sci fi.

If it has wheels but the friction between the wheels and the road does not provide the forward acceleration (e.g a rocket or jet engine), the tire friction provides only the centripetal acceleration.

Good point! May as well have those rockets provide the centripetal force as well.

Rocket steering wastes energy!

AM

 

[vijay123]

i dun understand wut you r trying to convey...wut do you mean by the friction provides only centripetal a.?

 

[Doc Al]

In an ordinary car (no rockets ) the only force available to accelerate the car is friction; that friction will accelerate the car both tangentially and centripetally. But Andrew gave an example of a rocket-powered car where the rocket provides the tangential force, leaving friction to handle the centripetal force.

 

[vijay123]

ok...i get it...