# Finding maximum acceleration with COF of Ms

1. Dec 26, 2007

### koolj

This problem seems simple enough but this coefficient of friction stuff easily confuses me..

1. The problem statement, all variables and given/known data
What is the maximum accleration a car can undergo if the coefficient of static friction between the tires and ground is .80?

2. Relevant equations
FFs = MsFn ?
a = f/m ?

3. The attempt at a solution

Im not really sure where to start with this, I have little idea how Im suppose to find the maximum acceleration with just the coefficient of friction given and nothing else. I assume I might need to switch some things around to find it?

2. Dec 26, 2007

### dynamicsolo

I'm assuming that you've talked about rolling in your course, at least enough to say that the portions of the tires in contact with the pavement are instantaneously stationary. This is why it is static friction that is involved in rolling, even though the vehicle is in motion.

I'll also point out that the question is assuming that the road is horizontal, which would lead to obtaining the maximum acceleration of the car. In that case, what is the normal force acting on each tire from the ground and what would the maximum static frictional force on each tire be? (For convenience, assume that the car's weight is evenly distributed on all four tires.)

Consider Newton's Third Law in dealing with the tires and the ground. Which way does the friction on each surface point? How does friction make the motion of the car possible?

3. Dec 27, 2007

### koolj

Well thats the thing, I cant find normal force because nothing other than the question was given. No masses at all, just the CoF. I believe that they would cancel out anyway and thats why they didnt list mass, but im still stuck in how Im suppose to solve this. We didn't really go over rolling, but i know what you mean when you say the tires surfaces are instantly stationary.

4. Dec 27, 2007

### Staff: Mentor

Just call the mass "m" and continue. You won't need it. Find the maximum force of friction, then apply Newton's 2nd law to find the corresponding maximum acceleration.

5. Dec 27, 2007

### koolj

ahhhh, wait I think I get it now. Thanks for the help, thats all I needed for now =)

6. Aug 31, 2009

could someone please clarify this? im studying this on my own (no teacher) and we havent really gone over rolling i have the exact same problem but have no idea how to start Thanks.

7. Aug 31, 2009

### Staff: Mentor

Follow my advice in post #4. If you still have problems, post your attempt and we can take a look at what you're doing.

8. Aug 31, 2009

Ffr $$\leq$$ uk x Fn

Fn = mg
Fn = 9.8m

Ffr $$\leq$$ .80 x 9.8m

m is of no regard in this problem therefore

Ffr $$\leq$$ 7.84 m/s2

9. Aug 31, 2009

### Staff: Mentor

Good. Since you want the maximum acceleration, choose the maximum value of static friction:
Ffr = μN = μmg.

Let's clean up your reasoning by applying Newton's 2nd law:
ΣF = ma
Ffr = ma
μmg = ma

so: a = μg

10. Aug 31, 2009