# Homework Help: Maximum Speed of Car

1. Nov 20, 2013

### RoyG

1. The problem statement, all variables and given/known data
"what is the maximum speed at which a car can safely travel if the radius of the track is 80.0 m and the coefficient of friction is .40"
friction is providing the force and the track is flat and circular.

2. Relevant equations
the equations that we've been using in class are:
Fnet=ma
a= V^2/r
w=mg
force of friction= (coefficient of friction)(normal force)

3. The attempt at a solution
I set up the Newton's Second Law for centripetal force (Fnet=ma) and know that the Fnet would be the coefficient times the normal force. I set up the acceleration equation (a=V^2/r). But I'm confused about finding the normal force without a mass. I know that velocity is distance divided by time and that the distance would be 2∏r, but I don't know how you would find it that way without time. What am I missing?

2. Nov 20, 2013

### Pythagorean

just set mass to m for now and go through with and see what happens.

3. Nov 20, 2013

### Tanya Sharma

Let normal force be N and mass be M .How are they related ?

4. Nov 20, 2013

### RoyG

okay so I did (.40)(m)(9.8)=m(V^2/80)
which comes to be 3.92m=m(V^2/80)

and then I tried substituting V^2 with 160pi/time because of 2(pi)(r)
how do I work with the two variables?

5. Nov 20, 2013

### RoyG

normal force is the mass times gravity?

6. Nov 20, 2013

### Tanya Sharma

Symbolically ,N=Mg

Now what is the equation of centripetal force ? Please do not plug in the values .Work in terms of symbols .

7. Nov 20, 2013

### Pythagorean

You have an m on each side... sooo...

8. Nov 20, 2013

### RoyG

F stands for centripetal force, M stands for mass, and a stands for centripetal acceleration. This is the formula we used in class:
F=ma
Is this the equation of centripetal force or just Newton's 2nd Law for Circular Motion?

9. Nov 20, 2013

### Tanya Sharma

Centripetal acceleration = v2/R .It is the same thing as 'a' in ƩF = Ma .There is nothing called Newton's Law for circular motion.

Which force provides the car centripetal acceleration (i.e acceleration towards the center) ? Equate this force to Mv2/R just like you do in ƩF = Ma .

Last edited: Nov 20, 2013