Max Speed of Car: 80m Track & .40 Coeff of Friction

[RoyG]

Homework Statement

"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.

Homework 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)

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?

 

[Pythagorean]

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

 

[Tanya Sharma]

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

 

[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?

 

[RoyG]

normal force is the mass times gravity?

 

[Tanya Sharma]

normal force is the mass times gravity?

Symbolically ,N=Mg

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

 

[Pythagorean]

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

 

[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?

 

[Tanya Sharma]

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?

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 .