Estimating Kinetic Friction Coefficient of Jet-Powered Car

[envscigrl]

Here is the problem:
When the jet-powered car "Spirit of America" went out of control during a test drive at Bonnevile Salt Flats, Utah, it left skid marks about 18.70km long. If the car was moving initially at a speed of 661.0km/hr, estimate the coefficient of kinetic friction between the tires and the road.

I know that the coefficient of kinetic friction can be found using the equation:
fk = u * N where u is the coefficient and N the normal force. But I cannot understand how I am supposed to find it with only the speed and distance. I tried finding the time (assuming V=0) then finding the acceleration and them finding the force with F=ma. But I was unsure if the f in the f=ma equation was equal to the f in the f=uN equation.

P.S.(I have converted the distance to meters (18700) and speed to m/s (186.618))
Thanks for your help and time!

 

[faust9]

Assume the engine shut down as soon as trouble occured. Furthermore, you'll have to assume that drag is zero (unless this is given to you). Draw a FBD. What forces are acting on the car and in which directions? Once you know the forces and how they are working with relation to the direction of motion you can use the work/energy theorm to figure out how much work is done by the forces slowing the car down in order to dissipate the energy of a car going 187 m/s. Where you also given the mass of the car?

Anyway, good luck.

 

[envscigrl]

No the problem did not supply a mass that is what is tripping me up on the problem. If I had the mass it would be much much easier.

 

[Soveraign]

Energy is certainly a way to solve this problem. If the car had a Kinetic Energy of (1/2)mv^2 and this was completely dissipated over some distance, you can figure through conservation of energy that all of the KE went into work as described by the work equation W = Fd (force times distance).

Ah, but we don't have mass! Well, let's just keep going to see how things turn out. Start out by saying
$$KE = W$$
so...
$$\frac 1 2 m v^2 = Fd$$
Now, what is this F in the right hand side (i.e. what creates this force and what is our formula for it?) In your first post you said you already knew that the force slowing down the car was the force of friction. The formula for this is:
$$F_{fric} = \mu N$$
Now, $\mu$ is what the question asks you to find, what about N? What is it based on? Find an expression for N, plug it into the frictional force equation, then plug that equation in for the force in our first relation and you might see some ways to simplify (i.e. cancel) a certain variable.

 

[envscigrl]

Thanks!