What is the magnitude of the force exerted by friction?

[CStudy]

Homework Statement

Question: [/B]A 600-kg car traveling at 30.0 m/s is going around a curve having a radius of 120 m that is banked at an angle of 25.0°. The coefficient of static friction between the car's tires and the road is 0.300. What is the magnitude of the force exerted by friction on the car?

Homework Equations

F = ma

The Attempt at a Solution

http://imgur.com/FLrr1D6

Netwon 2nd Law Equations:
$$\sum F_{net, x} = nsin\theta +f_{s}cos\theta =m\frac{v^2}{r}$$
$$\sum F_{net, y}=ncos\theta -f_{s}sin\theta -mg =0$$
$$f_{s} = \mu n$$

Can anyone verify I am on the right track for solving the magnitude of the force exerted by friction. I have a feeling my equations maybe incorrect.

Here is the link to my diagram if it does not show. http://imgur.com/FLrr1D6

 

[J Hann]

Your equations look OK.

 

[haruspex]

$f_{s} = \mu_s n$

That is not quite right.

 

[CStudy]

Any suggestions on how do define the static friction? Haruspex, what you have pointed out is the source of my confusion. I understand the the static friction combined with some of the normal force is the cause of the centripetal acceleration, but I am having difficulties creating a mathematical model.

Should I just ignored defining the static friction and just solve for the components? You think that would give me the correct answer.

 

[haruspex]

Any suggestions on how do define the static friction? Haruspex, what you have pointed out is the source of my confusion. I understand the the static friction combined with some of the normal force is the cause of the centripetal acceleration, but I am having difficulties creating a mathematical model.

Should I just ignored defining the static friction and just solve for the components? You think that would give me the correct answer.

I haven't done the calculation, but it probably would in the present case.
With static friction, it is important to remember the coefficient only tells you the maximum ratio of frictional force to normal force. If the surfaces are not sliding, the magnitude of the frictional force is anything up to $\mu_sN$.

Logically, you should assume no sliding, determine the force from the other information, then check if the static coefficient is high enough. If not, it will slde, so you then calculate the frictional force using the kinetic coefficient. Since you are not told the kinetic coefficient, it is very likely that it will not slide.