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## Homework Statement

If a curve with a radius of 90 m is properly banked for a car traveling 68 [tex]\frac{km}{h}[/tex], what must be the coefficient of static friction for a car not to skid when traveling at 98 [tex]\frac{km}{h}[/tex]?

## Homework Equations

I know I need

[tex]\Sigma \vec{F} = m \vec{a}[/tex]

[tex]f_s <= \mu_s N[/tex]

and

[tex] a_c = \frac{v^2}{r}[/tex]

## The Attempt at a Solution

I first solved for [tex]\theta[/tex], which is the angle of embankment at which a car traveling 68 [tex]\frac{km}{h}[/tex] will need no friction to travel along a curve of radius 90 m.

Given

[tex]\Sigma \vec{F} = m \vec{a}[/tex]

with pertinent variables:

[tex]f_s = ma_c[/tex]

substituting for [tex]a_c[/tex]:

[tex]f_s = m\frac{v^2}{r}[/tex]

substituting for [tex]f_s[/tex]:

[tex]\mu_s N = m\frac{v^2}{r}[/tex]

substituting for [tex]N[/tex]:

[tex]\mu_s mg\tan{\theta} = m\frac{v^2}{r}[/tex]

dividing by m:

[tex]\mu_s g\tan{\theta} = \frac{v^2}{r}[/tex]

solving for [tex]\mu_s[/tex]:

[tex]\mu_s = \frac{v^2}{gr\tan{\theta}}[/tex]

Now substituting in for all known variables ([tex]v, g, r, and \theta[/tex]), [tex]\mu_s[/tex] equals 2.077, which MasteringPhysics does not accept.

Now, I'm very confused on this problem, mainly because I'm unsure if my free body diagram is correct:

http://img227.imageshack.us/img227/5083/physfbd.th.png [Broken]

Note: image is not to scale

Any help or hints would be appreciated!

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