What Is the Maximum Speed to Navigate a Banked Curve Without Sliding?

[man00war]

Homework Statement

A concrete highway curve of radius 70.0 m is banked at a 13.0 degree angle.
What is the maximum speed with which a 1900 kg rubber-tired car can take this curve without sliding? (Take the static coefficient of friction of rubber on concrete to be 1.0.)

Homework Equations

the equation that i was told to use is

vmax=sqrroute(R*g*( (1 + Fs*cotan(13)) /cotan(13)-Fs) )

The Attempt at a Solution

so i plug in my numbers vmax= (70*9.8)* (1+1*cotan(13))/(cotan(13)-1)

i get the sqrout of (686*1.023)

which tells me vmax equals 26.49

this is wrong can anyone help?
h

 

[acws337]

I didn't check to see if that equation matches the one I came up with( and I know is right since I have the same problem in my textbook)..but if its consistently giving you the wrong answer you should probably go back to your fbd and try again. The normal and static friction forces both have radial and z components and the force of gravity is acting on the car in the downward z direction. When I solved my force equations, I eliminated n...so try that.

 

[man00war]

i found what i was doing wrong thanks for your help