Friction on a banked road and max velocity

AI Thread Summary
The discussion revolves around calculating the maximum speed of a vehicle on a wet banked road with given coefficients of static and kinetic friction, a banking angle of 25 degrees, and a curve radius of 50 meters. The user has set up the equations based on Newton's second law but is unsure how to proceed with solving them. They are seeking clarification on whether to treat the equations as a system and how to manipulate them, specifically whether to divide them and in what order. The conversation highlights the importance of understanding the relationship between forces acting on the vehicle and how to derive the maximum speed from the equations provided. The user is looking for guidance on the next steps in their calculations.
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Homework Statement


Consider a wet banked roadway, where there is a coefficient of static friction of 0.300 and a coefficient of kinetic friction of 0.250 between the tires and the roadway. The radius of the curve is 50.0 m. If the banking angle is 25˚, what is the maximum speed an automobile can have before sliding up the banking?

Homework Equations


Free body diagram-http://s3.amazonaws.com/answer-board-image/e89af301a0a3642873d7794ad22fba83.jpg

f=static friction
θ=25˚ angle
μ=friction coefficient=.300 static
r=50.0m
m=mass
g=gravity

Using ΣF=ma Newton's 2nd law:
x-> ΣF=μmgcos(25˚) + N*sin(25˚)=mv^2/r
y-> ΣF=Ncos(25˚)=μmgsin(25˚) +mg

The Attempt at a Solution


masses cancel I know.

x-> .300*9.8cos(25˚) + 9.8*sin(25˚)=v^2/50.0
y-> 9.8*cos(25˚)=.300*9.8sin(25˚) + 9.8

and that's as far as I get. Can anybody please explain what I need to do next?

Thanks
 
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I guess what I'm asking is do I need to treat this as a system of equations? Do I need to divide, and if so is it x/y or y/x?
 

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