Friction on a banked road and max velocity

  • Thread starter spark706
  • Start date
  • #1
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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
 

Answers and Replies

  • #2
3
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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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