Banked Curve Safety Speed Problem

[hanlon]

Homework Statement

A curve of radius 68m is banked for a design speed of 85km/h. If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely make the curve?

Homework Equations

1) F_Nsin(theta) = m*v²/r
2) F_Ncos(theta) - mg = 0
3) tan(theta) = v²/rg

The Attempt at a Solution

I used the third equation to find (theta) which is 39.9^o
but I can't find out how to find F_fr or the range of velocity
I understand that when the car goes slow the frictional force faces up the banked curve and when it goes fast the friction goes down the banked curve but I can't figure out how to solve the question.

 

[tiny-tim]

Hi hanlon!

(have a theta: θ and a mu: µ )

1) F_Nsin(theta) = m*v²/r
2) F_Ncos(theta) - mg = 0
3) tan(theta) = v²/rg
…
but I can't find out how to find F_fr or the range of velocity
I understand that when the car goes slow the frictional force faces up the banked curve and when it goes fast the friction goes down the banked curve but I can't figure out how to solve the question.

When the car is at its fastest safe speed, the friction force will be µ_sF_N, = 0.3F_N.

So rewrite 1) and 2) to include the friction …

what do you get? ​