Banked Curve perfectly banked

[starji]

Banked Curve "perfectly banked"

Homework Statement

if a curve with a radius of 88. is perfectly banked for a car traveling 75km/h, what must be the coefficient of static friction for a car not to skid when traveling 95km/h?

Homework Equations

ƩF=ma and a=v^2/r and Ff=μFn

The Attempt at a Solution

below is my attempt but i also want to know what they mean when they say "perfectly banked" is that a specific angle or a specific coefficient of friction? because i can't seem to get anywhere.

a=75²/88 Fnx=Fnsinθ, Fny=Fncosθ, Ffx=Ffcosθ, Ffy=Ffsinθ.
in the x-direction:
ƩF=ma
Fnx+Ffx=ma
Fnsinθ+μFncosθ=m(75²/88)
(88Fn(sinθ+μcosθ))/75²)=m

in the y-direction
ƩF=ma
Fny-Ffy-Fg=ma (no acc in y-dir)
Fncosθ-μFnsinθ=mg
(Fn(cosθ-μsinθ))/g=m

set the 2 equations equal to each other:
(88Fn(sinθ+μcosθ))/(75²)=(Fn(cosθ-μsinθ))/(9.8) (Fn divides out)
(88)(9.8)sinθ+(88)(9.8)μcos=75²(cosθ)-75²(μsinθ)
common factor, take sin and cos out of brackets on both sides, divide:
tanθ=(75²-(88)(9.8)μ)/(75²μ+(88)(9.8)

and that's as far as i got help me please!

 

[starji]

oh and the answer is 0.22

 

[Bread18]

Radius of 88 what? Meters?

I think by perfectly banked they mean no friction.

Remember to convert units as well.

Start by finding what angle its banked at.

 

[starji]

yes it is 88m

 

[starji]

and thank you