# Homework Help: Banked Curve perfectly banked

1. Oct 20, 2011

### starji

Banked Curve "perfectly banked"

1. The problem statement, all variables and given/known data

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?

2. Relevant equations
ƩF=ma and a=v^2/r and Ff=μFn

3. 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!

Last edited: Oct 20, 2011
2. Oct 20, 2011

### starji

Re: Banked Curve "perfectly banked"

oh and the answer is 0.22

3. Oct 20, 2011

Re: Banked Curve "perfectly banked"

I think by perfectly banked they mean no friction.

Remember to convert units as well.

Start by finding what angle its banked at.

4. Oct 20, 2011

### starji

Re: Banked Curve "perfectly banked"

yes it is 88m

5. Oct 20, 2011

### starji

Re: Banked Curve "perfectly banked"

and thank you