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Banked Curve perfectly banked

  1. Oct 20, 2011 #1
    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. jcsd
  3. Oct 20, 2011 #2
    Re: Banked Curve "perfectly banked"

    oh and the answer is 0.22
     
  4. Oct 20, 2011 #3
    Re: Banked Curve "perfectly banked"

    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.
     
  5. Oct 20, 2011 #4
    Re: Banked Curve "perfectly banked"

    yes it is 88m
     
  6. Oct 20, 2011 #5
    Re: Banked Curve "perfectly banked"

    and thank you
     
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