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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=75^{2}/88 Fnx=Fnsinθ, Fny=Fncosθ, Ffx=Ffcosθ, Ffy=Ffsinθ.

in the x-direction:

ƩF=ma

Fnx+Ffx=ma

Fnsinθ+μFncosθ=m(75^{2}/88)

(88Fn(sinθ+μcosθ))/75^{2})=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))/(75^{2})=(Fn(cosθ-μsinθ))/(9.8) (Fn divides out)

(88)(9.8)sinθ+(88)(9.8)μcos=75^{2}(cosθ)-75^{2}(μsinθ)

common factor, take sin and cos out of brackets on both sides, divide:

tanθ=(75^{2}-(88)(9.8)μ)/(75^{2}μ+(88)(9.8)

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

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# Homework Help: Banked Curve perfectly banked

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