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## Homework Statement

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

75km/h = 20.8m/s

95km/h = 26.4m/s

## Homework Equations

Fr=mv^2/r

Fr=centripetal force

m = mass

r = radius

v = velocity

Fn= normal force

Ffr= force of friction (Us*Fn)

g = gravitational acceleration

Us = coefficient of static friction

## The Attempt at a Solution

Horizontal component

sinθFn=mv^2/r Eq 1

Vertical component

cosθFn=mg

Fn=mg/cosθ Eq 2

Sub eq 2 into 1

sinθ (mg/cosθ) = mv^2/r (sinθ/cosθ = tanθ)

tanθ mg = mv^2/r

m cancels out

tanθ = v^2/gr

θ = arctan 20.8^2/9.8*88

**θ = 26.6 degrees**

Am I right up to there?

Now for the second part of the question. Solving for Us.Am I right up to there?

Now for the second part of the question. Solving for Us.

See diagram for force of friction and horizontal and vertical components

Vertical component

cosθFn - sinθFfr - mg = 0 ( there is no vertical displacement)

Solve for Fn

Fn= (sinθFfr + mg)/cosθ

Horizontal component

sinθFn + cosθFfr = mv^2/r

Sub Fn from above

sinθ ((sinθFfr + mg)/cosθ) + cosθFfr = mv^2/r

From here I am unable to isolate Ffr, or cancel out the mass.... Help!!

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