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## Homework Statement

If a curve with a tedious of 80m is perfectly banked for a car traveling 70km/h, what must be the coefficient of static friction for a car not to skid when traveling at 90 km/h ?

## Homework Equations

Newton’s second law

F=ma

## The Attempt at a Solution

To find the angle of the bank, I set the forces in the x-axis equal (because it’s perfectly banked In the first scenario) .

Fx = Fc

(Mg/cos(theta)• sin theta)=mv^2 / r

Mass cancels out

So we’re left with

g• (sin theta / cos theta) = v^2 /r

Sin over cos equals to tan , so

gtan theta = v^2/r

Isolate theta and you get

Theta = tan^-1 (v^2/r)

Theta = than^-1 (19.5^2/80)

Theta= 25.8

I will insert a photo of my free body diagram so it won’t seem confusing and my work just in case .

To find the static friction :

We can conclude that

Fnsin(theta) + Fcos(theta) =mv^2/r

And

Fncos(theta)= mg

So we isolate fn from the second equation and plug in into the first equation

So ..

(Mg/cos(theta))•sintheta + (mu)(mg/cos theta) • cos theta = mv^2/r

Simplify it to :

gtan(theta) + (mu)gcos theta= v^2/r

Isolate mu

Mu=[(v^2/r)-gtan theta]/gcos theta

When you plug in the numbers it’ll look like this

Mu= [(25^2/80)-9.8tan(25.8)]/9.8cos(25.8)

I keep getting

Mu= 0.345

The correct answer should be 0.2275

Where did I go wrong or did I miss a step ?View attachment 216722

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