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Michael

**1. Homework Statement**

A banked circular highway curve is designed for traffic moving at 70 km/h. The radius of the curve is 215 m. Traffic is moving along the highway at 40 km/h on a rainy day. What is the minimum coefficient of friction between tires and road that will allow cars to negotiate the turn without sliding off the road?

**2. Homework Equations**

f-mg*sin(x)=ma*cos(x)

N-mg*cos(x)=ma*sin(x)

tan(x)=v^2/Rg

where:

m= mass = cancels out

g= gravity = 9.8 m/s^2

a= acceleration = v^2/R = 11.11^2/215 = .574 m/s^2

x= angle

v= velocity = 40 km/h = 11.11 m/s

R= radius = 215m

**3. The Attempt at a Solution**

coefficent of friction = (g*sin(x)-a*cos(x))/(g*cos(x)+a*sin(x))

x= tan^-1(11.11^2/(215*9.8))

x= 3.353

f =

__(9.8*sin(3.353)-.574*cos(3.353))__

(9.8*cos(3.353)-.574*sin(3.353))

f = -1.01*10^-15