Engineers carefully designed a curved section of highway to prevent accidents. T

Question

Engineers carefully designed a curved section of highway to prevent accidents. The banking angle (theta) was chosen such that a car travelling at the standard speed limit of 29.0 ms (i.e. 65mhr) would not slide off the road if the roads became slick (fractionless). The radius of the curve was set to 200m. SHOW ALL YOUR WORK!

A) what acceleration would a vehicle experience if it travels around this curve at the speed limit?

B) Calculate the optimum banking angle by assuming there is no friction(just like the engineers did)

C) Sometime after the road is constructed, a 1000kg car enters the curve at a reckless 50 m/s (i.e ~ 112 mi/hr). If the coefficient of static friction between the road and the tires is .75, will the car make it around the curve safely.

Explanation / Answer

A) a =V^2/R = 29^2/200 = 4.205 m/s^2

B) theta = tan^-1V^2/Rg = 23.22 degrees

C) N = mg*cos(theta)

f = mue*mg*cos(theta) = m*V^2/R ..

V = mue*R*g*cos(theta)^1/2 = (0.75*200*9.8*cos23.22)^(1/2) .

V = 36.754 m/s < 50 the car will make it around the curve

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