For this assignment you submit answer by question parts. The number of submissio

Question

For this assignment you submit answer by question parts. The number of submission for each question part only changes if you submit or change the answer. You best submission for each question for your score. As a civil engineering Intern during one of your summers in college, you are asked to design a curved section of roadway that meets the following conditions: When ice is on me road, and the coefficient of static friction between the road and rubber is 0.066, a car a? rest must not slide into the ditch and a car travelling less than 59 km/h must not skid to the outside of the curve. Neglect effects of air drag and rolling friction. What is the minimum radius of curvature of the curve and at what angle should the road be banked?

Explanation / Answer

Friction down the incline= mg*0.068*cosTheta
so gravity down the incline can’t be greater than that.

(1) mg*sinTheta < mg*0.068*cosTheta
or TanTheta < 0.068
Now at 59 km/hr (16.4 m/s) centripetal force will have two components: up the plane (mv^2/r * cosTheta) and normal to the plane (mv^2/r*sinTheta). We still have the up the plane and normal components of the weight of the car.

So, the force up the plane < retarding friction force.
mv^2/r*cosTheta – mg*sinTheta < 0.068*(mg*cosTheta + mv^2/r * sinTheta)
Divide both sides by m*cosTheta

v^2/r - g TanTheta < 0.068*g + 0.068*v^2/r *tanTheta

solve for tan Theta in (1) put that into the equation and solve for r.

(16.4^2/r) – 9.8*0.068 < 0.068*9.8 + 0.068*(16.4^2/r)*0.068

(268.96/r)*(1 - 0.004624) < 1.3328

r > 200.8 m

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