As a civil engineering intern during one of your summers incollege, you are aske

Question

As a civil engineering intern during one of your summers incollege, you are asked to design a curved section of roadway thatmeets the following conditions: When ice is on the road, and thecoefficient of static friction between the road and rubber is0.096, a car at rest must not slideinto the ditch and a car traveling less than 62 km/h must not skid to the outside of the curve.Neglect the effects of air drag and rolling friction. What is theminimum radius of curvature of the curve and at what angle shouldthe road be banked?
rmin = m angle = ° rmin = m angle = °

Explanation / Answer

apply f = ma to the car at rest: Fy = fncos + fssin - mg = 0 .... (1) Fx = Fnsin - fscos = 0 ............ (2) Substitute in fs = sFn into equation 2 ... and solve for = tan^-1(s) = tan^-1(.096) = 5.48degrees Apply F=ma to the car with speed v Fy = fncos - fssin - mg = 0    (3) Fx = Fnsin + fscos = mv^2/r    (4) again... substitute in fs = sFn to equations 3/4 to get: Fn(cos-sin) = mg (5) Fn(cos + sin) = mv^2/r (6) substitutes in values and solve for equations 5 and 6 For equation 5: Fn(cos5.48 - .096sin5.48) = mg .986Fn = mg For equation 6: Fn(.096cos5.48+sin5.48) = mv^2/r .191Fn = mv^2/r Eliminate Fn and solve for r r = v^2/.193g Plug in and solve for r r = (62 km/hr x 1 h/3600 s x 1000 m/km)^2 / (.193 x 9.8) r = 156.2 m

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