A road with a radius of 75 meters is banked so that a car cannavigate the curve

Question

A road with a radius of 75 meters is banked so that a car cannavigate the curve at speed of 15 m/s without any frcition. On a cold day when the street is icy, the coefficient of staticfriction between the tires and the road is 0.120. What is theslowest speed the car can go around this curve without sliding downthe bank? I figured out that the angle of the bank is 17 degrees but Icannot get past that. The answer in the book is 11.5m/s A road with a radius of 75 meters is banked so that a car cannavigate the curve at speed of 15 m/s without any frcition. On a cold day when the street is icy, the coefficient of staticfriction between the tires and the road is 0.120. What is theslowest speed the car can go around this curve without sliding downthe bank? I figured out that the angle of the bank is 17 degrees but Icannot get past that. The answer in the book is 11.5m/s

Explanation / Answer

sorry, made a calculation mistake. answer again. r = 75 m, v = 15 m/s, = 0.120, find the slowest speed u = tan-1(v2/rg) = 17o a = u2/r mgsin - f = macos, so f = m(gsin -acos) N - mgcos = masin, so N = m(gcos +asin) use f = N gsin - acos = (gcos + asin) a = g(sin - cos)/(cos+sin) = 1.7557 m/s2 u = (ar) = 11.5 m/s

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