How large must the coefficient of static friction be between the tires and the road if a car is to round a level curve of radius 78 m at a speed of 104 km/h?

Coefficient of static friction needs to be 1.1 or larger. For this problem, we need to static friction to be at least as large as the centripetal acceleration that the car will experience. So let's get our formulas. Centripetal acceleration: F = mv^2/r where F = force m = mass v = velocity r = radius of curve Friction F = mac where F = force m = mass a = gravitational acceleration c = coefficient of friction Since the frictional force has to be at least as large as the Centripetal force, let's set an inequality between them. mv^2/r ≤ mac v^2/r ≤ ac v^2/(ar) ≤ c Now let's convert km/h to a more convenient m/s. 104 km/h / 3600 s/h * 1000 m/km = 28.88888889 m/s Let's substitute the known values into the inequality and calculate. v^2/(ar) ≤ c (28.88888889 m/s)^2/(9.8 m/s^2 * 78 m) ≤ c 834.5679012 m^2/s^2 / 764.4 m^2/s^2 ≤ c 1.091794743 ≤ c Rounded to 2 significant figures gives a required coefficient of static friction of 1.1 or greater. This is a rather large value and indicates that the car is not at all likely to be capable of taking that curve at that speed. There are some things that can be done to mitigate the issue. Those being 1. Reduce the velocity. 2. Increase the normal force. Perhaps by aerodynamic means 3. Bank the curve.

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