Halliday, Resnick & Walker — Force and Motion-II: Problem 58

58 Brake or turn? Figure 6-46 depicts an overhead view of a car's path as the car travels toward a wall. Assume that the driver begins to brake the car when the distance to the wall is \(d = 107 \text{ m}\), and take the car's mass as \(m = 1400 \text{ kg}\), its initial speed as \(v_0 = 35 \text{ m/s}\), and the coefficient of static friction as \(\mu_s = 0.50\). Assume that the car's weight is distributed evenly on the four wheels, even during braking. (a) What magnitude of static friction is needed (between tires and road) to stop the car just as it reaches the wall? (b) What is the maximum possible static friction \(f_{s,\max}\)? (c) If the coefficient of kinetic friction between the (sliding) tires and the road is \(\mu_k = 0.40\), at what speed will the car hit the wall? To avoid the crash, a driver could elect to turn the car so that it just barely misses the wall, as shown in the figure. (d) What magnitude of frictional force would be required to keep the car in a circular path of radius \(d\) and at the given speed \(v_0\), so that the car moves in a quarter circle and then parallel to the wall? (e) Is the required force less than \(f_{s,\max}\) so that a circular path is possible?