Three identical cars, A , B , and C , travel at the same speed across three bridges. Car A drives on a flat bridge, car B on a bridge that is convex upward, and car C on a bridge that is concave upward. Let F_A , F_B , and F_C denote the normal forces exerted by the cars on the bridges when they are at the center of the bridges. Which of the following statements is correct?

Step-by-step solution

For car A moving on a flat bridge, the vertical acceleration is zero. The normal force is given by F_A = mg . For car B moving on a convex upward bridge, the centripetal acceleration is directed downwards towards the center of curvature. The equation of motion is mg - F_B = mv^2 R , which gives F_B = mg - mv^2 R . For car C moving on a concave upward bridge, the centripetal acceleration is directed upwards towards the center of curvature. The equation of motion is F_C - mg = mv^2 R , which gives F_C = mg + mv^2 R .