Mary and her younger brother Alex decide to ride the carousel at the State Fair. Mary sits on one of the horses in the outer section at a distance of 2.0 m from the center. Alex decides to play it safe and chooses to sit in the inner section at a distance of 1.2 m from the center. The carousel takes 4.3 s to make each complete revolution. (a) What is Mary's angular speed wand tangential speed VM? WM VM 1.46 Consider the definition of angular speed. rev/s 2.92 m/s (b) What is Alex's angular speed w, and tangential speed VA? WA 1.46 Consider the definition of angular speed. rev/s VA 1.75 m/s A jet fighter flying at 300 m/s (just below the speed of sound) makes a turn of radius 2.75 km. (a) What is its centripetal acceleration in gs? 1.09 Consider the dependence of centripetal acceleration on tangential speed and radius of circular path.g (b) Suppose the pilot makes an emergency turn to avoid an approaching missile, subjecting himself to a centripetal acceleration of 10 gs, while flying at 625 m/s (supersonic). What is the radius, in km, of his turn? (This must be short-lived because fighter planes can only briefly endure such large accelerations without serious damage, and the pilot will soon black out at 10 gs.) 3.985 km A rotating space station is said to create "artificial gravity"-a loosely-defined term used for an acceleration that would be crudely similar to gravity. The outer wall of the rotating space station would become a floor for the astronauts, and centripetal acceleration supplied by the floor would allow astronauts to exercise and maintain muscle and bone strength more naturally than in non-rotating space environments. If the space station is 240 m in diameter, what angular velocity would produce an "artificial gravity" of 9.80 m/s at the rim? 0.2858 x Consider the dependence of centripetal acceleration on tangential speed and radius of the circular path. rpm What is the ideal banking angle for a gentle turn of 1.45 km radius on a highway with a 115 km/h speed limit (about 71 mph), assuming everyone travels at the limit? 89.20 Did you draw a free-body diagram and label all forces acting on a vehicle? Identify the force that supplies the centripetal force needed to keep a vehicle in this circular path. A stunt pilot in an air show performs a loop-the-loop in a vertical circle of radius 2.81 x 103 m. During this performance the pilot whose weight is 625 N, maintains a constant speed of 2.10 102 m/s. Q R (a) When the pilot is at the highest point of the loop determine his apparent weight in N. 375.96 N 165.95 (b) At what speed, in m/s, will the pilot experience weightlessness? m/s (c) When the pilot is at the lowest point of the loop determine his apparent weight in N. 1000.96 In what direction does the centripetal force act when the pilot is at the lowest point in the circle? N