1. A train moves on a circular track at constant speed. (a) What is the direction of its acceleration? (b) As the train changes its position on the circle, what happens to the magnitude of the acceleration? (c) If the train doubles its speed, what happens to the magnitude of its acceleration? 2. (a) Why is a centripetal force needed to keep a body moving in a circular path? (b) Upon what three factors does the centripetal force keeping a body moving in a circular path depend? (c) Why do water drops fly tangentially off the wheels of a rapidly moving car on a rainy day? (d) How does banking a road on a turn help a speeding car make the turn safely? 3. A 1000-kg car moves around a circular section of a road having a radius of 50 m at a constant speed of 20 m/s. What is the centripetal acceleration of the car? What is the centripetal force required to keep the car on the road? 4. An airplane flying at constant speed in a circular course of radius 5000 m is observed to complete each round trip in 400 s. (a) What is the speed of the airplane? (b)What is its centripetal acceleration? 5. A force of 10 N applied to one end of a cord keeps an object tied to the other end moving at a speed of 2.0 m/s in a horizontal circle of radius 3.0 m. What is the mass of the object