6. A Puzzling Question to Think About: If an object is in uniform circular motion, then it is accelerating towards the center of the circle; yet the object never gets any closer to the center of the circle. It maintains a circular path at a constant radius from the circle's center. Suggest a reason as to how this can be. How can an object accelerate towards the center without ever getting any closer to the center? 7. A Thought Experiment: Suppose that an object is moving in a clockwise circle (or at least trying to move in a circle. a. Suppose that at point A the object traveled in a straight line at constant speed towards B'. In what direction must a force be applied to force the object back towards B? Draw an arrow on the diagram in the direction of the required force b. Repeat the above procedure for an object moving from C to D' In what direction must a force be applied in order for the object to move back to point D along the path of the circle? Draw an arrow on the diagram. c. If the acceleration of the body is towards the center, what is the direction of the unbalanced force? Using a complete sentence, describe the direction of the net force that causes the body to travel in a circle at constant speed. 8. Thinking Mathematically: Explore the quantitative dependencies of the acceleration upon the speed and the radius of curvature. Then answer the following questions. a. For the same speed, the acceleration of the objects varies (directly, inversely) with the radius of curvature. b. For the same radius of curvature, the acceleration of the object varies (directly, inversely) with the speed of the object. C. As the speed of an object is doubled, the acceleration is ('4 x, /4 x. 2x, 4x) the original value. d. As the speed of an object is tripled, the acceleration is (1/3, 1/9, 3x, 9x) the original value. e. As the radius of the circle is doubled, the acceleration is (1/4, /2, 2x, 4x) the original value f. As the radius of the circle is tripled, the acceleration is (1/3, 1/9, 3x, 9x) the original value