# Name St. Mary's HS AP Physics Circular Motion HW

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1 Name St. Mary's HS AP Physics Circular Motion HW Base your answers to questions 1 and 2 on the following situation. An object weighing 10 N swings at the end of a rope that is 0.72 m long as a simple pendulum. At the bottom of the of the swing, the tension in the string is 12 N. 1. What is the speed of the object at the bottom of the swing? 2. What is the magnitude of the centripetal acceleration at the bottom of the swing? 3. An object moves at constant speed in a circular path of radius r with a period of T. What is the object's acceleration? A) 0 B) 2 Tr 2 C) 2 r T D) 4 2 r T 2 E) 4 2 Tr 2 4. An object is tied to a string and moves in a circular path at constant speed. Which of the following statements are accurate? I. The net force on the object is zero. II. The acceleration is zero. III. The acceleration is constant. A) II only B) II and III only C) I and III only D) I, II, and III E) None of the above are accurate

2 5. An object is undergoing uniform circular motion. Which of the following statements is true? A) The velocity is constant. B) The acceleration is constant. C) The acceleration is constant, but the velocity varies. D) The velocity is constant, but the acceleration varies. E) Both the acceleration and velocity are constant. 6. What is the centripetal acceleration of a ball swinging around a string when it passes one revolution in 5 seconds and the radius of its path is 1m? 7. A ball attached to a string is whirled around a horizontal circle of radius r with a tangential velocity v. If the radius is changed to 2r and the magnitude of the centripetal force is doubled the new speed is 8. A satellite orbits a planet at a radius R with a period T. What is the magnitude of its centripetal acceleration? A) 4 2 R 2 T B) 4 2 R 2 T 2 C) 4 2 R 2 T 2 D) 4 2 R T 2 E) 4 2 R T 9. An object moves, starting from rest, along a frictionless track with a loop shown below. What is the minimum height, h, of the track for the object to make it completely around the circle? A) 12.5 m B) 25 m C) 50 m D) 62.5 m E) 100 m

3 10. A 60 kg adult and a 30kg child are passengers on a rotor ride at an amusement park as shown in the diagram above. When the rotating hollow cylinder reaches a certain constant speed, v, the floor moves downward. Both passengers stay "pinned" against the wall of the rotor, as shown in the diagram below. The magnitude of the frictional force between the adult and the wall of the spinning rotor is F. What is the magnitude of the frictional force between the child and the wall of the spinning rotor? A) F B) F C) F D) 2F E) 4F Base your answers to questions 11 and 12 on the following situation. An engineer wishes to design a roller coaster so that the cars will not fall when they are at the top of their circular path. 11. A 500 kg roller coaster car is designed to travel at 20 m/s at the top of the circle. The engineer wants to make the circle as large as possible while still being at least one quarter the maximum radius for safety reasons. How large can the radius of the circle be? 12. Which of the following will have no effect on whether the cars remains on the track? A) The velocity of the cars as the pass the top of the circle. B) The radius of the circular track. C) The mass of the cars. D) The distance from the top of the circle to the bottom. E) The acceleration due to gravity.

4 Base your answers to questions 13 and 14 on the following situation. An object with a mass of 5 kg is attached to a 1 meter long rope and whirled in a vertical circle. 13. Of the following, which is the greatest speed of the object for which the rope would become slack at the top of its circular path? 14. At the bottom of its path, the rope has a tension of 95 N. The object is moving most nearly 15. Which of the following is true of the velocity and acceleration vectors of an object moving with a uniform speed in a circular path? A) They are in opposite directions. B) They are always equal in magnitude. C) They are perpendicular in direction. D) They are both tangent to the path of motion. E) They are both directed toward the center of the circle. 16. The diagram below shows a satellite of mass m orbiting Earth in a circular path of radius R. If a centripetal force Fc is acting on the satellite, then its speed is equal to A) B) C) D)

5 17. A ball rolls down a curved ramp as shown in the diagram below. Which dotted line best represents the path of the ball after leaving the ramp? A) A B) B C) C D) D E) E 18. A small block of mass M is traveling on a track where a loop of radius R exists. What minimum speed is needed to keep the block on the track? A) B) C) D) E) 19. What is the maximum speed a vehicle can travel along a circular turn without leaving the road, if the turn has a radius of 50 m and the coefficient of static friction between the road and the tires is 0.20? 20. The maximum speed a car can travel around an unbanked curve depends on all of the following EXCEPT A) the diameter of the curve. B) the acceleration due to gravity. C) the mass of the car. D) the coefficient of kinetic friction between the road and the tires. E) the surface of the curve. 21. A vehicle of mass 3000 kg travels along an unbanked circular turn without leaving the road. If the turn has a radius of 10 m, and the coefficient of static friction between the road and the tires is 0.25, what is the maximum speed the vehicle can travel without slipping? A) 5 m/s B) 7.5 m/s C) 10 m/s D) 25 m/s E) 16 m/s

6 22. Base your answer to the following question on the diagram below. A horizontal turntable rotates with a constant rate. As viewed from above, an object on the turntable moves clockwise in a circle. Which of the following best describes the direction of the velocity of the object when it is in the position shown? A) Down and to the left B) Down C) Down and to the right D) To the left E) To the right

### B) v `2. C) `2v. D) 2v. E) 4v. A) 2p 25. B) p C) 2p. D) 4p. E) 4p 2 25

1. 3. A ball attached to a string is whirled around a horizontal circle of radius r with a tangential velocity v. If the radius is changed to 2r and the magnitude of the centripetal force is doubled the

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