5. A car moves with a constant speed in a clockwise direction around a circular path of radius r, as represented in the diagram above.

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1 1. The magnitude of the gravitational force between two objects is 20. Newtons. If the mass of each object were doubled, the magnitude of the gravitational force between the objects would be A) 5.0 N B) 10. N C) 20. N D) 80 N 5. A car moves with a constant speed in a clockwise direction around a circular path of radius r, as represented in the diagram above. 2. In the diagram below, a cart travels clockwise at constant speed in a horizontal circle. When the car is in the position shown, its acceleration is directed toward the A) north B) west C) south D) east At the position shown in the diagram, which arrow indicates the direction of the centripetal acceleration of the cart? A) A B) B C) C D) D 6. In the diagram below, a student compresses the spring in a pop-up toy meter. 3. A satellite weighs 200 newtons on the surface of Earth. What is its weight at a distance of one Earth radius above the surface of Earth? A) 50 N B) 100 N C) 400 N D) 800 N If the spring has a spring constant of 340 newtons per meter, how much energy is being stored in the spring? A) J B) 0.14 J C) 3.4 J D) 6.8 J 4. As the mass of a body increases, its gravitational force of attraction on the Earth A) decreases B) increases C) remains the same

2 7. Base your answer to the following question on the information and diagram below. A kilogram car is driven clockwise around a flat circular track of radius 25.0 meters. The speed of the car is a constant 5.00 meters per second. 10. A boy pushes his sister on a swing. What is the frequency of oscillation of his sister on the swing if the boy counts 90. complete swings in 300. seconds? A) 0.30 Hz B) 2.0 Hz C) 1.5 Hz D) 18 Hz 11. A 20.-newton weight is attached to a spring, causing it to stretch, as shown in the diagram below. If the circular track were to suddenly become frictionless at the instant shown in the diagram, the car s direction of travel would be A) toward E B) toward N C) toward W D) a clockwise spiral 8. The time required to produce one cycle of a wave is known as the wave's A) amplitude B) frequency C) period D) wavelength 9. What is the magnitude of the gravitational force between two 5.0-kilogram masses separated by a distance of 5.0 meters? A) N B) N C) N D) N What is the spring constant of this spring? A) N/m B) 0.25 N/m C) 20. N/m D) 40. N/m 12. A kilogram car travels at a constant speed of 20. meters per second around a horizontal circular track. Which diagram correctly represents the direction of the car s velocity (v) and the direction of the centripetal force (Fc) acting on the car at one particular moment? A) B) C) D)

3 13. When Earth and the Moon are separated by a distance of meters, the magnitude of the gravitational force of attraction between them is newtons. What would be the magnitude of this gravitational force of attraction if Earth and the Moon were separated by a distance of meters? A) N B) N C) N D) N Base your answers to questions 14 and 15 on the information below. A kilogram car travels at a constant speed of 12 meters per second around a circular curve of radius 30. meters. 14. As the car goes around the curve, the centripetal force is directed A) toward the center of the circular curve B) away from the center of the circular curve C) tangent to the curve in the direction of motion D) tangent to the curve opposite the direction of motion 17. A 0.50-kilogram object moves in a horizontal circular path with a radius of 0.25 meter at a constant speed of 4.0 meters per second. What is the magnitude of the object s acceleration? A) 8.0 m/s 2 B) 16 m/s 2 C) 32 m/s 2 D) 64 m/s The gravitational force of attraction between two objects would be increased by A) doubling the mass of both objects, only B) doubling the distance between the objects, only C) doubling the mass of both objects and doubling the distance between the objects D) doubling the mass of one object and doubling the distance between the objects 15. What is the magnitude of the centripetal acceleration of the car as it goes around the curve? A) 0.40 m/s 2 B) 4.8 m/s 2 C) 800 m/s 2 D) 9,600 m/s As the distance between two objects increases, the gravitational force of attraction between them will A) decrease B) increase C) remain the same

4 19. Base your answer to the following question on the information and diagram below. The diagram shows a student seated on a rotating circular platform, holding a 2.0-kilogram block with a spring scale. The block is 1.2 meters from the center of the platform. The block has a constant speed of 8.0 meters per second. [Frictional forces on the block are negligible.] Which statement best describes the block s movement as the platform rotates? A) Its velocity is directed tangent to the circular path, with an inward acceleration. B) Its velocity is directed tangent to the circular path, with an outward acceleration. C) Its velocity is directed perpendicular to the circular path, with an inward acceleration. D) Its velocity is directed perpendicular to the circular path, with an outward acceleration. 20. If the mass of one of two objects is increased, the force of attraction between them will A) decrease B) increase C) remain the same

5 Base your answers to questions 21 and 22 on the information and diagram below. Spacecraft S is traveling from planet P1 toward planet P2 At the position shown, the magnitude of the gravitational force of planet P1 on the spacecraft is equal to the magnitude of the gravitational force of planet P2 on the spacecraft. 21. If distance X is greater than distance Y, then the mass of P1 must be A) less than the mass of P2 B) greater than the mass of P2 C) equal to the mass of P2 22. As the spacecraft moves from the position shown toward planet P2, the ratio of the gravitational force of P2 on the spacecraft to the gravitational force of P1 on the spacecraft will A) decrease B) increase C) remain the same

6 Base your answers to questions 23 and 24 on the diagram below which represents a mass of 10.0 kilograms traveling at constant speed of 4. meters per second in a horizontal circular path about point D. 25. Base your answer to the following question on the information and diagram below. An athlete in a hammer-throw event swings a 7.0-kilogram hammer in a horizontal circle at a constant speed of 12 meter per second. The radius of the hammer's path is 2.0 meters 23. Which quantity would increase if the radius increased? A) period B) tangential velocity C) mass D) centripetal acceleration 24. The centripetal acceleration of the satellite is directed toward point A) A B) B C) C D) D What is the magnitude of the centripetal acceleration of the hammer? A) 6.0 m/s 2 B) 24 m/s 2 C) 72 m/s 2 D) 500 m/s The diagram below represents a mass, m, being swung clockwise at constant speed in a horizontal circle. At the instant shown, the centripetal force acting on mass m is directed toward point A) A B) B C) C D) D

7 27. Which diagram best represents the gravitational forces, Fg, between a satellite, S, and Earth? A) B) 29. A ball attached to a string is moved at constant speed in a horizontal circular path. A target is located near the path of the ball as shown in the diagram. C) D) At which point along the ball's path should the string be released, if the ball is to hit the target? A) A B) B C) C D) D 30. Base your answer to the following question on the diagram below which represents a simple pendulum with a 2.0-kilogram bob and a length of 10. meters. The pendulum is released from rest at position 1 and swings without friction through position 4. At position 3, its lowest point, the speed of the bob is 6.0 meters per second. 28. As the pendulum swings from position A to position B as shown in the diagram above, what is the relationship of kinetic energy to potential energy? [Neglect friction.] A) The kinetic energy decrease is more than the potential energy increase. B) The kinetic energy increase is more than the potential energy decrease. C) The kinetic energy decrease is equal to the potential energy increase. D) The kinetic energy increase is equal to the potential energy decrease. At which position does the bob have its maximum kinetic energy? A) 1 B) 2 C) 3 D) 4

8 31. Base your answer to the following question on the information and diagram below. The diagram shows the top view of a -kilogram student at point A on an amusement park ride. The ride spins the student in a horizontal circle of radius meters, at a constant speed of meters per second. The floor is lowered and the student remains against the wall without falling to the floor. 33. Base your answer to the following question on the diagram below. The diagram shows a student spinning a 0.10-kilogram ball at the end of a 0.50-meter string in a horizontal circle at a constant speed of 10. meters per second. [Neglect air resistance.] The magnitude of the centripetal force acting on the student at point A is approximately A) B) C) D) Which is the best description of the force keeping the ball in the circular path? A) perpendicular to the circle and directed toward the center of the circle B) perpendicular to the circle and directed away from the center of the circle C) tangent to the circle and directed in the same direction that the ball is moving D) tangent to the circle and directed opposite to the direction that the ball is moving 32. The diagram below shows a 5.0-kilogram bucket of water being swung in a horizontal circle of-meter radius at a constant speed of 2.0 meters per second. 34. The centers of two 15.0-kilogram spheres are separated by 3.00 meters. The magnitude of the gravitational force between the two spheres is approximately A) N B) N C) N D) N The magnitude of the centripetal force on the bucket of water is approximately A) 5.7 N B) 14 N C) 29 N D) 200 N

9 35. The diagram below represents a 0.40-kilogram stone attached to a string. The stone is moving at a constant speed of 4.0 meters per second in a horizontal circle having a radius of 0.80 meter. 39. The diagram below shows an object moving counterclockwise around a horizontal, circular track. The magnitude of the centripetal acceleration of the stone is A) 0.0 m/s 2 B) 2.0 m/s 2 C) 5.0 m/s 2 D) 20. m/s 2 Which diagram represents the direction of both the object's velocity and the centripetal force acting on the object when it is in the position shown? A) 36. The time required for a wave to complete one full cycle is called the wave s A) frequency B) period C) velocity D) wavelength 37. The magnitude of the centripetal force acting on an object traveling in a horizontal, circular path will decrease if the A) radius of the path is increased B) mass of the object is increased C) direction of motion of the object is reversed D) speed of the object is increased B) C) D) 38. An object weighs 100. Newtons on Earth s surface. When it is moved to a point one Earth radius above Earth s surface, it will weigh A) 25.0 N B) 50.0 N C) 100. N D) 400. N

10 40. The diagram below shows three positions, A, B, and C, in the swing of a pendulum, released from rest at point A. [Neglect friction.] 41. Base your answer to the following question on the diagram and information below. At an amusement park, a passenger whose mass is 50. kilograms rides in a cage. The cage has a constant speed of 10. meters per second in a vertical circular path of radius R, equal to 10. meters. Which statement is true about this swinging pendulum? A) The potential energy at A equals the kinetic energy at C. B) The speed of the pendulum at A equals the speed of the pendulum at B. C) The potential energy at B equals the potential energy at C. D) The potential energy at A equals the kinetic energy at B. What is the direction of the centripetal acceleration of the passenger at the instant the cage reaches the highest point in the circle? A) to the left B) to the right C) up D) down 42. The diagram shows two bowling balls, A and B, each having a mass of 7.00 kilograms, placed 2.00 meters apart. What is the magnitude of the gravitational force exerted by ball A on ball B? A) N B) N C) N D) N

11 43. An unbalanced force of 40. newtons keeps a 5.0-kilogram object traveling in a circle of radius 2.0 meters. What is the speed of the object? A) 8.0 m/s B) 2.0 m/s C) 16 m/s D) 4.0 m/s Base your answers to questions 44 and 45 on the information below and on your knowledge of physics. Using a spring toy like the one shown in the diagram, a physics teacher pushes on the toy, compressing the spring, causing the suction cup to stick to the base of the toy. When the teacher removes her hand, the toy pops straight up and just brushes against the ceiling. She does this demonstration five times, always with the same result. When the teacher repeats the demonstration for the sixth time the toy crashes against the ceiling with considerable force. The students notice that in this trial, the spring and toy separated from the base at the moment the spring released. The teacher puts the toy back together, repeats the demonstration and the toy once again just brushes against the ceiling. 44. Describe the conversions that take place between pairs of the three forms of mechanical energy, beginning with the work done by the teacher on the toy and ending with the form(s) of energy possessed by the toy as it hits the ceiling. [Neglect friction.]

12 45. Explain, in terms of mass and energy, why the spring toy hits the ceiling in the sixth trial and not in the other trials. Base your answers to questions 46 and 47 on the information and diagram below. A block of mass m starts from rest at height h on a frictionless incline. The block slides down the incline across a frictionless level surface and comes to rest by compressing a spring through distance x, as shown in the diagram below. 46. Determine the spring constant, k, in terms of g, h, m, and x. [Show all work including formulas and an algebraic solution for k.] 47. Name the forms of mechanical energy possessed by the system when the block is in position A and in position B.

13 Base your answers to questions 48 through 50 on the information and diagram below. A mass, M, is hung from a spring and reaches equilibrium at position B. The mass is then raised to position A and released. The mass oscillates between positions A and C. [Neglect friction.] 48. At which position, A, B, or C, is mass M located when the gravitational potential energy of the system is at a maximum? Explain your choice. 49. At which position, A, B, or C, is mass M located when the kinetic energy of the system is at a maximum? Explain your choice. 50. At which position, A, B, or C, is mass M located when the elastic potential energy of the system is at a maximum? Explain your choice.

14 Base your answers to questions 51 through 54 on the information and diagram below. In an experiment, a rubber stopper is attached to one end of a string that is passed through a plastic tube before weights are attached to the other end. The stopper is whirled in a horizontal circular path at constant speed. 51. The rubber stopper is now whirled in a vertical circle at the same speed. On the diagram, draw and label vectors to indicate the direction of the weight (Fg) and the direction of the centripetal force (Fc) at the position shown. 52. Describe what would happen to the radius of the circle if the student whirls the stopper at a greater speed without changing the balancing weights. 53. List three measurements that must be taken to show that the magnitude of the centripetal force is equal to the balancing weights. [Neglect friction.]

15 54. On the diagram of the top view, draw the path of the rubber stopper if the string breaks at the position shown. 55. Base your answer to the following question on the information and diagram below and on your knowledge of physics. A toy airplane flies clockwise at a constant speed in a horizontal circle of radius 8.0 meters. The magnitude of the acceleration of the airplane is 25 meters per second squared. The diagram shows the path of the airplane as it travels around the circle. Calculate the speed of the airplane. [Show all work, including the equation and substitution with units.]

16 56. A baby and stroller have a total mass of 20. kilograms. A force of 36 newtons keeps the stroller moving in a circular path with a radius of 5.0 meters. Calculate the speed at which the stroller moves around the curve. [Show all work, including the equation and substitution with units.] 58. Determine the speed of the whirling stopper. Base your answers to questions 57 and 58 on the information below. In an experiment, a kilogram rubber stopper is attached to one end of a string. A student whirls the stopper overhead in a horizontal circle with a radius of 1.0 meter. The stopper completes 10. revolutions in 10. seconds. 57. Calculate the magnitude of the centripetal force on the whirling stopper. [Show all work, including the equation and substitution with units.]

17 Base your answers to questions 59 and 60 on the information below. A student conducted a series of experiments to investigate the effect of mass, length, and amplitude (angle of release) on a simple pendulum. The table below shows the initial conditions for a series of trials. 59. Which three trials should the student use to test the effect of length on the period of the pendulum? 60. Which three trials should the student use to test the effect of mass on the period of the pendulum? 61. A 0.65-meter-long pendulum consists of a 1.0-kilogram mass at the end of a string. The pendulum is released from rest at position A, 0.25 meter above its lowest point. The pendulum is timed at five positions, A through E. Based on the information in the diagram and the data table, determine the period of the pendulum.

18 Answer Key Pendulum,Springs,Circular,G Review 1. D 2. A 3. A 4. B 5. D 6. A 7. B 8. C 9. C 10. A 11. D 12. A 13. D 14. A 15. B 16. A 17. D 18. A 19. A 20. B 21. A 22. B 23. A 24. D 25. C 26. C 27. C 28. D 29. B 30. C 31. B 32. C 33. A 34. C 35. D 36. B 37. A 38. A 39. B 40. D 41. D 42. C 43. D 44. examples: work of teacher into the P.E. (spring) into the K.E. of launch into P.E. (gravity) and sound energy. 45. examples: The toy has less mass without the base but the same energy. Therefore it can go higher. The work put into the toy is the same but the mass is less. With less mass the toy could go higher because it is moving faster. 46. PE = mg h PEs = kx 2 kx 2 = mg h k = 2mg h / x Credit for indicating kinetic energy when the block is in position A and credit for indicating potential energy when the block is in position B. Appropriate responses include, but are not limited to: Position A: kinetic or KE, or energy of motion Position B: elastic or potential, or energy of position 48. A, because it is the highest point of travel 49. B, because the mass has the greatest speed or B, because the total potential energy is least or B, the speed at A and C is zero 50. C, because the spring is stretched the maximum amount or C, because the KE and gravitational PE are a minimum R increases 53. mass of stopper, radius of path, velocity of stopper or frequency or period, weight of the balancing weights m/s 59. Credit for W, X, Z 60. Credit for R, U, Y seconds