3 UCM & Gravity Student Physics Regents Date

Transcription

1 Student Physics Regents Date 1. Which diagram best represents the gravitational forces, Fg, between a satellite, S, and Earth? A) B) 4. Gravitational force exists between point objects and separated by distance. If the mass of is doubled and distance is tripled, what is the new gravitational force between and? A) B) C) C) D) 2. Gravitational forces differ from electrostatic forces in that gravitational forces are A) attractive, only B) repulsive, only C) neither attractive nor repulsive D) both attractive and repulsive 3. The diagram shows two bowling balls, A and B, each having a mass of 7.00 kilograms, placed 2.00 meters apart. D) 5. The radius of Mars is approximately one-half the radius of Earth, and the mass of Mars is approximately one-tenth the mass of Earth. Compared to the acceleration due to gravity on the surface of Earth, the acceleration due to gravity on the surface of Mars is A) smaller B) larger C) the same What is the magnitude of the gravitational force exerted by ball A on ball B? A) N B) N C) N D) N

2 6. Base your answer to the following question 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. 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 7. If the Earth were twice as massive as it is now, then the gravitational force between it and the Sun would be A) the same B) twice as great C) half as great D) four times as great 8. Two equal point masses are separated by a distance of 1 meter. If one mass is doubled, the gravitational force between the two masses would be A) one-half as great B) two times greater C) one-fourth as great D) four times greater 9. The weight of a 2.0-kilogram mass on planet A is 40 Newtons. The acceleration due to gravity on planet A is closest to A) 20 m/s 2 B) 2.0 m/s 2 C) 80 m/s 2 D) 40 m/s Two bodies attract each other with a gravitational force of 10.0 Newtons. What will be the force of attraction if the mass of each body is doubled? A) 5 N B) 10 N C) 20 N D) 40 N 11. Base your answer to the following question 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. Determine the speed of the whirling stopper.

3 12. Which graph best represents the relationship between the magnitude of the centripetal acceleration and the speed of an object moving in a circle of constant radius? A) 14. Base your answer to the following question 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. B) C) D) If the 10.-kilogram mass is replaced with a greater mass, the centripetal acceleration will A) decrease B) increase C) remain the same 15. 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.] 13. 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. If the magnitude of the force applied to the string by the student's hand is increased, the magnitude of the acceleration of the ball in its circular path will A) decrease B) increase C) remain the same 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

4 16. Base your answer to the following question on the information and diagram below. A 60.-kilogram adult and a 30.-kilogram child are passengers on a rotor ride at an amusement park. 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. 18. 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. Compared to the magnitude of the acceleration of the adult, the magnitude of the acceleration of the child is A) less B) greater C) the same 17. Base your answer to the following question on the diagram below which represents a ball of mass M attached to a string. The ball moves at a constant speed around a flat horizontal circle of radius R. Which vector best represents the direction of the centripetal acceleration of the student at point A. A) B) C) D) If the string is shortened while the speed of the ball remains the same, the centripetal acceleration will A) decrease B) increase C) remain the same

5 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.] 21. Centripetal force Fc acts on a car going around a curve. If the speed of the car were twice as great, the magnitude of the centripetal force necessary to keep the car moving in the same path would be A) B) C) D) 22. 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. The reading on the spring scale is approximately A) 20. N B) 53 N C) 110 N D) 130 N 20. Base your answer to the following question on the diagram below which represents a 5.0-kilogram object revolving around a circular track in a horizontal plane at a constant speed. The radius of the track is 20. meters and the centripetal force on the object is Newtons. 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 In the position shown, the object's centripetal acceleration is directed toward point A) A B) B C) C D) D

6 23. Base your answer to the following question on the information and diagram below. A 1200-kilogram car traveling at a constant speed of 9.0 meters per second turns at an intersection. The car follows a horizontal circular path with a radius of 25 meters to point P. 24. Base your answer to the following question on the diagram below which represents an object M suspended by a string from point P. When object M is swung to a height of h and released, it passes through the rest position at a speed of 10 meters per second. The magnitude of the centripetal force acting on the car as it travels around the circular path is approximately A) N B) N C) N D) N The centripetal force on object M could be halved as it passes through the rest position by doubling the A) weight of the object, only B) length of the string, only C) height h and the weight of the object D) the length of the string and the height h 25. 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. 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

7 Base your answers to questions 26 and 27 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 28. Base your answer to the following question on the diagram below which represents a satellite in an elliptical orbit about the Earth. The highest point, A, is four Earth radii ( ) from the center of the Earth. The lowest point, B, is two Earth radii ( ) from the center of the Earth. The mass of the satellite is kilograms. 26. 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 If the hammer is released at the position shown, it will travel toward point A) A B) B C) C D) D Which vector represents the direction of the satellite's velocity at A? A) B) C) D) 29. A plane flying horizontally above Earth s surface at 100. meters per second drops a crate. The crate strikes the ground 30.0 seconds later. What is the magnitude of the horizontal component of the crate s velocity just before it strikes the ground? [Neglect friction.] A) 0 m/s B) 100. m/s C) 294 m/s D) 394 m/s

8 30. In the diagram below, a stationary observer on the ground watches as a seagull flying horizontally to the right drops a clamshell. 31. The diagram below shows the muzzle of a cannon located 50. meters above the ground. When the cannon is fired, a ball leaves the muzzle with an initial horizontal speed of 250. meters per second. [Neglect air resistance.] Which diagram best represents the path of the falling clamshell as seen by the observer? [Neglect air resistance.] A) B) Which action would most likely increase the time of flight of a ball fired by the cannon? A) pointing the muzzle of the cannon toward the ground B) moving the cannon closer to the edge of the cliff C) positioning the cannon higher above the ground D) giving the ball a greater initial horizontal velocity C) D)

9 32. Base your answer to the following question on the information and diagram below. A student standing on a knoll throws a snowball horizontally 4.5 meters above the level ground toward a smokestack 15 meters away. The snowball hits the smokestack 0.65 second after being released. [Neglect air resistance.] At the instant the snowball is released, the horizontal component of its velocity is approximately A) 6.9 m/s B) 9.8 m/s C) 17 m/s D) 23 m/s 33. The diagram below represents the path of an object after it was thrown. What happens to the object's acceleration as it travels from A to B? [Neglect friction.] A) It decreases. B) It increases. C) It remains the same. 34. Base your answer to the following question on the information and diagram below. A child kicks a ball with an initial velocity of 8.5 meters per second at an angle of 35 with the horizontal, as shown. The ball has an initial vertical velocity of 4.9 meters per second and a total time of flight of 1.0 second. [Neglect air resistance.] The horizontal component of the ball's initial velocity is approximately A) 3.6 m/s B) 7.0 m/s C) 4.9 m/s D) 13 m/s

10 35. A 2-kilogram block is dropped from the roof of a tall building at the same time a 6-kilogram ball is thrown horizontally from the same height. Which statement best describes the motion of the block and the motion of the ball? [Neglect air resistance.] A) The 2-kg block hits the ground first because it has no horizontal velocity. B) The 6-kg ball hits the ground first because it has more mass. C) The 6-kg ball hits the ground first because it is round. D) The block and the ball hit the ground at the same time because they have the same vertical acceleration. 36. Base your answer to the following question on the following information. In the diagram below, a 10.-kilogram sphere, A, is projected horizontally with a velocity of 30. meters per second due east from a height of 20. meters above level ground. At the same instant, a 20.-kilogram sphere, B, is projected horizontally with a velocity of 10. meters per second due west from a height of 80. meters above level ground. [Neglect air friction.] 37. Base your answer to the following question on the diagram below which shows a ball projected horizontally with an initial velocity of 20. meters per second east, off a cliff 100. meters high. [Neglect air resistance.] During the flight of the ball, what is the direction of its acceleration? A) downward B) upward C) westward D) eastward 38. Base your answer to the following question on the information below. A ball is projected vertically upward from the surface of the Earth with an initial speed of +49 meters per second. The ball reaches its maximum height in 5.0 seconds. (Disregard air resistance.) Which graph best represents the relationship between velocity and time for the motion of the ball? A) B) C) D) Compared to the vertical acceleration of sphere A, the vertical acceleration of sphere B is A) the same B) twice as great C) one-half as great D) four times as great

11 39. Base your answer to the following question on the information below. 3 UCM & Gravity A 28-gram rubber stopper is attached to a string and whirled clockwise in a horizontal circle with a radius of 0.80 meter. The diagram below represents the motion of the rubber stopper. The stopper maintains a constant speed of 2.5 meters per second. On the diagram above, draw an arrow showing the direction of the centripetal force acting on the stopper when it is at the position shown. Base your answers to questions 40 through 42 on the information below. A kicked soccer ball has an initial velocity of 25 meters per second at an angle of 40º above the horizontal, level ground. [Neglect friction.] 40. On the diagram below, sketch the path of the ball s flight from its initial position at point P until it returns to level ground. 42. Calculate the magnitude of the vertical component of the ball s initial velocity [Show all work, including the equation and substitution with units.] 41. Calculate the maximum height the ball reaches above its initial position. [Show all work, including the equation and substitution with units.]

12 Base your answers to questions 43 and 44 on the passage and data table below. 3 UCM & Gravity The net force on a planet is due primarily to the other planets and the Sun. By taking into account all the forces acting on a planet, investigators calculated the orbit of each planet. A small discrepancy between the calculated orbit and the observed orbit of the planet Uranus was noted. It appeared that the sum of the forces on Uranus did not equal its mass times its acceleration, unless there was another force on the planet that was not included in the calculation. Assuming that this force was exerted by an unobserved planet, two scientists working independently calculated where this unknown planet must be in order to account for the discrepancy. Astronomers pointed their telescopes in the predicted direction and found the planet we now call Neptune. 43. The magnitude of the force the Sun exerts on Uranus is newtons. Explain how it is possible for the Sun to exert a greater force on Uranus than Neptune exerts on Uranus. 44. The diagram represents Neptune, Uranus, and the Sun in a straight line. Neptune is meters from Uranus. Calculate the magnitude of the interplanetary force of attraction between Uranus and Neptune at this point. [Show all work, including the equation and substitution with units.] Base your answers to questions 45 and 46 on the information below and on your knowledge of physics. Pluto orbits the Sun at an average distance of meters. Pluto's diameter is meters and its mass is kilograms. Charon orbits Pluto with their centers separated by a distance of meters. Charon has a diameter of meters and a mass of kilograms. 45. State the reason why the magnitude of the Sun s gravitational force on Pluto is greater than the magnitude of the Sun s gravitational force on Charon. 46. Calculate the magnitude of the acceleration of Charon toward Pluto. [Show all work, including the equation and substitution with units.]

13 47. A car travels at constant speed around a section of horizontal, circular track. On the diagram below, draw an arrow at point P to represent the direction of the centripetal acceleration of the car when it is at point P. 48. Calculate the magnitude of the centripetal force acting on Earth as it orbits the Sun, assuming a circular orbit and an orbital speed of meters per second. [Show all work, including the equation and substitution with units.] 49. Base your answer to the following question on the information below. Io (pronounced EYE oh ) is one of Jupiter s moons discovered by Galileo. Io is slightly larger than Earth s Moon. The mass of Io is kilograms and the mass of Jupiter is kilograms. The distance between the centers of Io and Jupiter is meters. Calculate the magnitude of the gravitational force of attraction that Jupiter exerts on Io. [Show all work, including the equation and substitution with units.] Base your answers to questions 50 and 51 on the information below. A projectile is launched into the air with an initial speed of vi at a launch angle of 30. above the horizontal. The projectile lands on the ground 2.0 seconds later. 50. How does the total horizontal distance traveled by the projectile change as the launch angle is increased from 30. to 45 above the horizontal? [Assume the same initial speed, vi.] 51. How does the maximum altitude of the projectile change as the launch angle is increased from 30. to 45 above the horizontal? [Assume the same initial speed, vi.]

14 52. Base your answer to the following question on the information and diagram below. A projectile is launched horizontally at a speed of meters per second from a platform located a vertical distance above the ground. The projectile strikes the ground after time at horizontal distance from the base of the platform. [Neglect friction.] Base your answers to questions 53 through 55 on the information below. The combined mass of a race car and its driver is 600. kilograms. Traveling at constant speed, the car completes one lap around a circular track of radius 160 meters in 36 seconds. 53. Calculate the magnitude of the centripetal acceleration of the car. Express the projectile's total time of flight,, in terms of the vertical distance,, and the acceleration due to gravity,. [Write an appropriate equation and solve it for.] 54. On the diagram above, draw an arrow to represent the direction of the net force acting on the car when it is in position A. 55. Calculate the speed of the car.

15 Answer Key 3 UCM & Gravity Rev 1. C 2. A 3. C 4. A 5. A 6. B 7. B 8. B 9. A 10. D m/s 12. B 13. D 14. C 15. B 16. C 17. B 18. A 19. C 20. D 21. D 22. C 23. C 24. B 25. B 26. C 27. B 28. C 29. B 30. D 31. C 32. D 33. C 34. B 35. D 36. A 37. A 38. D m m/s 43. The sun is larger in mass. 44. F = Gm1m 2 r 2 F = ( N m 2 /kg 2 )( kg)( kg) ( m) 2 F = N 45. Pluto has a greater mass than Charon or The total horizontal distance will increase. 51. The projectile s maximum altitude will increase ac = 4.9 m/s m/s or 27.9 m/s