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Gravitational Force Date: Name: 1. 2. What is the magnitude of the centripetal acceleration of a 4-kilogram mass orbiting at 10 meters per second with a radius of 2 meters? A. 5 m/sec2 B. C. 80 m/sec2 D. 200 m/sec2 4. 50 m/sec2 5. In the diagram shown, satellite S moves in a circular orbit around the Earth (E). The direction of the acceleration of the satellite is toward point A. A B. B C. C A student using a stopwatch nds that the time for 10 complete orbits of a ball on the end of a string is 25 seconds. The period of the orbiting ball is A. 25 sec B. 2.0 sec C. 2.5 sec D. 5.0 sec In order for a satellite to remain in orbit, the satellite must have reached the required orbital A. velocity B. acceleration C. displacement D. momentum D. D 6. 3. The diagram shows positions of a satellite as it orbits the Earth. At which position will the satellite achieve its highest velocity? The gravitational force between two objects is inversely proportional to A. mass squared B. distance squared C. mass D. distance A. page 1 A B. B C. C D. D 7. The shape of natural orbits of satellites is best described as being A. circular B. C. elliptical D. hyperbolic 10. parabolic 11. 8. The diagram here represents a mass of 1.0 kilogram traveling at 8.0 meters per second in a circular path of radius 4.0 meters. The orbit of the Moon around the Earth is A. circular B. parabolic C. hyperbolic D. elliptical The minimum velocity which a rocket must have to leave the Earth's gravitational in uence is called the A. orbital velocity B. escape velocity C. elliptical velocity D. launching velocity What is the centripetal acceleration of the object? 9. A. 10 m/sec2 B. C. 16 m/sec2 D. 4.0 m/sec2 12. 2.0 m/sec2 The diagram shown represents a mass of 10.0 kilograms traveling at a constant speed of 4 meters per second in a horizontal circular path about point D. If the mass of the object is doubled, the magnitude of the centripetal force will be A. one-half as much B. twice as much C. one-fourth as much D. four times as much The centripetal acceleration of the satellite is directed toward point A. page 2 A B. B C. C D. D Gravitational Force 13. 14. 15. What is the magnitude of the centripetal acceleration? A. 1 m/sec2 B. C. 40 m/sec2 D. 4 m/sec2 16. 10 m/sec2 If object O is moving in a uniform circular motion around point P at constant speed, which vector shown represents a centripetal force? A. B. C. D. If the 10-kilogram mass is replaced with a greater mass, the centripetal acceleration will A. decrease C. remain the same B. increase Which diagram best represents a natural space orbit? 17. A. B. In the diagram shown, satellite S, which continually emits a signal, orbits the Earth. For reception to occur at point R on the Earth, the satellite must be in position A. A B. C. C D. D B C. D. page 3 Gravitational Force 18. 19. If the distance between a spaceship and the center of the Earth is increased from one Earth radius to 4 Earth radii, the gravitational force acting on the spaceship becomes approximately A. 1 16 C. 16 times greater as great B. 1 4 21. as great The weight of the satellite on the Earth's surface would be A. 560 N B. 980 N C. 1,900 N D. 3,900 N D. 4 times greater 22. The diagram represents a 4:0 102 -kilogram satellite, S, in a circular orbit at an altitude of 5:0 106 meters. The orbital speeds of the satellite is 6:0 103 meters per second and the radius of the Earth, R, is 6:4 106 meters. Which graph best represents the relationship between the mass of an object and its distance from the center of the Earth? A. B. C. D. The centripetal acceleration of the satellite shown is closest to A. 9.8 m/s2 B. 4.9 m/s2 C. 3.2 m/s2 D. 1.6 m/s2 23. 20. If the altitude of the satellite decreased, its centripetal acceleration would Gravitational force of attraction F exists between two point masses A and B when they are separated by a xed distance. After mass A is tripled and mass B is halved, the gravitational attraction between the two masses is A. decrease A. C. remain the same B. increase page 4 1 6F B. 2 3F C. 3 2F D. 6F Gravitational Force 24. A satellite orbits the Earth in a circular orbit. Which statement best explains why the satellite does not move closer to the center of the Earth? A. The gravitational eld of the Earth does not reach the satellite's orbit. B. The Earth's gravity keeps the satellite moving with constant velocity. C. The satellite is always moving perpendicularly to the force due to gravity. 26. 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 D. The satellite does not have any weight. 27. 25. In the diagrams shown, P represents a planet and S represents the Sun. Which best represents the path of planet P as it orbits the Sun? [The diagrams are not drawn to scale.] A. What is the gravitational force of attraction between a planet and a 17-kilogram mass that is freely falling toward the surface of the planet at 8.8 meters per second2 ? A. 150 N B. 8.8 N C. 1.9 N D. 0.52 N B. 28. C. When a satellite is a distance d from the center of the Earth, the force due to gravity on the satellite is F. What would be the force due to gravity on the satellite when its distance from the center of the Earth is 3d ? A. D. page 5 F B. F 9 C. F 3 D. 9F Gravitational Force 29. In which diagram do the arrows best represent the path of a satellite in a geosynchronous orbit? Note: 30. gures not drawn to scale The data table shown gives the mean radius of orbit R and the period T of some planets orbiting the Sun. Which ratio is constant for these planets? A. Planet Mercury Venus Mean Radius of Orbit (R) ( 106 km) 58 Orbital Period (T) (days) 150 365 Earth Mars B. A. R T B. 88 108 225 228 687 R2 T C. R2 T2 D. R3 T2 C. D. page 6 Gravitational Force 31. Base your answer(s) to the following question(s) on the passage and data table blelow 32. 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. The diagram below represents Neptune, Uranus, and the Sun in a straight line. Neptune is 1:63 1012 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.] Data Table Mass of the Sun 1:99 Mass of Uranus 8:73 Mass of Neptune 1:03 Mean distance of Uranus to the Sun 2:87 Mean distance of Neptune to the Sun 4:50 1030 kg 1025 kg 1026 kg 1012 m 1012 m What fundamental force is the author referring to in this passage as a force between planets? 33. page 7 The magnitude of the force the Sun exerts on Uranus is 1:41 1021 newtons. Explain how it is possible for the Sun to exert a greater force on Uranus than Neptune exerts on Uranus. Gravitational Force 34. The accompanying graph shows the relationship between the elongation of a spring and the force applied to the spring causing it to stretch. 35. The accompanying graph shows elongation as a function of the applied force for two springs, A and B. What is the spring constant for this spring? A. 0.020 N/m B. 2.0 N/m C. 25 N/m D. 50. N/m Compared to the spring constant for spring A, the spring constant for spring B is A. page 8 smaller B. larger C. the same Gravitational Force