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CHAPTER 6 Review K/U Knowledge/Understanding Knowledge For each question, select the best answer from the four alternatives. 1. Which of the following best describes the strength of the gravitational force on Earth due to your mass? (6.1) K/U (a) It is zero as long as you are standing on Earth’s surface. (b) It is much greater than Earth’s gravitational force on you because Earth’s mass is so great. (c) It is equal to the magnitude of the force that Earth exerts on you. (d) It is negligible compared to the force of gravity on you because your mass is so small when compared to Earth’s mass. 2. The gravitational force on a small rock sitting on a 20 m–high cliff on Earth is Fg. How does the gravitational force on the rock change if a hiker picks up the rock and carries it to a 200 m–high cliff? (6.1) K/U (a) It will decrease by an insignificant amount. (b) It will decrease by about one-tenth. (c) It will decrease by about one-fourth. (d) It will decrease by about one-half. 3. What major obstacle did Henry Cavendish face when measuring the gravitational force between two objects on Earth? (6.1) K/U (a) The masses required had to be very small. (b) The gravitational force between the two masses was very small. (c) The distance between the two masses had to be extremely large. (d) The gravitational force between the two masses was extremely large. 4. Ball A, with mass m, is a distance d from ball B, which has a mass of 3m. At which of the following distances is the gravitational attraction of the balls on each other equal? (6.1) K/U d (a) 9 d (b) 3 2d (c) 3 (d) any separation distance 312 Chapter 6 • Gravitational Fields 8160_CH06_p282-317.indd 312 T/I Thinking/Investigation C Communication A Application 5. Spherical planet A has mass m and radius r. Spherical m planet B has mass and radius 2r. How does the 2 gravitational field strength at the surface of planet B compare to the gravitational field strength at the surface of planet A? (6.1) K/U (a) It is the same as planet A. (b) It is twice that of planet A. (c) It is half that of planet A. (d) It is one-eighth that of planet A. 6. Two satellites are orbiting a planet at the same height above its surface. The mass of satellite A is m, and the mass of satellite B is 2m. What can you conclude about the planet’s gravitational force on the satellites? (6.2) K/U (a) The planet’s gravitational force on both satellites is the same. (b) The planet’s gravitational force on satellite B is half the gravitational force on satellite A. (c) The planet’s gravitational force on satellite B is twice the gravitational force on satellite A. (d) The planet’s gravitational force on satellite B is four times the gravitational force on satellite A. 7. How does a planet’s gravity help keep a satellite in a circular orbit? (6.2) K/U (a) It pulls the satellite in the same direction as its motion. (b) It pulls the satellite at an angle of 30° to its direction of motion. (c) It pulls the satellite at an angle of 60° to its direction of motion. (d) It pulls the satellite at an angle of 90° to its direction of motion. 8. To pinpoint the location of your vehicle within 15 m using a Global Positioning System (GPS), how many satellites’ signals must interact? (6.2) K/U (a) 1 (b) 2 (c) 3 (d) 4 9. Which of the following conditions are necessary to place a satellite in geosynchronous orbit? (6.2) K/U (a) a varying orbital velocity so that it maintains a constant position (b) a varying orbital radius so that it maintains a constant height above Earth (c) a constant period that is equal to the orbital speed of Earth about the Sun (d) a constant period that matches the revolution rate of Earth about its axis NEL 4/27/12 9:00 AM 10. The period of a satellite is independent of (a) its own mass (b) the mass of the planet it orbits (c) the value of the gravitational constant (d) the orbital radius (6.2) K/U Indicate whether each statement is true or false. If you think the statement is false, rewrite it to make it true. 11. The gravitational constant, G, near the Moon is different than G near Earth. (6.1) K/U 12. The gravitational field around Earth at a fixed distance from its centre would be the same if Earth had half the radius but the same mass. (6.1) K/U 13. A book is surrounded by its own gravitational field. (6.1) K/U 14. Unlike most satellites, a geosynchronous satellite has a fixed position and does not orbit Earth. (6.2) K/U 15. In order for a satellite to stay in a uniform circular orbit, its speed must be constant. (6.2) K/U 16. The velocity of a satellite in uniform circular motion depends on the satellite’s mass. (6.2) K/U 17. Satellites are useful for communication, astronomical observations, and atmospheric studies. (6.3) K/U 18. According to the theory of general relativity, gravity has no effect on light because light has no mass. (6.4) K/U 19. Gravitational lensing occurs when the gravitational field changes the direction of motion of a massive object. (6.4) T/I Match each term on the left with the most appropriate description on the right. 20. (a) satellite (b) artificial satellite (c) space station (i) a spacecraft in which people live and work (ii) an object or body that revolves around another body (iii) an object that has been intentionally placed by humans into orbit around Earth or another body (6.2) K/U Understanding 21. The gravitational force is inversely proportional to 1 the square of the separation of two masses: Fg ~ 2 . r Earth’s gravitational pull on an object is defined as the object’s weight. Explain why the weight of any object on Earth is not infinite, even though the distance between the object and Earth is zero. (6.1) T/I A 22. An Internet site states that the value of g on Earth is 9.806 65 N/kg. Is this figure accurate for all places on Earth? Why or why not? (6.1) K/U T/I C 23. Relate the universal law of gravitation to Newton’s third law of motion. (6.1) K/U C NEL 8160_CH06_p282-317.indd 313 24. Henry Cavendish conducted experiments to measure the force of gravity between two objects on Earth. In a short paragraph, summarize Cavendish’s experimental setup and results. (6.1) K/U C 25. Explain why you do not feel the gravitational force between you and a car 5 m away, even though a car’s mass is so great that you cannot lift it. (6.1) T/I 26. Every object is surrounded by a gravitational field. (6.1) K/U C (a) The unit of the gravitational field strength g is newtons per kilogram (N/kg). Explain how the unit of gravitational field strength relates to the unit of force. (b) How does g vary with distance? How does it vary with the object’s mass? (c) Describe the direction of the gravitational field around a spherical object. 27. The universal law of gravitation describes the force of gravity between two bodies. What does it say about the strength of the gravitational field? How does the size of the object affect the use of the gravitational force equation? (6.1) K/U 28. Rank the following from least to greatest gravitational attraction on you. (6.1) T/I (a) a mass of 4m a distance of 2d away (b) a mass of 6m a distance of 5d away (c) a mass of 2m a distance of 3d away (d) a mass of m a distance of 2d away 29. A 68 kg spherical boulder is sitting 1.5 m from a 27 kg spherical rock. What is the gravitational force between the boulder and the rock? (6.1) K/U 30. A traffic officer is standing 4.5 m from a 1200 kg pickup truck. The gravitational force between the officer and the truck is 1.7 3 10–7 N. What is the officer’s mass? (6.1) T/I A 31. In 2005, the space probe Deep Impact launched a 370 kg projectile into Comet Tempel 1. Observing the collision helped scientists learn about the comet’s characteristics. The comet is estimated to have a mass of about 9.0 3 1013 kg. (6.1) K/U T/I (a) Assuming the estimated mass of the comet at that time was correct, at what distance from the comet’s centre was the gravitational force between the comet and the projectile 32 N? (b) What was the magnitude of the gravitational force between the comet and the projectile at a distance of 350 m? (c) Deep Impact also released a probe to fly by the comet and record images of the collision. Determine the strength of the comet’s gravitational field at the probe’s distance of 5.0 3 103 km from the comet. Chapter 6 Review 313 4/27/12 9:00 AM 32. Which is a more important factor in order for a satellite to remain in orbit at a certain distance above Earth’s surface: the speed or the mass of the satellite? Explain your answer. (6.2) T/I A 33. Two identical satellites are orbiting different planets at the same orbital radius, but one planet has twice the mass of the other planet. How do the satellite’s orbital speeds compare with each other? (6.2) K/U T/I 34. Two identical satellites are orbiting different planets at the same orbital radius, but one satellite’s orbital speed is twice as fast as the other’s. What can you conclude about the masses of the planets the satellites are orbiting? (6.2) K/U T/I A 35. The RADARSAT-1 and RADARSAT-2 satellites were placed in orbit at an altitude of approximately 800 km and have a mass of about 2750 kg each. RADARSAT Constellation satellites orbit at approximately 600 km and have masses of about 1300 kg. (6.3) K/U A (a) Which set of satellites has greater speeds? (b) What effect does the mass have on the speeds? 36. Why is the concept of dark matter sometimes referred to as the missing mass problem? (6.4) K/U C 40. Henry Cavendish used freely moving balls to measure the gravitational force between two masses on Earth’s surface. Suppose a scientist repeated the measurement using masses m1 5 0.032 kg and m2 5 5500 kg. What is the gravitational force between the masses when the distance between their centres is r 5 0.75 m? (6.1) T/I 41. Calculate the strength of the gravitational field of a 6520 kg elephant at a distance of 5.75 m. (6.1) T/I 42. The world’s largest ball of twine was made by one man in Minnesota in the United States. A basketball sitting 55.0 m (measured from centre to centre) from the ball of twine would experience a gravitational field of 1.74 3 10–10 N/kg from the ball of twine. Calculate the ball of twine’s mass. (6.1) T/I 43. The highest peak in Canada is Mount Logan (Figure 2), which has an altitude of 5959 m above sea level. Assume that sea level defines the height of Earth’s surface. (6.1) T/I Analysis and Application 37. Three balls are sitting on the ground, as shown in Figure 1. The centre of each ball is an equal distance from you. Ball A has mass m and radius r. Ball B has mass 2m and radius r. Ball C has mass m and radius 2r. Compare the gravitational force of each ball on you. Explain your answer. (6.1) T/I A 2m Figure 2 B m A C m Figure 1 38. Two people are standing 1.0 m apart (centre to centre). Assume that each person has a mass of 45 kg. Calculate the gravitational force between the two people. (6.1) T/I 39. Two small balls of mass 22 kg and 25 kg are a distance of 1.2 m apart. (6.1) T/I (a) Calculate the gravitational force between the balls. (b) How far apart would two balls of mass 16 kg and 21 kg have to be to have this same gravitational force between them? 314 Chapter 6 • Gravitational Fields 8160_CH06_p282-317.indd 314 (a) Calculate the strength of Earth’s gravitational field at the altitude of Mount Logan. (b) What is the ratio of the strength of Earth’s gravitational field at the top of Mount Logan to the strength at Earth’s surface? 44. Neptune, the most distant planet in our solar system, is at an average distance of 4.5 3 109 km from the Sun. Its mass is 1.03 3 1026 kg. (6.1) T/I A (a) Calculate the strength of the Sun’s gravitational field at Neptune’s location. (b) Calculate the strength of Neptune’s gravitational field at the Sun’s location. (c) Calculate the gravitational force between the Sun and Neptune. NEL 4/27/12 9:00 AM 45. The gravitational force due to the Sun on the planets in our solar system decreases as the planetary distance from the Sun increases. In your notebook, draw a larger version of Figure 3, and complete it for the force of gravity on an imaginary Earth–mass planet if its distance were between the Sun’s radius, rS, and 100rS. (6.1) K/U T/I C Fg on planet (N) Sun rS rS 50rS 100rS Distance from the centre of the Sun Figure 3 46. How does the weight of a Mars lander change as it travels from Earth to Mars? Does the weight ever equal zero? Does the mass of the lander change? Explain your answers. (6.1) K/U T/I C 47. Ceres is a dwarf planet located in the asteroid belt between the orbits of Mars and Jupiter. The radius of Ceres is 4.76 3 105 m. Suppose an astronaut stands on the surface of Ceres and drops a 0.85 kg hammer from a height of 1.25 m. The hammer takes 3.0 s to reach the ground. (6.1) T/I A (a) Determine the gravitational field strength of Ceres at this height. (b) Calculate the mass of Ceres. (c) Determine the gravitational field strength of Ceres at an altitude of 150 km above its surface. 48. Three balls of mass m1 5 13 kg, m2 5 17 kg, and m3 5 12 kg are arranged in a straight line. Mass m1 is in the middle, 6 m from both mass m2 and mass m3. Calculate the total gravitational force exerted by balls 2 and 3 on ball 1. State both the magnitude and the direction of the force in your answer. (6.1) T/I 49. Titan, one of the moons of Saturn, has a radius of 2.57 3 106 m and a mass of 1.35 3 1023 kg. (6.1) T/I A (a) Determine the gravitational field strength on the surface of Titan. (b) What is the ratio of Titan’s gravitational field strength at its surface to the gravitational field strength on the surface of Earth? NEL 8160_CH06_p282-317.indd 315 50. The International Space Station (ISS) orbits Earth at a height of approximately 375 km. (6.1) T/I A (a) Calculate the gravitational field strength on the ISS. (b) Are astronauts truly weightless? (c) Why do astronauts and other objects on the ISS appear to float? 51. Consider what you have learned about the inversesquare law. Would it be possible for the force of gravity between two very heavy supertankers to cause them to float toward each other and collide? Explain your reasoning. (6.1) T/I C A 52. A satellite in orbit above Earth’s equator is travelling at an orbital speed of 7.45 km/s. (6.2) T/I (a) Determine the altitude of the satellite. (b) Determine the satellite’s period. 53. Saturn rotates once in 645 min (just under 11 h) and has a mass of 5.69 3 1026 kg. Suppose that scientists have placed a satellite in orbit around Saturn that has the same period as Saturn. (6.2) T/I C (a) Calculate the radius at which the satellite must orbit. (b) In a few sentences, compare this radius to Saturn’s equatorial radius of 6.03 3 107 m, and compare the ratio of these two numbers to the same ratio for a satellite in geostationary orbit (around Earth). 54. Neptune has an orbital radius from the Sun of 4.5 3 109 km. (6.2) T/I A (a) Assume the orbit is circular. Calculate the orbital speed of Neptune. Express your answer in metres per second and in kilometres per hour. (b) Calculate Neptune’s orbital period in Earth years. 55. Two satellites are placed in their desired orbit by releasing them from the International Space Station using the Canadarm2. Satellite A is released to an orbital radius of r. Satellite B is released to an orbital 9 radius of r. How does the velocity of satellite B 10 compare to the velocity of satellite A? (6.2) K/U T/I 56. The microsatellite MOST (Microvariability and Oscillations of STars) has a mass of just 52 kg. It travels in an almost circular orbit at an average altitude of 820 km above Earth’s surface. (6.2) T/I A (a) Calculate the gravitational force between Earth and the MOST satellite at this altitude. (b) What speed does the MOST satellite need to maintain its altitude? Express the speed in metres per second and in kilometres per hour. (c) Determine the orbital period of MOST. Chapter 6 Review 315 4/27/12 9:00 AM 57. Determine the ratio of the speed of a satellite in orbit around Earth to the speed of a similar satellite in orbit around the Moon, assuming the satellites have equal orbital radii. The Moon’s mass is 1.23 % of Earth’s mass and its radius is 27.2 % of Earth’s radius. (6.2) T/I A 58. A space vehicle is in circular orbit at a height of 390 km above Earth’s surface. Explain how the orbital speed of the vehicle would have to change in order for its altitude above Earth to decrease by 75 km. (6.2) T/I 59. The Canadian Telesat communications satellite Anik F2 has a mass of 5900 kg and orbits 35 000 km above the equator. (6.2, 6.3) T/I A (a) Determine the gravitational field of Earth at this altitude. (b) Determine the gravitational force between the satellite and Earth. (c) Calculate the speed needed by Anik F2 to maintain its orbit. Express the speed in metres per second and in kilometres per hour. (d) Calculate the orbital period of Anik F2. 60. The black hole at the centre of the Milky Way galaxy is called Sagittarius A* (Figure 4). Determining its mass is difficult, but a typical value calculated for the mass is 4.3 3 106 times the mass of the Sun. The mass of the Sun is 1.99 3 1030 kg. (6.4) T/I Figure 4 (a) If this value for the mass of Sagittarius A* is correct, how would the black hole’s gravitational force on a 1 kg object compare with the gravitational force on a 1 kg object the same distance from the Sun? (b) Suppose an 8.5 kg space probe is a distance of 4.5 3 1012 m from the black hole’s centre. (This is about the distance from Neptune to the Sun.) What gravitational force does the black hole exert on the probe? 316 Chapter 6 • Gravitational Fields 8160_CH06_p282-317.indd 316 Evaluation 61. A magazine article claims that people are influenced by the movement of the planets. Use the following steps to evaluate this claim. (6.1) T/I A (a) The planet closest to Earth is Venus. It has a mass of 4.85 3 1024 kg, and its distance to Earth is 1.5 3 1010 m. Calculate the gravitational force of Venus on an 85 kg person. (b) Calculate the gravitational pull on an 85 kg person by a 10 000 kg school bus a distance of 0.5 m away. (c) What is the ratio of the gravitational pull of the bus to the gravitational pull of Venus? (d) Interpret your findings. 62. Isaac Newton developed the equation for universal gravitation several decades before Henry Cavendish did his experiment. It was not until he did his experiment that calculations using Newton’s equation could produce data from observations. Cavendish’s experiment yielded a value for G that is slightly higher than today’s accepted value of 6.67 3 10211N # m2/kg 2. Some more recent measurements have shown the value to be 6.69 3 10211N # m2/kg2. What would be the effect of changing the value of the constant? (6.1) T/I A 63. In 1970, a NASA spacecraft called Apollo 13 experienced an explosion which crippled the spacecraft. Engineers and scientists evaluated whether they should turn the spacecraft around immediately and use rockets to get the astronauts aboard the spacecraft home or use the Moon’s gravitational field to get back. They opted for the use of the Moon’s gravitational field. Suggest some reasons for this decision. (6.2) T/I A 64. A satellite is in orbit with velocity v at a distance d above Earth’s surface. A student says that the satellite’s velocity would not change if it were in orbit at the same distance d around a planet with twice the mass and twice the radius. (6.2) T/I C A Gm to determine Å r whether or not the student is correct. (b) Would the satellite’s velocity around the more massive planet be higher or lower? Defend your answer. (a) Use the equation v 5 NEL 4/27/12 9:00 AM 65. Earth’s orbit around the Sun is almost but not quite circular. We can approximate, however, a small piece of the orbit as though it is part of a perfectly circular orbit of the same radius. Earth’s orbital speed is slightly greater during the winter in the northern hemisphere than during the summer in the northern hemisphere. (6.2) K/U T/I C A (a) In which season, winter or summer, is Earth closest to the Sun? (b) Does your answer to (a) explain why summer in the northern hemisphere is so much warmer than in the winter? Why or why not? 66. Consider a specific type of artificial satellite and assess the impact of that satellite technology on society or the environment. (6.3) T/I C A 67. Canada first used satellites in the early 1960s for atmospheric observations. In the 1970s, however, the use shifted to communications satellites. Satellites are also used in Canada for weather and environmental observations. Make a poster explaining the ways that satellites affect your everyday life. Evaluate how your life would be different without this type of technology. (6.3) T/I C A 68. Communication satellites have made talking anywhere in the world on a cellphone possible. These communication satellites are difficult to service if anything goes wrong. If a satellite has stopped working completely, it is often left up in space to orbit. As more and more satellites end up in orbit, they will create clutter and possibly space junk. How will this clutter affect future space travel? (6.3) T/I A Reflect on Your Learning 69. When studying this chapter, you first read about universal gravitation and then about gravitational fields. Write a short paragraph explaining why it was helpful to learn about these topics in this order instead of the reverse order. T/I C 70. Look back at the diagrams and images in this chapter. Create a slide show presentation that shows how they helped you understand universal gravitation and orbits. Be sure to include specific examples in your presentation. T/I C 71. Consider the different topics you have studied in this chapter. Choose one that you feel has an important impact on your life. Formulate your thoughts on paper and then express your thoughts to a parent or sibling, explaining about the topic and why it is important to you. What else would you like to know about this topic? How could you go about learning this? T/I C NEL 8160_CH06_p282-317.indd 317 Research WEB LINK 72. View some actual radar images of Earth. Choose a current meteorological or environmental event, explore the information available on the Internet, and then report your findings in the form of a brief news release. T/I C 73. Application of gravitational concepts has enabled great advancements in astronomical research and understanding. Gravity explains how stars are bound together in galaxies, how galaxies are bound together in groups, and how groups of stars and galaxies are bound together in clusters. Knowledge of gravity helps scientists develop theories about black holes and dark matter. Research and prepare a report, two pages or longer, about how the application of gravitational concepts has helped astronomers. T/I C 74. The Lagrange points, labelled numerically as shown in Figure 5, are positions in space where satellites can be placed in stationary orbits relative to two larger objects, such as Earth and the Sun. Research Lagrange points. T/I C A 4 2 1 3 5 Figure 5 (a) In an email to a peer, explain why there are five Lagrange points in the Earth–Sun system. (b) What do the designations 1, 2, and so on, mean? (c) How do scientists use these points when choosing the placement of satellites in orbits? (d) What satellites are currently in orbit at different Lagrange points and why? 75. A geostationary satellite is a geosynchronous satellite in orbit directly above the equator. In a few sentences, describe why a satellite must orbit above the equator to be geostationary and not just geosynchronous. K/U T/I 76. Technology now allows researchers to map Earth’s gravitational field and to use the map to study the material making up Earth’s interior. Research gravity surveys and how gravitational fields are used to search for mineral deposits. C A Chapter 6 Review 317 4/27/12 9:00 AM