Hobson Physics: Concepts & Connections 4e

Chapter 5 review questions The Idea of Gravity 1. What is the direction of a falling apple’s motion? Of its acceleration? 2. What is the direction of the moon’s motion? Of its acceleration? 3. Does Earth exert a force on the moon? What is its direction? How would the moon move if this force did not act? 4. In what ways are the moon and a falling apple similar? In what ways do they differ? The Law of Gravity 5. Does this book exert a gravitational force on your body? 6. What would happen to this book’s weight if you managed to double Earth’s mass? What if, instead, you doubled the book’s mass? What if you doubled both? 7. In order to use Newton’s law of gravity to calculate your weight, what data would you need? 8. If you were orbiting Earth in a satellite 200 km above the ground, would you be weightless? Would your weight be as large as it is when you are on the ground? Would you feel weightless? Explain. Gravitational Collapse 9. What caused the sun to get hot? What keeps it hot today? 10. Describe the process that formed the planets. 11. Since gravity pulls inward on the material in the sun and since the sun is made only of gas, why doesn’t the sun collapse? 12. Are there places in our galaxy where stars are being born? 13. Name the process and also the substance that fuels the sun. 14. What will happen to the sun after it runs out of fuel? 15. Name and describe the object into which the sun will evolve after it runs out of fuel. 16. What causes different stars to evolve differently? 17. All stars eventually evolve into one of three types of objects. Name them. What kinds of stars evolve into each of the three types of objects? 18. Describe a neutron star. 19. Describe a black hole. Since nothing can come out of a black hole, how can we detect it? The Newtonian Worldview 20. List some ways in which ancient Greek astronomy and Aristotelian physics support the traditional philosophical and religious worldview. 21. List some of the ways in which Copernican and Newtonian science are less supportive of the medieval worldview. 22. How is Newtonian physics related to democracy? 23. According to the Newtonian worldview, is a red napkin really “red”? Explain. 24. List several ways in which, according to the Newtonian worldview, the universe is similar to a clock. Beyond Newton 25. For what kinds of phenomena is Newtonian physics incorrect? Why did it take so long to discover such exceptions? 26. List the three theories that give correct predictions for the situations in which Newtonian physics is incorrect. conceptual exercises The Idea of Gravity 1. Does Earth’s gravity pull more strongly on a block of wood or on a block of iron having the same size? Which one falls faster when dropped (neglect air resistance)? 2. Does Earth’s gravity pull more strongly on a block of wood or on a block of iron having the same mass? 3. What is the magnitude (strength) and direction of the gravitational force on you right now? 4. When you crumple a sheet of paper into a tight ball, does its mass change? Does its weight change? 5. Are you in orbit around (falling around) Earth’s center? Is there anything around which you are in orbit? 6. The moon is in orbit around two objects simultaneously. Which two? (Actually, there is a third—our galaxy’s center.) 7. Do you exert a gravitational pull on people around you? Do they exert a gravitational pull on you? 8. Do you exert a gravitational force on Earth? If so, how large is it, and in what direction is it? 9. How far does Earth’s gravitational influence extend? 10. As a spacecraft travels from Earth to the moon, does it ever entirely leave Earth’s gravitational influence? 11. An orbiting satellite weighs 8000 N. How big and in what direction is the gravitational force on it? How big and in what direction is the gravitational force by the satellite on Earth? 12. What would be the approximate orbital period (time for one complete orbit) for an apple placed in circular orbit around Earth at the moon’s distance from Earth? 13. If gravity suddenly shut off right now, what would be the shape of Earth’s orbit? What about the moon’s orbit? 14. What force (if any) keeps the planets moving along their orbits? The Law of Gravity 15. Which is larger, the gravitational force by Earth on the moon or the gravitational force by the moon on Earth? 16. How strongly and in what direction does Earth pull on a 1 N apple? How strongly and in what direction does the apple pull on Earth? 17. Suppose you went to another planet that was identical to Earth on the surface but that was mostly hollow inside. Would this affect your weight? How? 18. Suppose you went to another planet having a larger radius than Earth but having the same total mass as Earth. Would this affect your weight? How? 19. List at least three bodies that have a detectable (measurable) gravitational effect on Earth’s motion. 20. The giant planet Jupiter is about 300 times more massive than Earth. It seems, then, that an object on Jupiter’s surface should weigh 300 times more than it weighs on Earth. But it actually weighs only about 3 times as much. Explain. 21. If you were in a freely falling elevator and you dropped your keys, they would hover in front of you. Are the keys falling? Are the keys weightless? 22. If gold were always sold by weight, could you make money buying gold at one altitude above the ground and selling it at a different altitude? Where would you want to buy—at a high altitude or a low altitude? 23. Would you weigh more in Denver or in Los Angeles? Why? 24. Is there any net force (Chapter 4) acting on the moon? 25. Is the moon accelerated? If so, in what direction is the acceleration? In what direction is the moon’s velocity? 26. Suppose that a heavy- and a lightweight satellite are put into low orbits around Earth. Could you tell, by observing the shape or speed of the two orbits, which satellite was the heavy one? 27. Suppose that two satellites are put into orbit, one around Earth and one around the moon, and suppose that the radii of the two orbits (the distance from the center of Earth and the moon) are the same. From the knowledge that Earth’s mass is larger than the moon’s mass, can you make any predictions about the speeds of the two orbits? 28. Communications satellites must be in geosynchronous orbits. That is, they must remain above a fixed point on Earth’s surface, enabling sending and receiving antennas to be aimed at a fixed point overhead. What, then, must be a communication satellite’s orbital period (the time for one complete orbit around Earth)? 29. In the “orbital” case in Figure 5.4, draw three arrows—labeled f, a, v—attached to the apple that show the direction of the gravitational force on the apple, the direction of the apple’s acceleration, and the direction of the apple’s velocity. 30. Figure 5.3 shows two possible paths for an apple that has been thrown horizontally. Assume that air resistance is negligible. For each path, draw three arrows— labeled f, a, v—attached to the apple that show the direction of the gravitational force on the apple, the direction of the apple’s acceleration, and the direction of the apple’s velocity. 31. Suppose that the gravitational force between an apple and an orange placed a short distance apart is one-trillionth What would the force be if the distance were doubled? Halved? Tripled? Quartered? 32. Referring to the previous exercise, what would the force be if the mass of the apple were doubled? Tripled? What if the mass of the apple were tripled and the mass of the orange were quadrupled? 33. Referring to the previous exercise, what would the force be if the mass of the apple were doubled, the mass of the orange were doubled, and the distance between them were doubled? Gravitational Collapse 34. If Earth collapsed to one-tenth of its present radius, how much would you then weigh? 35. If Earth expanded to 10 times its present radius, how much would you then weigh? 36. Find your weight at a distance of 10 Earth radii from Earth’s center. Compare with the preceding question. 37. Will Earth ever collapse to become a black hole? Why? Will the sun? 38. The orbits of all nine planets lie approximately in the same flat plane. Why? Beyond Newton 39. What theory or theories would be needed to predict the behavior of an atom moving at half the speed of light? 40. According to the most widely accepted scientific theory of the creation of the universe, the observable universe during the first few moments (much less than 1 second) of its existence was extremely hot, was full of densely packed matter, and was very tiny—smaller than an atom. What theory or theories would be needed to explain what was happening during these first few moments? problems The Law of Gravity 1. Find the change in the gravitational force between two planets when the distance between them is decreased to one-third of its previous value. 2. Find the change in the gravitational force between two planets when the distance between them is increased to three times its previous value. 3. Earth’s mass is and its radius is Use Newton’s law of gravity to find the weight of (i.e., the force of gravity on) a 1 kg object lying on Earth’s surface. 4. The moon’s mass is and its radius is Use Newton’s law of gravity to find the weight of a 1 kg object lying on the moon’s surface. If you did the preceding problem, then compare the two answers. 5. A certain neutron star has a mass of (twice the sun’s mass) compressed into a sphere of radius only 10,000 m (10 km). Find the gravitational force on a cubic centimeter of water, whose mass is 1 gram, lying on the surface (in reality, this “water” would no longer be in its normal liquid state, if it were on the surface of a neutron star!). 6. Find the force by the moon on Earth. Their masses are and and it is between their centers. 7. In the preceding question, how large is the force by Earth on the moon? In what direction is the force by Earth on the moon?8. Find the force by the sun on Earth. Their masses are and and it is 150 million kilometers between their centers. 9. In the preceding question, how large is the force by Earth on the sun? In what direction is the force by Earth on the sun? 10. Find the force by a 0.1 kg apple on another 0.1 kg apple, if their centers are 2 m apart. 11. Making estimates. Estimate the gravitational force, in newtons, that you exert on a person standing near you. Is the answer closer to 1000 N, 1 N, one-thousandth N, one-millionth N, or one-billionth N?