Hobson Physics: Concepts & Connections 4e

CHAPTER 10 review questions Galilean Relativity 1. What is meant by relative motion, reference frame, a theory of relativity? 2. A train moves at 70 m/s. A ball is thrown toward the front of the train at 20 m/s relative to the train. How fast does the ball move relative to the tracks? What if the ball had instead been thrown toward the rear of the train? 3. A spaceship moves at 0.25c relative to Earth. A light beam passes the spaceship, in the forward direction, at speed c relative to Earth. According to Galilean relativity, how fast does the light beam move relative to the spaceship? Is this answer experimentally correct? If not, then what answer is correct? The Principles of Relativity and Constancy of Lightspeed 4. How does travel in a jet airplane illustrate the principle of relativity? How must the airplane be moving in order to illustrate this principle? 5. State the principle of relativity in your own words. Does it apply to every observer? Explain. 6. State the principle of the constancy of lightspeed in your own words. Does it apply to every observer? Explain. 7. Use the principle of the constancy of lightspeed to explain why no observer can move at precisely speed c relative to any other observer. 8. What did the Michelson–Morley experiment measure, and what was the result? 9. In Galilean relativity, space and time are absolute and lightspeed is relative. What is the situation in Einstein’s relativity? 10. What distinguishes the special from the general theory of relativity? 11. List the basic “laws” of the special theory of relativity. The Relativity of Time 12. How is time defined in physics? 13. Describe the light clock. 14. Velma passes Mort at a high speed. Both observers have clocks. What does each observer say about Velma’s clock? What do they each say about Mort’s clock? 15. One twin goes on a fast trip and returns. Does the special theory of relativity apply to the observations of both twins? Why, or why not? 16. One twin goes on a fast trip and returns. Have the two twins aged differently during the trip? If so, how do their ages differ? 17. Explain how you can travel to the future. The Relativity of Space and Mass 18. What do we mean by “space” or “distance”? 19. What does “space is relative” mean? 20. Velma passes Mort at a high speed. Each of them holds a meter stick parallel to the direction of motion. What does each observer say about Velma’s meter stick? What does each say about Mort’s meter stick? 21. In the preceding question, which items are relative according to Einstein’s theory? 22. Velma passes Mort at a high speed. Both observers carry a standard kilogram. What does Mort say about the mass of each of the standard kilograms? What does Velma say? 23. Mort exerts a 1 newton force on his standard kilogram. What acceleration does this give to the kilogram? What will he find if he exerts the same force on Velma’s standard kilogram if Velma is passing him at a high speed? 24. What is the distinction, if any, between rest-mass, mass, and matter? Which ones increase with speed? 25. What is the distinction between matter and radiation? 26. Why can’t material objects be sped up to lightspeed? Does anything move at lightspeed? 27. What does mean? Does it mean that mass can be converted to energy? Explain. 28. Is matter always conserved? Is mass always conserved? Is rest-mass always conserved? Is energy always conserved? 29. According to Einstein’s relativity, is rest-mass precisely conserved in chemical reactions? Can this effect be measured? 30. Describe an experiment in which a system’s entire rest-mass vanishes. Is matter conserved here? Mass? Energy? conceptual exercises Galilean Relativity 1. Two bicyclers, on different streets in the same city, are both moving directly north at 15 km/hr. Are they in relative motion? 2. According to the Galilean theory of relativity, does every observer measure the same speed for a light beam? 3. Velma moves toward Mort at half of lightspeed. Mort shines a searchlight toward Velma. What does Galilean relativity predict about the speed of the searchlight beam as observed by Velma? 4. Velma bicycles northward at 4 m/s. Mort, standing by the side of the road, throws a ball northward at 10 m/s. What is the ball’s speed and direction of motion, relative to Velma? What if Mort had instead thrown the ball southward at 10 m/s? 5. A desperado riding on top of a train car fires a gun toward the front of the train. The gun’s muzzle speed (speed of the bullet relative to the gun) is 500 m/s, and the train’s speed is 40 m/s. What is the bullet’s speed and direction of motion as observed by the sheriff standing beside the tracks? What does a passenger on the train say about the bullet’s speed? What if the desperado had instead pointed his gun toward the rear of the train? 6. Velma is in a train moving eastward at 70 m/s. Mort, standing beside the tracks, throws a ball at 20 m/s eastward. What is the ball’s speed and direction relative to Velma? 7. Velma is in a train moving eastward at 70 m/s. Mort, standing beside the tracks, throws a ball at 20 m/s westward. What is the ball’s speed and direction relative to Velma? The Principle of Relativity 8. Does the principle of relativity require that every observer observe the same laws of physics? Explain. 9. If you were riding on a train moving at constant speed along a straight track and you dropped a ball directly over a white dot on the floor, where would the ball land relative to the dot? 10. Suppose that you drop a ball while riding on a train moving at constant speed along a straight track. If you measure the ball’s acceleration, will your result be greater than, less than, or equal to, the usual acceleration due to gravity? 11. Think of several ways that you could determine from inside an airplane whether the plane was flying smoothly or parked on the runway. Do each of these ways involve some direct or indirect contact with the world outside the airplane? 12. How fast are you moving right now? What meaning does this question have? 13. If you drop a coin inside a car that is turning a corner to the right, where will the coin land? The Constancy of Lightspeed 14. Does every observer measure the same speed for a light beam? Explain. 15. A star headed toward Earth at 20% of lightspeed suddenly explodes as a bright supernova. With what speed does the light from the explosion leave the star? With what speed (as measured on Earth) does it approach Earth? 16. Is it physically possible for a person to move past Earth at exactly lightspeed? Explain. 17. Velma’s spaceship approaches Earth at 0.75c. She turns on a laser and beams it toward Earth. How fast does she see the beam move away from her? How fast does an Earth-based observer see the beam approach Earth? 18. A desperado riding on top of a freight-train car fires a laser gun pointed forward. What is this gun’s “muzzle velocity”? Suppose the train is moving at 40 m/s (0.04 km/s). How fast does the tip of the laser beam move relative to the sheriff, who is standing on the ground beside the train? What answer would the Galilean theory of relativity have given to this question? 19. Earth orbits the sun at a speed of about 30 km/s. If we assume that ether fills all space and that the sun is at rest in the ether, then it follows that Earth moves at about 30 km/s through the ether. Assuming also that light is a wave in the ether, what speed would the observer in Figure 10.7 observe for lightbeam A? For lightbeam B? The Relativity of Time 20. Velma passes you at a high speed. According to you, she ages slowly. How does she age according to her own observations? How do you age according to her? 21. Suppose you have a twin brother. What could be done to make him older than you? 22. The center of our galaxy is about 26,000 light-years away. Could a person possibly travel there in less than 26,000 years as measured on Earth? Could a person possibly travel there in less than 26,000 years of his or her own time? Explain. 23. A woman conceives a child while on a fast-moving space colony moving toward a distant planetary system. How long should it take before the baby is born, as measured by the woman? Would an Earth observer measure the same amount of time? 24. A certain fast-moving particle is observed to have a lifetime of 2 seconds. If the same particle was at rest in the laboratory, would its lifetime still be 2 seconds, or would it be more, or less, than 2 seconds? 25. Does the special theory of relativity allow you to go on a trip and return older than your father? 26. Does the special theory of relativity allow your father to go on a trip and return younger than you? 27. Does the special theory of relativity allow you to go on a trip and return younger than you were when you left? 28. When you go on a very fast trip, must you always return older than you were when you left? 29. Find the speed of a low-orbit satellite (8 km/s) as a fraction of lightspeed. Would an orbiting astronaut be able to directly notice the effects of time dilation without using sophisticated measurement techniques? 30. Velma passes Earth moving at 50% of lightspeed. On her video player, she watches a taped video program that runs 1 hour. How long does the program run as measured by an Earth-based observer? 31. Your fantastic rocketship moves at 30,000 km/s. If you took off, moved at this speed for 24 hours as measured by you, and returned to Earth, by how much time would your clock differ from Earth-based clocks? Would you have aged more than, or less than, people on Earth? By how much? 32. Answer the preceding question assuming that your extraordinarily fantastic rocketship moves at 99% of lightspeed. 33. Mort and Velma have identical 10-minute ice-cream cones. Velma passes Mort at 75% of lightspeed. How long does Mort’s cone take to melt as measured by Velma? 34. How fast must Velma move in order for her 10-minute ice-cream cone to melt in 30 minutes as measured by Mort? The Relativity of Space and Mass 35. How fast must Velma move past Mort if Mort is to observe her spaceship’s length to be reduced by 50%? If Velma is flying over the United States (about 5000 km wide) at this speed, how wide will she observe the United States to be? 36. Mort’s swimming pool is 20 m long and 10 m wide. If Velma flies lengthwise over the pool at 60% of lightspeed, how long and how wide will she observe it to be? 37. Mort’s automobile is 4 m long as measured by Mort. What length does Velma measure for Mort’s auto, as she passes him at 90% of lightspeed? 38. Velma, who is carrying a clock and a meter stick, passes Mort. Is it possible that Mort could observe length contraction of Velma’s meter stick but observe no time dilation of her clock? If so, how? 39. Velma, who is carrying a clock and a meter stick, passes Mort. Is it possible that Mort could observe time dilation of Velma’s clock but observe no length contraction of her meter stick? If so, how? 40. Velma drives a really fast rocket train northward past Mort, who is standing beside the tracks. Two posts are driven into the ground along the tracks. How does Mort’s measurement of the distance between the posts compare with Velma’s: longer, shorter, or the same? 41. If Velma passes Mort at a high speed, Mort will find her mass to be larger than normal. Will he also find her to be larger in size? 42. Velma’s spaceship has a rest-mass of 10,000 kg, and she measures its length to be 100 m. She moves past Mort at 0.8c. According to Mort’s measurements, what are the mass and the length of her spaceship? 43. How fast must Velma move past Mort if Mort is to observe her spaceship’s mass to be increased by 50%? How fast must she move if Mort is to observe her spaceship’s length to be reduced by 50%? 44. A meter stick with a rest-mass of 1 kg moves past you. Your measurements show it to have a mass of 2 kg and a length of 1 m. What is the orientation of the stick, and how fast is it moving? 45. Use Figure 10.13 to estimate how fast Velma must move, relative to Mort, for Mort to observe that her body’s mass is 50% larger than normal. 46. When you throw a stone, does its mass increase, decrease, or neither? Can this effect be detected? 47. A red-hot chunk of coal is placed in a large air-filled container where it completely burns up. The container is a perfect thermal insulator—in other words, thermal energy is unable to pass through the container’s walls. According to does the total mass of the container and its contents change during the burning process? If so, does the mass increase, or decrease? 48. Referring to the previous question: Suppose that the container is not a thermal insulator—in other words, thermal energy is able to pass through the walls. In this case, does the total mass of the container and its contents change during the burning process? If so, does the mass increase, or decrease? 49. An electron and an antielectron annihilate each other. In this process, is energy conserved? Is mass conserved? Is rest-mass conserved? 50. Two mousetraps are identical except that one of them is set to spring shut when the trigger is released, and the other is not set. They are placed in identical vats of acid. After they are completely dissolved, what, if any, are the differences between the two vats? Will the masses differ? 51. In a physics laboratory, an electron is accelerated to nearly lightspeed. If you were riding on the electron, would you notice that the electron’s mass had increased? If you were standing in the laboratory, what would you notice concerning the electron’s mass and energy? problems Use the time-dilation formula (explained in footnote 4) to answer questions 1–6. 1. Time dilation depends on the quantity which in turn depends on the fraction Evaluate the fraction for each of the following speeds: 3 km/s (high-powered rifle bullet), 30 km/s (speed of Earth in its orbit around the sun), 3000 km/s (fast enough to cross the United States in about 1 second). Is time dilation a very significant, noticeable, effect at these speeds? 2. Time dilation depends on the factor Evaluate this factor for each of the following speeds: 30,000 km/s (fast enough to circle the globe in 1 second), 150,000 km/s. 3. Velma passes Mort at 30,000 km/s. What fraction of lightspeed is this? What is the duration of one of Velma’s seconds (a time interval that Velma observes to be 1 second in duration) as observed by Mort? 4. Velma passes Mort at 150,000 km/s. What fraction of lightspeed is this? What is the duration of one of Mort’s seconds (a time interval that Mort observes to be 1 second in duration) as observed by Velma? 5. Velma passes Mort at a high speed. His clock, as observed by her, runs at half of its normal speed—for example, his clock advances by only 30 minutes during a time of 1 hour as recorded on her own clock. What must be the value of the quantity Find Velma’s speed relative to Mort. 6. Velma passes Mort at a high speed. Her clock, as observed by him, runs at 25% of its normal speed—for example, her clock advances by only 15 minutes during a time of 1 hour as recorded on his own clock. What must be the value of the quantity Find Velma’s speed relative to Mort. 7. You give 90 J of kinetic energy to a 1 kg stone when you throw it. By how much do you increase its mass? 8. A large nuclear power plant generates electric energy at the rate of 1000 MW. How many joules of electricity does the plant generate in one day? What is the mass of this much energy? 9. If you had two shoes, an ordinary shoe and an “antishoe” made of antiparticles, and you annihilated them together, by how far could you lift the U.S. population? Assume that each person weighs 600 N, that each shoe’s rest-mass is 0.5 kg, and that all the energy goes into lifting. 10. Making estimates. Show that, if all the energy released (transformed) in fissioning 1 kg of uranium were used to heat water, about 2 billion kg of water could be heated from freezing up to boiling. (Assume that the uranium’s rest-mass is reduced by about 0.1%. Roughly 4 J of thermal energy is needed to raise the temperature of 1 gram of water by 1°C.) How many tonnes of water is this (a tonne is 1000 kg)? How many large highway trucks, each loaded to about 30 tonnes, would be needed to carry this much water? 11. Solar radiation reaches Earth at the rate of 1400 watts for every square meter directly facing the sun. Using the formula for the area of a circle of radius R, find the amount of solar energy entering Earth’s atmosphere every second. Earth’s radius is 6400 km. 12. Use the answer to the preceding question to find how many kilograms of sunlight hit Earth every second.