Chapter #35 Solutions - University Physics with Modern Physics Volume 2 (Chapters 21-40) - Gary Westfall, Wolfgang Bauer - 2nd Edition

1cc. An event 0 takes place at some point in space-time, as shown in the figure. Which of the five other events in space-time—A, B, C, D, and/or E— can be influenced by the event 0?... Get solution

1mcq. The most important fact we learned about the aether is thata) no experimental evidence of its effects was ever found.b) its existence was proven experimentally.c) it transmits light in all directions equally.d) it transmits light faster in the longitudinal direction.e) it transmits light slower in the longitudinal direction. Get solution

2cc. An event 0 takes place at some point in space-time, as shown in the figure. Which of the five other events in spacetime—A, B, C, D, and/or E—form a timelike space-time interval with the event 0?... Get solution

2mcq. If spaceship A is traveling at 70% of the speed of light relative to an observer at rest, and spaceship B is traveling at 90% of the speed of light relative to an observer at rest, which of the following have the greatest velocity as measured by an observer in spaceship B?a) a cannonball shot from A to B at 50% of the speed of light as measured in A’s reference frameb) a ball thrown from B to A at 50% of the speed of light as measured in B’s reference framec) a particle beam shot from a stationary observer to B at 70% of the speed of light as measured in the stationary reference framed) a beam of light shot from A to B, traveling at the speed of light in A’s reference framee) All of the above have the same velocity as measured in B’s reference frame. Get solution

3cc. A clock on a spaceship shows that a time interval of 1.00 s has expired. If this clock is moving with a speed of 0.860c relative to a stationary observer, what time period has expired in the reference frame of the stationary observer?a) 0.860 sb) 1.00 sc) 1.25 sd) 1.77 se) 1.96 s Get solution

4cc. State whether each of the following statements is true or false.a) For a moving object, its length along the direction of motion is shorter than when it is at rest.b) When you are stationary, a clock moving past you at a significant fraction of the speed of light seems to run faster than the watch on your wrist.c) When you are moving with a speed that is a significant fraction of the speed of light and you pass by a stationary observer, you observe that your watch seems to be running faster than the watch of the stationary observer. Get solution

4mcq. Which quantity is invariant—that is, has the same value—in all reference frames?a) time interval, ∆tb) space interval, ∆xc) velocity, vd) space-time interval, c2 (∆t)2 – (∆x)2 Get solution

5cc. The nearest star to us other than the Sun is Proxima Centauri, which is 4.22 light-years away. Suppose a spaceship could travel at a speed of 90.0% of the speed of light. If you were in that spaceship, how long would it take you to travel from the Sun to Proxima Centauri, from your point of view?a) 2.04 yearsb) 2.29 yearsc) 3.42 yearsd) 3.80 yearse) 4.22 years Get solution

6cc. Which of the following statements about the red-shift parameter is (are) true?a) The red-shift is always positive.b) The red-shift depends on the wavelength of the light.c) The red-shift depends on the frequency of the light.d) The red-shift is always less than 1.e) The red-shift depends on how fast the light is moving. Get solution

6mcq. A proton has a momentum of 3.0 GeV/c. With what velocity is it moving relative to a stationary observer?a) 0.31cb) 0.33cc) 0.91cd) 0.95ce) 3.2c Get solution

7cc. Which of the following are invariants under the nonrelativistic Galilean transformation of equation 35.14?a) xb) yc) zd) tEquation 35.14... Get solution

7mcq. A square of area 100 m2 that is at rest in a reference frame is moving with a speed ... Which of the following statements is incorrect?a) ...b) γ = 2c) To an observer at rest, it looks like a square with an area less than 100 m2.d) The length along the direction of motion is contracted by a factor of ½ Get solution

8cc. We have just seen that the real sum of two positive velocities consistent with relativity is less than the sum resulting from nonrelativistic velocity addition. What about velocity differences? Assume that two velocity vectors ...and ... both point in the positive x-direction. Call the relative velocity between the two ... Which of the following is correct?a) ...b) ...c) ...d) Either (a) or (c) is correct, depending on which of the two velocities, ...or ... is larger. Get solution

8mcq. Consider a particle moving with a speed less than 0.5c. If the speed of the particle is doubled, by what factor will the momentum increase?a) less than 2b) 2c) greater than 2 Get solution

9cc. What is the Schwarzschild radius of a black hole with a mass of 14.6 solar masses (mSun = 1.99 · 1030 kg)?a) 43.2 cmb) 55.1 mc) 1.55 kmd) 43.1 kme) 4.55 · 104 km Get solution

9mcq. Three groups of experimenters measure the average decay time for a specific type of radioactive particle. Group 1 accelerates the particles to 0.5c, moving from left to right, and then measures the decay time in the beam, obtaining a result of 20 ms. Group 2 accelerates the particles to –0.5c, from right to left, and then measures the decay time in the beam. Group 3 keeps the particles at rest in a container and measures their decay time. Which of the following is true about these measurements?a) Group 2 measures a decay time of 20 ms.b) Group 2 measures a decay time less than 20 ms.c) Group 3 measures a decay time of 20 ms.d) Both (a) and (c) are true.e) Both (b) and (c) are true. Get solution

10mcq. A person in a spaceship holds a meter stick parallel to the motion of the ship as it passes by the Earth with γ = 2. What length does an observer at rest on the Earth measure for the meter stick?a) 2 mb) 1 mc) 0.5 md) 0.0 me) none of the above Get solution

11mcq. A person in a spaceship holds a meter stick as the ship moves parallel to the Earth’s surface with γ = 2. What does the person in the ship notice if she rotates the stick from parallel to perpendicular to the ship’s motion?a) The stick becomes shorter.b) The stick becomes longer.c) The length of the stick stays the same. Get solution

12mcq. A person in a spaceship holds a meter stick as the ship moves parallel to the Earth’s surface with γ = 2. What does an observer on the Earth notice as the person in the spaceship rotates the stick from parallel to perpendicular to the ship’s motion?a) The stick becomes shorter.b) The stick becomes longer.c) The length of the stick stays the same. Get solution

13mcq. As the velocity of an object increases, so does its energy. What does this imply?a) At very low velocities, the object’s energy is equal to its mass times c2.b) In order for an object with mass m to reach the speed of light, infinite energy is required.c) Only objects with m = 0 can travel at the speed of light.d) all of the abovee) none of the above Get solution

14mcq. In the LHC at CERN in Geneva, Switzerland, two beams of protons are accelerated to E = 7 TeV. The proton’s rest mass is approximately m = 1 GeV/c2. When the two proton beams collide, what is the rest mass of the heaviest particle that can possibly be created?a) 1 GeV/c2b) 2 GeV/c2c) 7 TeV/c2d) 14 TeV/c2 Get solution

15cq. In mechanics, one often uses the model of a perfectly rigid body to determine the motion of physical objects (see, for example, Chapter 10 on rotation). Explain how this model contradicts Einstein’s special theory of relativity. Get solution

16cq. Use light cones and world lines to help solve the following problem. Eddie and Martin are throwing water balloons very fast at a target. At t = –13 µs, the target is at x = 0, Eddie is at x = –2 km, and Martin is at x = 5 km; all three remain in these positions for all time. The target is hit at t = 0. Who made the successful shot? Prove this using the light cone for the target. When the target is hit, it sends out a radio signal. When does Martin know the target has been hit? When does Eddie know the target has been hit? Use the world lines to show this. Before starting to draw the diagrams, consider this: If your x position is measured in kilometers and you are plotting t versus x/c, what unit must t be in? Get solution

17cq. A gravitational lens should produce a halo effect and not arcs. Given that the light travels not only to the right and left of the intervening massive object but also to the top and bottom, why do we typically see only arcs? Get solution

19cq. Consider a positively charged particle moving at constant speed parallel to a current-carrying wire, in the direction of the current. As you know (after studying Chapters 27 and 28), the particle is attracted to the wire by the magnetic force due to the current. Now suppose another observer moves along with the particle, so according to him the particle is at rest. Of course, a particle at rest feels no magnetic force. Does that observer see the particle attracted to the wire or not? How can that be? (Either answer seems to lead to a contradiction: If the particle is attracted, it must be by an electric force because there is no magnetic force, but there is no electric field from a neutral wire; if the particle is not attracted, the observer sees that the particle is, in fact, moving toward the wire.) Get solution

20cq. At rest, a rocket has an overall length of L. A garage at rest (built for the rocket by the lowest bidder) is only L/2 in length. Luckily, the garage has both a front door and a back door, so that when the rocket flies at a speed of v = 0.866c, it fits entirely into the garage. However, according to the rocket pilot, the rocket has length L and the garage has length L/4. How does the rocket pilot observe that the rocket does not fit into the garage? Get solution

21cq. A rod at rest on Earth makes an angle of 10° with the x-axis. If the rod is moved along the x-axis, what happens to this angle, as viewed by an observer on the ground? Get solution

23cq. Consider two clocks carried by observers in a reference frame moving at speed v in the positive x-direction relative to Earth’s rest frame. Assume that the two reference frames have parallel axes and that their origins coincide when clocks at that point in both frames read zero. Suppose the clocks are separated by a distance l in the x'-direction in their own reference frame; for instance, x' = 0 for one clock and x' = l for the other, with y' = z' = 0 for both. Determine the readings t' on both clocks as functions of the time coordinate t in Earth’s reference frame. Get solution

24cq. Prove that in all cases, adding two sub-light-speed velocities relativistically will always yield a sub-light-speed velocity. Consider motion in one spatial dimension only. Get solution

25cq. A famous result in Newtonian dynamics is that if a particle in motion collides elastically with an identical particle at rest, the two particles emerge from the collision on perpendicular trajectories. Does the same hold in the special theory of relativity? Suppose a particle of rest mass m and total energy E collides with an identical particle at rest, and the two particles emerge from the collision with new velocities. Are those velocities necessarily perpendicular? Explain. Get solution

26cq. Suppose you are watching a spaceship orbiting Earth at 80% of the speed of light. What is the length of the ship as viewed from the center of the orbit? Get solution

27. Find the speed of light in feet per nanosecond, to three significant figures. Get solution

28. Find the value of g, the gravitational acceleration at Earth’s surface, in light-years per year per year, to three significant figures. Get solution

29. Michelson and Morley used an interferometer to show that the speed of light is constant, regardless of Earth’s motion through any purported luminiferous aether. An analogy can be made with the different times it takes a rowboat to travel two different round-trip paths in a river that flows at a constant velocity (u) downstream. Let one path be for a distance D directly across the river, then back again; and let the other path be the same distance D directly upstream, then back again. Assume that the rowboat travels at a constant speed v (with respect to the water) for both trips. Neglect the time it takes for the rowboat to turn around. Find the ratio of the cross-stream time to the upstream-downstream time, as a function of the given constants. Get solution

30. What is the value of γ for a particle moving at a speed of 0.800c? Get solution

31. An astronaut on a spaceship traveling at a speed of 0.50c is holding a meter stick parallel to the direction of motion.a) What is the length of the meter stick as measured by another astronaut on the spaceship?b) If an observer on Earth could observe the meter stick, what would be the length of the meter stick as measured by that observer? Get solution

32. A spacecraft travels along a straight line from Earth to the Moon, a distance of 3.84 · 108 m. Its speed measured on Earth is 0.50c.a) How long does the trip take, according to a clock on Earth?b) How long does the trip take, according to a clock on the spacecraft?c) Determine the distance between Earth and the Moon if it were measured by a person on the spacecraft. Get solution

33. A 30.-year-old says goodbye to her 10.-year-old son and leaves on an interstellar trip. When she returns to Earth, both she and her son are 40. years old. What was the speed of the spaceship? Get solution

34. If a muon is moving at 90.0% of the speed of light, how does its measured lifetime compare to its lifetime of 2.2 · 10–6 s when it is in the rest frame of a laboratory? Get solution

35. A fire truck 10.0 m long needs to fit into a garage 8.00 m long (at least temporarily). How fast must the fire truck be going to fit entirely inside the garage, at least temporarily? How long does it take for the truck to get inside the garage, froma) the garage’s point of view?b) the fire truck’s point of view? Get solution

36. In Jules Verne’s classic Around the World in Eighty Days, Phileas Fogg travels around the world in, according to his calculation, 81 days. Because he crossed the International Date Line, he actually made it only 80 days. How fast would he have to go in order to have time dilation make 80 days seem like 81? (Of course, at this speed, it would take a lot less than 1 day to get around the world. . . .) Get solution

37. Suppose NASA discovers a planet just like Earth orbiting a star just like the Sun. This planet is 35 light-years away from our Solar System. NASA quickly plans to send astronauts to this planet, but with the condition that the astronauts not age more than 25 years during the journey.a) At what speed must the spaceship travel, in Earth’s reference frame, so that the astronauts age 25 years during their journey?b) According to the astronauts, what will be the distance of their trip? Get solution

38. Consider a meter stick at rest in a reference frame F. It lies in the x,y-plane and makes an angle of 37° with the x-axis. The reference frame F then moves with a constant velocity v parallel to the x-axis of another reference frame F'.a) What is the velocity of the meter stick measured in F' at an angle 45° to the x-axis?b) What is the length of the meter stick in F' under these conditions? Get solution

39. A spaceship shaped like an isosceles triangle has a width of 20.0 m and a length of 50.0 m. What is the angle between the base of the ship and the side of the ship as measured by a stationary observer if the ship is moving past the observer at a speed of 0.400c? Plot this angle as a function of the speed of the ship. Get solution

40. How fast must you be traveling relative to a blue light (480 nm) for it to appear red (660 nm)? Get solution

41. In your physics class, you have just learned about the relativistic frequency shift, and you decide to amaze your friends at a party. You tell them that once you drove through a stoplight and when you were pulled over, you did not get ticketed because you explained to the police officer that the relativistic Doppler shift made the red light of wavelength 650 nm appear green to you, with a wavelength of 520 nm. If your story were true, how fast would you have been traveling? Get solution

42. A meteor made of pure kryptonite (yes, we know that there really isn’t such a thing as kryptonite . . .) is moving toward Earth. If the meteor eventually hits Earth, the impact will cause severe damage, threatening life as we know it. If a laser hits the meteor with light of wavelength 560 nm, the meteor will blow up. The only laser on Earth powerful enough to hit the meteor produces light with a 532-nm wavelength. Scientists decide to launch the laser in a spacecraft and use special relativity to get the right wavelength. The meteor is moving very slowly, so there is no correction for relative velocities. At what speed does the spaceship need to move so that the laser light will have the right wavelength, and should it travel toward or away from the meteor? Get solution

43. Radar-based speed detection works by sending an electromagnetic wave out from a source and examining the Doppler shift of the reflected wave. Suppose a wave of frequency 10.6 GHz is sent toward a car moving away from the source at a speed of 32.0 km/h. What is the difference between the frequency of the wave emitted by the source and the frequency of the wave an observer in the car would detect? Get solution

45. Sam sees two events as simultaneous:(i) Event A occurs at the point (0,0,0) at the instant 0:00:00 universal time.(ii) Event B occurs at the point (500. m,0,0) at the same moment. Tim, moving past Sam with a velocity of 0.999..., also observes the two events.a) Which event occurs first in Tim’s reference frame?b) How long after the first event does the second event happen in Tim’s reference frame? Get solution

46. Use relativistic velocity addition to reconfirm that the speed of light with respect to any inertial reference frame is c. Assume one-dimensional motion along a common x-axis. Get solution

47. You are driving down a straight highway at a speed of v = 50.0 m/s relative to the ground. An oncoming car travels with the same speed in the opposite direction. What relative speed do you observe for the oncoming car? Get solution

48. A rocket ship approaching Earth at 0.90c fires a missile toward Earth with a speed of 0.50c, relative to the rocket ship. As viewed from Earth, how fast is the missile approaching Earth? Get solution

49. In the twin paradox example (in Section 35.2), Alice boards a spaceship that flies to a space station 3.25 light-years away and then returns with a speed of 0.65c.a) Calculate the total distance Alice traveled during the trip, as measured by Alice.b) Using the total distance from part (a), calculate the total time duration for the trip, as measured by Alice. Get solution

50. In the twin paradox example, Alice boards a spaceship that flies to a space station 3.25 light-years away and then returns with a speed of 0.650c. View the trip in terms of Alice’s reference frame.a) Show that Alice must travel with a speed of 0.914c to establish a relative speed of 0.650c with respect to Earth when she is returning to Earth.b) Calculate the time duration for Alice’s return flight to Earth at the speed of 0.914c. Get solution

51. Robert, standing at the rear end of a railroad car of length 100. m, shoots an arrow toward the front end of the car. He measures the velocity of the arrow as 0.300c. Jenny, who was standing on the platform, saw all of this as the train passed her with a velocity of 0.750c. Determine the following as observed by Jenny:a) the length of the carb) the velocity of the arrowc) the time taken by arrow to cover the length of the card) the distance covered by the arrow Get solution

52. Consider motion in one spatial dimension. For any velocity v, define the parameter θ via the relation v = c tanh θ, where c is the speed of light in vacuum. This quantity is called the velocity parameter or the rapidity corresponding to velocity v.a) Prove that for two velocities, which add via a Lorentz transformation, the corresponding velocity parameters simply add algebraically, that is, like Galilean velocities.b) Consider two reference frames in motion at speed v in the x-direction relative to one another, with axes parallel and origins coinciding when clocks at the origin in both frames read zero. Write the Lorentz transformation between the two coordinate systems entirely in terms of the velocity parameter corresponding to v and the coordinates. Get solution

53. What is the speed of a particle whose momentum is p = mc? Get solution

54. An electron’s rest mass is 0.511 MeV/c2.a) How fast must an electron be moving if its energy is to be 10 times its rest energy?b) What is the momentum of the electron at this speed? Get solution

55. The Relativistic Heavy Ion Collider (RHIC) can produce colliding beams of gold nuclei with beam kinetic energy of A · 100. GeV in the center-of-mass frame, where A is the number of nucleons in a gold nucleus (197). You can approximate the mass energy of a nucleon as 1.00 GeV. What is the equivalent beam kinetic energy for a fixed-target accelerator? (See Example 35.6.)Example 35.6 Colliders vs. Fixed-Target Accelerators...... Get solution

57. In proton accelerators used to treat cancer patients, protons are accelerated to 0.61c. Determine the energy of each proton, expressing your answer in mega-electron-volts (MeV). Get solution

58. In some proton accelerators, proton beams are directed toward each other to produce head-on collisions. Suppose that in such an accelerator, protons move with a speed relative to the lab reference frame of 0.9972c.a) Calculate the speed of approach of one proton with respect to another one with which it is about to collide head on. Express your answer as a multiple of c, using six significant figures.b) What is the kinetic energy of each proton (in units of MeV) in the laboratory reference frame?c) What is the kinetic energy of one of the colliding protons (in units of MeV) in the rest frame of the other proton? Get solution

60. Consider a one-dimensional collision at relativistic speeds between two particles with masses m1 and m2. Particle 1 is initially moving with a speed of 0.700c and collides with particle 2, which is initially at rest. After the collision, particle 1 recoils with a speed of 0.500c, while particle 2 starts moving with a speed of 0.200c. What is the ratio m2/m1? Get solution

61. In an elementary-particle experiment, a particle of mass m is fired, with momentum mc, at a target particle of mass 2 .... The two particles form a single new particle (in a completely inelastic collision). Find the following:a) the speed of the projectile before the collisionb) the mass of the new particlec) the speed of the new particle after the collision Get solution

62. Show that momentum and energy transform from one inertial frame to another as p'x = γ(px – vE/c2); p'y = py; p'z = pz; E' = γ (E – vpx). (Hint: Look at Derivation 35.4 for the space-time Lorentz transformation.) Get solution

63. Show that E2 – p2c2 = E'2 – p'2c2, that is, that E2 – p2c2 is a Lorentz invariant. (Hint: Look at Derivation 35.4, which shows that the space-time interval is a Lorentz invariant.) Get solution

64. The deviation of the space-time geometry near the Earth from the flat space-time of the special theory of relativity can be gauged by the ratio Φ/c2, where Φ is the Newtonian gravitational potential at the Earth’s surface. Find the value of this quantity. Get solution

65. Calculate the Schwarzschild radius of a black hole with the mass ofa) the Sun.b) a proton. How does this result compare with the size scale of 10–15 m usually associated with a proton? Get solution

66. Assuming that the speed of GPS satellites is approximately 4.00 km/s relative to Earth, calculate how much slower per day the atomic clocks on the satellites run, compared to stationary atomic clocks on Earth. Get solution

67. What is the Schwarzschild radius of the black hole at the center of our Milky Way? (Hint: The mass of this black hole was determined in Example 12.4.) Get solution

68. In order to fit a 50.0-foot-long stretch limousine into a 35.0-footlong garage, how fast would the limousine driver have to be moving, in the garage’s reference frame? Comment on what happens to the garage in the limousine’s reference frame. Get solution

69. Using relativistic expressions, compare the momentum of two electrons, one moving at 2.00·108 m/s and the other moving at 2.00·103 m/s. What is the percent difference between nonrelativistic momentum values and these values? Get solution

70. Rocket A passes Earth at a speed of 0.75c. At the same time, rocket B passes Earth moving with a speed of 0.95c relative to Earth in the same direction. How fast is B moving relative to A when it passes A? Get solution

71. Determine the difference in kinetic energy of an electron traveling at 0.9900c and one traveling at 0.9999c, first using standard Newtonian mechanics and then using special relativity. Get solution

72. Right before take-off, a passenger on a plane flying from town A to town B synchronizes his clock with the clock of his friend who is waiting for him in town B. The plane flies with a constant velocity of 240 m/s. The moment the plane touches the ground, the two friends check their clocks simultaneously. The clock of the passenger on the plane shows that it took exactly 3.00 h to travel from A to B. Ignoring any effects of acceleration:a) Will the clock of the friend waiting in B show a shorter or a longer time interval?b) What is the difference between the readings of the two clocks? Get solution

73. The explosive yield of the atomic bomb dropped on Hiroshima near the end of World War II was approximately 15.0 kilotons of TNT. One kiloton corresponds to about 4.18 · 1012 J of energy. Find the amount of mass that was converted into energy in this bomb. Get solution

74. At what speed will the length of a meter stick appear to be 90.0 cm? Get solution

75. What is the relative speed between two objects approaching each other head on, if each is traveling at speed of 0.600c as measured by an observer on Earth? Get solution

76. An old song contains these lines: “While driving in my Cadillac, what to my surprise; a little Nash Rambler was following me, about onethird my size.” The singer of that song assumes that the Nash Rambler is driving at a similar velocity. Suppose, though, rather than actually being one-third the Cadillac’s size, the proper length of the Rambler is the same as that of the Cadillac. What would be the velocity of the Rambler relative to the Cadillac for the song’s observation to be accurate? Get solution

77. You shouldn’t invoke time dilation due to your relative motion with respect to the rest of the world as an excuse for being late to class. While it is true that relative to those at rest in the classroom, your time while you are in motion runs more slowly, the difference is negligible. Suppose over a weekend you drove from your college in the Midwest to New York City and back, a round-trip of 2200. mi, driving for 20.0 h in each direction. By what amount, at most, would your watch differ from your professor’s watch? Get solution

78. A spaceship is traveling at two-thirds of the speed of light directly toward a stationary asteroid. If the spaceship turns on its headlights, what will be the speed of the light traveling from the spaceship to the asteroid as observed bya) someone on the spaceship?b) someone on the asteroid? Get solution

79. Two stationary space stations are separated by a distance of 100. light-years, as measured by someone on one of the space stations. A spaceship traveling at 0.950c relative to the space stations passes by one of them heading directly toward the other one. How long will it take to reach the other space station, as measured by someone on the spaceship? How much time will have passed for a traveler on the spaceship as it travels from one space station to the other, as measured by someone on one of the space stations? Round the answers to the nearest year. Get solution

80. An electron is accelerated from rest through a potential of 1.0·106 V. What is its final speed? Get solution

81. In the age of interstellar travel, an expedition is mounted to an interesting star 2000.0 light-years from Earth. To make it possible to get volunteers for the expedition, the planners guarantee that the round-trip to the star will take no more than 10.000% of a normal human lifetime. (At the time, the normal human lifetime is 400.00 years.) What is the minimum speed with which the ship carrying the expedition must travel? Get solution

82. What is the energy of a particle with speed of 0.800c and a momentum of 1.00·10–20 N s? Get solution

83. In a high-speed football game, a running back traveling at 55.0% of the speed of light relative to the field throws the ball to a receiver running in the same direction at 65.0% of the speed of light relative to the field. The speed of the ball relative to the running back is 80.0% of the speed of light.a) How fast does the receiver perceive the speed of the ball to be?b) If the running back shines a flashlight at the receiver, how fast will the photons appear to be traveling to the receiver? Get solution

84. You have been presented with a source of electrons, 14C, having kinetic energy equal to 0.305 times the rest energy. Suppose you have a pair of detectors that can detect the passage of the electrons without disturbing them. You wish to show that the relativistic expression for momentum is correct and the nonrelativistic expression is incorrect. If a 2.0-m-long baseline between your detectors is used, what timing accuracy is needed to show that the relativistic expression for momentum is correct? Get solution

85. A spacecraft travels a distance of 1.00·10–3 light-years in 20.0 h, as measured by an observer stationed on Earth. How long does the journey take as measured by the captain of the spacecraft? Get solution

86. More significant than the kinematic features of the special theory of relativity are the dynamical processes it describes that Newtonian dynamics does not. Suppose a hypothetical particle with rest mass 1.000 GeV/c2 and kinetic energy 1.000 GeV collides with an identical particle at rest. Amazingly, the two particles fuse to form a single new particle. Total energy and momentum are both conserved in the collision.a) Find the momentum and speed of the first particle.b) Find the rest mass and speed of the new particle. Get solution

88. A gold nucleus of rest mass 183.473 GeV/c2 is accelerated from 0.5785c to 0.8433c. How much work is done on the gold nucleus in this process? Get solution

89. A gold nucleus of rest mass 183.473 GeV/c2 is accelerated from 0.4243c to some final speed. In this process, 140.779 GeV of work is done on the gold nucleus. What is the final speed of the gold nucleus as a fraction of c? Get solution

90. A gold nucleus of rest mass 183.473 GeV/c2 is accelerated from some initial speed to a fi nal speed of 0.8475c. In this process, 137.782 GeV of work is done on the gold nucleus. What was the initial speed of the gold nucleus as a fraction of c? Get solution

91. Two identical nuclei, each with rest mass 50.30 GeV/c2, are accelerated in a collider to a kinetic energy of 503.01 GeV and made to collide head on. If one of the two nuclei were instead kept at rest, what would the kinetic energy of the other nucleus have to be for the collision to achieve the same center-of-mass energy? Get solution

92. Two identical nuclei are accelerated in a collider to a kinetic energy of 621.38 GeV and made to collide head on. If one of the two nuclei were instead kept at rest, the kinetic energy of the other nucleus would have to be 15,161.70 GeV for the collision to achieve the same center-of-mass energy. What is the rest mass of each of the nuclei? Get solution

93. A nucleus with rest mass 23.94 GeV/c2 is at rest in the lab. An identical nucleus is accelerated to a kinetic energy of 10,868.96 GeV and made to collide with the first nucleus. If instead the two nuclei were made to collide head on in a collider, what would the kinetic energy of each nucleus have to be for the collision to achieve the same center-of-mass energy? Get solution


Chapter #40 Solutions - University Physics with Modern Physics Volume 2 (Chapters 21-40) - Gary Westfall, Wolfgang Bauer - 2nd Edition

1cc. Which isotope X is needed to complete the reaction ...a) ...b) ...c) ...d) ...e) ... Get solution 1mcq. Radium-226 decays by e...