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Chapter 28 Special Relativity
AP Learning Objectives <ul><li>Nuclear Physics   </li></ul><ul><li>Mass-energy equivalence </li></ul><ul><li>Students shou...
Table Of Contents <ul><li>Events and Inertial Reference Frames </li></ul><ul><li>The Postulates of Special Relativity </li...
Chapter 28: Special Relativity Section 1: Events and  Inertial Reference Frames
Events and Reference Frames <ul><li>An  event  is a physical “happening” that occurs at a certain place and time. </li></u...
Events and Reference Frames <ul><li>In this example, the event is the space shuttle lift off. </li></ul><ul><li>Each obser...
Inertial Reference Frames <ul><li>Special Relativity deals with reference frames that are at constant velocity  </li></ul>...
PSSC Frame of Reference http://www.youtube.com/watch?v=Y3xnVti7htQ
28.1.1. Which one of the following systems is an inertial frame of reference? a)  Space Station Freedom orbits the Earth a...
28.1.2. During a practice flight, a Corsair, a World War II fighter plane, is flying at 181 m/s, due west relative to the ...
Chapter 28: Special Relativity Section 2: The Postulates of Special Relativity
The Postulates of Special Relativity <ul><li>The Relativity Postulate.  The laws of physics are the same in every inertial...
Relative Speeds
28.2.1. Two alien spaceships are traveling at 0.95 c , one directly toward the Earth and one directly away from the Earth....
28.2.2. Which one of the following statements concerning relativity is true? a)  Light has the same speed for all accelera...
28.2.3. Within an alien spaceship there is a room that has a light bulb that flashes one time each day.  When the bulb fla...
28.2.4. Is  everything relative  according to the postulates of Special Relativity? a)  No, mass is the same everywhere. b...
28.2.5. Which one of the following statements concerning the postulates of Special Relativity is true? a)  The postulates ...
Chapter 28: Special Relativity Section 3: The Relativity of Time:  Time Dilation
Time Dilation A light clock (like a Grand Father Clock,  only faster)
Time Dilation of Light Clock <ul><li>An observer on the earth (in one frame of reference)  </li></ul><ul><li>Sees the ligh...
Equation of Time Dilation Time dilation Your frame Other frame
Example 1  Time Dilation The spacecraft is moving past the earth at a constant speed of  0.92 times the speed of light.  t...
Proper Time Interval <ul><li>The time interval measured at rest with respect to the clock is called the  proper time inter...
28.3.1. Gax and Zax are intergalactic travelers in two different spaceships.  During one interval of their mission, Zax no...
28.3.2. Gax is standing on his home planet as he observes his wife Zax pass their planet at near-light speed.  By a strang...
28.3.3. Mick and Rick are twins born on Earth in the year 2175.  Rick grows up to be an Earth-bound robotics technician wh...
28.3.4. The center of the Milky Way Galaxy is about 26 000 light years from the Earth.  By what means could a human being ...
28.3.5. Mars rotates about its axis once every 88 642 s.  A spacecraft comes into the solar system and heads directly towa...
28.3.6. Observer A witnesses two lights flash at the same time.  Observer B is moving relative to observer A.  What, in ge...
Chapter 28: Special Relativity Section 4: The Relativity of Length:  Length Contraction
Length Contraction The shortening of the distance between two points is one example of a phenomenon known as  length contr...
Example 4  The Contraction of a Spacecraft An astronaut, using a meter stick that is at rest relative to a cylindrical spa...
28.4.1. Gax is standing on his home planet as he observes his wife Zax orbit their planet at near-light speed.  Gax and Za...
28.4.2. Gax is standing on his home planet as he observes his wife Zax orbit their planet at near-light speed.  Gax and Za...
28.4.3. An alien observer passes the earth at 0.60 c  and measures the length of an American football field while travelin...
28.4.4. A perfect cube with 2.00-m sides is constructed in an alien space station.  It is then launched from the station. ...
28.4.5. Complete the following statement: According to relativity, the time between two events and the distance between th...
28.4.6. If one wants to determine the proper frequency of a wave, which of the following statements is true? a)  The prope...
28.4.7. An observed on Earth sees two rocket ships moving toward each other, each at a speed of 0.25 c .  An observer is l...
28.4.8. The pilot of an airplane flying due south at a constant speed  v  observes three sources of electromagnetic waves....
Chapter 28: Special Relativity Section 5: Relativistic Momentum
Relativistic Momentum <ul><li>Since momentum is a product of mass and velocity </li></ul><ul><li>Momentum is also relative...
28.5.1. Gax is standing on his home planet as he observes his wife Zax zoom past him along the horizon of their planet at ...
28.5.2. You are in a closed room (no windows and closed doors) on a ship that is traveling very close to the speed of ligh...
28.5.3. One electron is traveling due east at 0.9950 c  and another electron is moving due west, away from the other elect...
Chapter 28: Special Relativity Section 6: The Equivalence of Mass and Energy
The Total Energy of an Object Total energy of an object Rest energy of an object
Example 8  The Sun is Losing Mass The sun radiates electromagnetic energy at a rate of 3.92x10 26 W. What is the change in...
Conceptual Example 9  When is a Massless Spring Not Massless? The spring is initially unstrained and assumed to be massles...
28.6.1. An electron (rest mass = 0.511 MeV) has a total energy of 10.00 MeV.  What is the speed of this electron? a)  0.99...
28.6.2.  Determine the speed at which the kinetic energy of an electron is equal to twice its rest energy. a)  0.45 c b)  ...
28.6.3. Space and time are intertwined when considering relativistic effects.  Which of the following pairs are also inter...
28.6.4. Determine the speed at which the kinetic energy of an electron is equal to twice its rest energy. a)  0.45 c b)  0...
Chapter 28: Special Relativity Section 7: The Relativistic Additions of Velocities
Relativistic Addition of Velocities
<ul><li>+ c </li></ul><ul><li>+ c  – (+0.7 c ) = +0.3  c </li></ul>Conceptual Example 11  The Speed of a Laser Beam The cr...
28.7.1. Two airplanes are headed due west.  Plane A is flying above plane B.  The pilot of plane A observes that plane B i...
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Ch 28 Special Relativity

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Ch 28 Special Relativity

  1. 1. Chapter 28 Special Relativity
  2. 2. AP Learning Objectives <ul><li>Nuclear Physics </li></ul><ul><li>Mass-energy equivalence </li></ul><ul><li>Students should understand the relationship between mass and energy (mass-energy equivalence), so they can: </li></ul><ul><ul><li>Apply the relationship  E = (  m)c 2 in analyzing nuclear processes. </li></ul></ul>
  3. 3. Table Of Contents <ul><li>Events and Inertial Reference Frames </li></ul><ul><li>The Postulates of Special Relativity </li></ul><ul><li>The Relativity of Time: Time Dilation </li></ul><ul><li>The Relativity of Length: Length Contraction </li></ul><ul><li>Relativistic Momentum </li></ul><ul><li>The Equivalence of Mass and Energy </li></ul><ul><li>The Relativistic Additions of Velocities </li></ul>
  4. 4. Chapter 28: Special Relativity Section 1: Events and Inertial Reference Frames
  5. 5. Events and Reference Frames <ul><li>An event is a physical “happening” that occurs at a certain place and time. </li></ul><ul><li>To record the event, each observer uses a reference frame that consists of a coordinate system (x, y, and z) and a clock (time). </li></ul><ul><li>Each observer is at rest relative to her own reference frame. </li></ul><ul><li>An inertial reference frame is one in which Newton’s law of inertia is valid. </li></ul>
  6. 6. Events and Reference Frames <ul><li>In this example, the event is the space shuttle lift off. </li></ul><ul><li>Each observer could note the position and time of lift-off </li></ul>
  7. 7. Inertial Reference Frames <ul><li>Special Relativity deals with reference frames that are at constant velocity </li></ul><ul><ul><li>Not moving </li></ul></ul><ul><ul><li>Moving at constant speed </li></ul></ul><ul><li>Since the objects on Earth are rotating/revolving </li></ul><ul><ul><li>Earth is not an inertial reference frame </li></ul></ul><ul><li>However, the acceleration of the Earth can usually be omitted with little effect. </li></ul>
  8. 8. PSSC Frame of Reference http://www.youtube.com/watch?v=Y3xnVti7htQ
  9. 9. 28.1.1. Which one of the following systems is an inertial frame of reference? a) Space Station Freedom orbits the Earth at an altitude of 350 km. b) A train is traveling around an unbanked curve at 12 m/s. c) The space shuttle is accelerating upward at 28 m/s 2 . d) A carousel rotates uniformly with a period of 25 seconds. e) A man suspended from a rectangular parachute descends at a constant speed of 8 m/s.
  10. 10. 28.1.2. During a practice flight, a Corsair, a World War II fighter plane, is flying at 181 m/s, due west relative to the ground below. The pilot fires his guns and the bullets leave the guns at a speed of 890 m/s, relative to the guns. The velocity of the bullets as they leave the gun, relative to the ground, is a) 181 m/s, due west b) 709 m/s, due west c) 709 m/s, due east d) 890 m/s, due west e) 1071 m/s, due east
  11. 11. Chapter 28: Special Relativity Section 2: The Postulates of Special Relativity
  12. 12. The Postulates of Special Relativity <ul><li>The Relativity Postulate. The laws of physics are the same in every inertial reference frame. </li></ul><ul><li>The Speed of Light Postulate. The speed of light in a vacuum, measured in any inertial reference frame, always has the same value of c , no matter how fast the source of light and the observer are moving relative to one another. </li></ul>
  13. 13. Relative Speeds
  14. 14. 28.2.1. Two alien spaceships are traveling at 0.95 c , one directly toward the Earth and one directly away from the Earth. At one instant, both spaceships happen to be the same distance from the Earth and they fire a laser at the Earth. The light from which laser reaches the Earth first according to an observer on Earth? a) The light from the spaceship moving toward the Earth arrives first. b) The light from the spaceship moving away from the Earth arrives first. c) The light from the two ships arrives at the same time. d) The observer has no way to determine which light reaches the Earth first.
  15. 15. 28.2.2. Which one of the following statements concerning relativity is true? a) Light has the same speed for all accelerated observers, regardless of the motion of the source or the observer. b) No physical experiment can be conducted by an observer within his or her own system that can allow the observer to determine how fast he or she is moving relative to anything outside his or her own system. c) Depending on the state of motion of your laboratory, experiments within your lab will have different outcomes. d) The speed of light in all media has the same value, c .
  16. 16. 28.2.3. Within an alien spaceship there is a room that has a light bulb that flashes one time each day. When the bulb flashes, it sends light out uniformly in all directions. On two opposite walls, there is a light detector that turns on another light as soon as light is detected. Let’s call the wall closest to the forward part of the ship, wall A, and the opposite one, wall B. One day, the aliens decide to test this set up while they are sitting motionless in interstellar space. They activate the system and the central bulb flashes. At the same time, the lights on the two walls light up. The next day when the alien ship is traveling at 0.955 c through interstellar space, what do they observe when the flash occurs? a) Lights A and B light up at the same instant of time. b) Light B lights up a little earlier than A does. c) Light A lights up a little earlier than B does. d) Light B lights up much earlier than A does. e) Light A lights up much earlier than B does.
  17. 17. 28.2.4. Is everything relative according to the postulates of Special Relativity? a) No, mass is the same everywhere. b) No, velocity is not relative. c) Yes, everything, all physical measurements are relative. d) No, the speed of light is not relative. e) No, space is the same everywhere.
  18. 18. 28.2.5. Which one of the following statements concerning the postulates of Special Relativity is true? a) The postulates have been proven to be true. b) The postulates have been proven to be false at the sub-atomic scale. c) The postulates cannot be proven to be true, but they do provide the foundation for Einstein’s Theory of Special Relativity. d) Einstein did not actually develop these postulates. He borrowed them from others in developing his theory.
  19. 19. Chapter 28: Special Relativity Section 3: The Relativity of Time: Time Dilation
  20. 20. Time Dilation A light clock (like a Grand Father Clock, only faster)
  21. 21. Time Dilation of Light Clock <ul><li>An observer on the earth (in one frame of reference) </li></ul><ul><li>Sees the light pulse travel a greater distance between tick (in the second frame of reference). </li></ul>
  22. 22. Equation of Time Dilation Time dilation Your frame Other frame
  23. 23. Example 1 Time Dilation The spacecraft is moving past the earth at a constant speed of 0.92 times the speed of light. the astronaut measures the time interval between ticks of the spacecraft clock to be 1.0 s. What is the time interval that an earth observer measures?
  24. 24. Proper Time Interval <ul><li>The time interval measured at rest with respect to the clock is called the proper time interval . </li></ul><ul><li>In general, the proper time interval between events is the time interval measured by an observer who is at rest relative to the events. </li></ul>Proper time interval
  25. 25. 28.3.1. Gax and Zax are intergalactic travelers in two different spaceships. During one interval of their mission, Zax notices that her clock advances 40 minutes while Gax’s clock advances only 20 minutes. What does Gax observe during this same interval? a) Gax notices that his clock advances only 20 minutes while Zax’s clock advances 40 minutes. b) Gax notices that his clock advances 40 minutes while Zax’s clock advances only 20 minutes. c) Gax notices that both clocks advance 40 minutes. d) Gax notices that both clocks advance 20 minutes. e) Gax notices that both clocks advance 60 minutes.
  26. 26. 28.3.2. Gax is standing on his home planet as he observes his wife Zax pass their planet at near-light speed. By a strange quirk, at precisely the same instant, their clocks are synchronized at 1:00:00 PM. As Gax continues to observe the clock on his wife’s ship, what does he observe relative to his own clock? a) His clock reaches 1:00:02 before his wife’s clock does. b) His clock reaches 1:00:02 after his wife’s clock does. c) His clock reaches 1:00:02 at the same time as his wife’s clock does. d) His clock reaches 1:00:02, but his wife’s clock appears to be going in reverse.
  27. 27. 28.3.3. Mick and Rick are twins born on Earth in the year 2175. Rick grows up to be an Earth-bound robotics technician while Mick becomes an intergalactic astronaut. Mick leaves the Earth on his first space mission in the year 2200 and travels, according to his clock, for 10 years at a speed of 0.75 c . Unfortunately, at this point in his journey, the structure of his ship undergoes mechanical breakdown and the ship explodes. How old is Rick when his brother dies? a) 35 years old b) 40 years old c) 50 years old d) 65 years old e) 95 years old
  28. 28. 28.3.4. The center of the Milky Way Galaxy is about 26 000 light years from the Earth. By what means could a human being travel to the center of the Milky Way? a) Even with time dilation, it isn’t possible to travel that far within a normal human lifetime. b) A person would have to travel at the speed of light, but that isn’t possible. c) A person would only have to travel very close to the speed of light for it to be possible within a normal human lifetime. d) A person would only have to travel a little faster than the speed of light for it to be possible within a normal human lifetime.
  29. 29. 28.3.5. Mars rotates about its axis once every 88 642 s. A spacecraft comes into the solar system and heads directly toward Mars at a speed of 0.800c. What is the rotational period of Mars according to the beings on the spaceship? a) about 53 100 s b) about 88 600 s c) about 105 000 s d) about 148 000 s e) about 181 000 s
  30. 30. 28.3.6. Observer A witnesses two lights flash at the same time. Observer B is moving relative to observer A. What, in general, would observer B see with regard to the two lights? a) Observer B would also see the lights flash at the same time. b) Observer B would see the lights flash at different times. c) Observer B would see only one of the lights flash. d) Observer B would see neither light flash.
  31. 31. Chapter 28: Special Relativity Section 4: The Relativity of Length: Length Contraction
  32. 32. Length Contraction The shortening of the distance between two points is one example of a phenomenon known as length contraction . Length contraction
  33. 33. Example 4 The Contraction of a Spacecraft An astronaut, using a meter stick that is at rest relative to a cylindrical spacecraft, measures the length and diameter to be 82 m and 21 m respectively. The spacecraft moves with a constant speed of 0.95 c relative to the earth. What are the dimensions of the spacecraft, as measured by an observer on earth. Diameter stays the same.
  34. 34. 28.4.1. Gax is standing on his home planet as he observes his wife Zax orbit their planet at near-light speed. Gax and Zax have identical sticks that are one meter long and each are holding them parallel to the direction that Zax is moving. What does Gax observe about the length of the sticks? a) Zax’s stick is more than one meter long, while his stick is exactly one meter long. b) Both sticks are still exactly one meter long. c) Zax’s stick is less than one meter long, while his stick is exactly one meter long.
  35. 35. 28.4.2. Gax is standing on his home planet as he observes his wife Zax orbit their planet at near-light speed. Gax and Zax have identical sticks that are one meter long and each are holding them perpendicular to the direction that Zax is moving. What does Gax observe about the length of the sticks? a) Zax’s stick is more than one meter long, while his stick is exactly one meter long. b) Both sticks are still exactly one meter long. c) Zax’s stick is less than one meter long, while his stick is exactly one meter long.
  36. 36. 28.4.3. An alien observer passes the earth at 0.60 c and measures the length of an American football field while traveling in the direction from one end zone to the other end zone. On the field, the distance from end zone to end zone is 91.4 m. How long does the field appear to be according to the alien observer? a) 59.6 m b) 73.1 m c) 74.6 m d) 91.4 m e) 114 m
  37. 37. 28.4.4. A perfect cube with 2.00-m sides is constructed in an alien space station. It is then launched from the station. Sometime later, the cube passes the station with a speed 0.800 c , relative to the observers on the station. What is the volume of the cube as measured by the observers on the station? a) 4.80 m 3 b) 6.40 m 3 c) 8.00 m 3 d) 10.0 m 3 e) 13.3 m 3
  38. 38. 28.4.5. Complete the following statement: According to relativity, the time between two events and the distance between those events, a) are the same for all observers in all inertial reference frames. b) cannot be defined because space and time no longer have any meaning. c) are different in different frames of reference.
  39. 39. 28.4.6. If one wants to determine the proper frequency of a wave, which of the following statements is true? a) The proper frequency must be measured in the same frame as the proper length is measured. b) The proper frequency must be measured in the same frame as the proper time is measured. c) Choices (a) and (b) are both correct. d) None of the above answers are correct.
  40. 40. 28.4.7. An observed on Earth sees two rocket ships moving toward each other, each at a speed of 0.25 c . An observer is located on one of the moving ships. What speed does the observer measure for the approaching ship? a) 0.25 c b) between 0.25 c and 0.50 c c) 0.50 c d) between 0.50 c and c e) c
  41. 41. 28.4.8. The pilot of an airplane flying due south at a constant speed v observes three sources of electromagnetic waves. Each source emits light with the same frequency f . Source A is moving due south at a speed v , source B is moving due north at a speed v, and source C is moving due south at a speed 2 v . Rank the three frequencies of the observed waves in increasing order (smallest first, largest last) according to magnitude. a) A = C < B b) A = B < C c) B < A < C d) A < C < B e) B < C < A
  42. 42. Chapter 28: Special Relativity Section 5: Relativistic Momentum
  43. 43. Relativistic Momentum <ul><li>Since momentum is a product of mass and velocity </li></ul><ul><li>Momentum is also relative to the frame of reference </li></ul>
  44. 44. 28.5.1. Gax is standing on his home planet as he observes his wife Zax zoom past him along the horizon of their planet at near-light speed. Before she left the planet, the length of her ship was 100 m and the mass of her ship (not including fuel) was 10 000 kg. As she moves past him, Gax observes the length and mass of her ship. What does he observe? a) The mass of her ship is still 10 000 kg, but its length is somewhat smaller. b) The mass of her ship is still 10 000 kg, but its length is somewhat longer. c) The mass of her ship is somewhat larger than 10 000 kg, but its length is somewhat smaller. d) The mass of her ship is somewhat larger than 10 000 kg, but its length is somewhat longer. e) The mass of her ship is somewhat less than 10 000 kg; and its length is somewhat smaller.
  45. 45. 28.5.2. You are in a closed room (no windows and closed doors) on a ship that is traveling very close to the speed of light. Which of the following effects would you notice while sitting in this room? a) My wristwatch seems to be ticking more slowly. b) My mass has increased. c) I seem to be skinnier than usual. d) I seem to be taller than usual. e) None of the above observations could be made.
  46. 46. 28.5.3. One electron is traveling due east at 0.9950 c and another electron is moving due west, away from the other electron, at 0.9798 c . The rest mass of an electron is 0.511 MeV. What is the total relativistic momentum of these electrons? a) 2.50 MeV/ c , due west b) 5.08 MeV/ c , due east c) 7.58 MeV/ c , due east d) 5.36 MeV/ c , due west e) 2.58 MeV/ c , due east
  47. 47. Chapter 28: Special Relativity Section 6: The Equivalence of Mass and Energy
  48. 48. The Total Energy of an Object Total energy of an object Rest energy of an object
  49. 49. Example 8 The Sun is Losing Mass The sun radiates electromagnetic energy at a rate of 3.92x10 26 W. What is the change in the sun’s mass during each second that it is radiating energy? What fraction of the sun’s mass is lost during a human lifetime of 75 years.
  50. 50. Conceptual Example 9 When is a Massless Spring Not Massless? The spring is initially unstrained and assumed to be massless. Suppose that the spring is either stretched or compressed. Is the mass of the spring still zero, or has it changed? If the mass has changed, is the mass change greater for stretching or compressing? Since energy was added when it is stretched or compressed, the mass has increased.
  51. 51. 28.6.1. An electron (rest mass = 0.511 MeV) has a total energy of 10.00 MeV. What is the speed of this electron? a) 0.9959 c b) 0.9987 c c) 0.9991 c d) 0.9995 c e) 0.9999 c
  52. 52. 28.6.2. Determine the speed at which the kinetic energy of an electron is equal to twice its rest energy. a) 0.45 c b) 0.63 c c) 0.87 c d) 0.94 c e) 0.99 c
  53. 53. 28.6.3. Space and time are intertwined when considering relativistic effects. Which of the following pairs are also intertwined for relativistic objects? a) mass and momentum b) mass and kinetic energy c) force and inertia d) linear and angular momenta e) momentum and energy
  54. 54. 28.6.4. Determine the speed at which the kinetic energy of an electron is equal to twice its rest energy. a) 0.45 c b) 0.63 c c) 0.87 c d) 0.94 c e) 0.99 c
  55. 55. Chapter 28: Special Relativity Section 7: The Relativistic Additions of Velocities
  56. 56. Relativistic Addition of Velocities
  57. 57. <ul><li>+ c </li></ul><ul><li>+ c – (+0.7 c ) = +0.3 c </li></ul>Conceptual Example 11 The Speed of a Laser Beam The cruiser is approaching a hostile spacecraft. The velocity of the cruiser relative to the spacecraft is +0.7 c . Both vehicles are moving at constant velocity. The cruiser fires a beam of laser light at the enemy. The velocity of the laser beam relative to the cruiser is + c . (a) What is the velocity of the laser beam relative to the renegades aboard the spacecraft? (b) At what velocity do the renegades aboard the spacecraft see the laser beam move away from the cruiser?
  58. 58. 28.7.1. Two airplanes are headed due west. Plane A is flying above plane B. The pilot of plane A observes that plane B is flying 22 m/s faster relative to the ground below than plane A is flying. According the special relativity, the speed of plane B relative to that of plane A is a) less than 22 m/s. b) equal to 22 m/s. c) greater than to 22 m/s.
  59. 59. END

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