Chapter 26: Special Theory Of Relativity

55 Questions
Experiment Quizzes & Trivia
Sample Question

You are riding in a spaceship that has no windows, radios, or other means for you to observe or measure what is outside. You wish to determine if the ship is stopped or moving at constant velocity. What should you do?

You can determine if the ship is moving by determining the apparent velocity of light.

You can determine if the ship is moving by checking your precision time piece. If it's running slow, the ship is moving.

You can determine if the ship is moving either by determining the apparent velocity of light or by checking your precision time piece. If it's running slow, the ship is moving.

You should give up because you have taken on an impossible task.

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Questions and Answers
  • 1. 
    • A. 

      You can determine if the ship is moving by determining the apparent velocity of light.

    • B. 

      You can determine if the ship is moving by checking your precision time piece. If it's running slow, the ship is moving.

    • C. 

      You can determine if the ship is moving either by determining the apparent velocity of light or by checking your precision time piece. If it's running slow, the ship is moving.

    • D. 

      You should give up because you have taken on an impossible task.

  • 2. 
    The Michelson-Morley experiment was designed to measure
    • A. 

      The relativistic mass of the electron.

    • B. 

      The relativistic energy of the electron.

    • C. 

      The velocity of the Earth relative to the ether.

    • D. 

      The acceleration of gravity on the Earth's surface.

  • 3. 
    Michelson and Morley concluded from the results of their experiment that
    • A. 

      The experiment was a failure since there was no detectable shift in the interference pattern.

    • B. 

      The experiment was successful in not detecting a shift in the interference pattern.

    • C. 

      The experiment was a failure since they detected a shift in the interference pattern.

    • D. 

      The experiment was successful in detecting a shift in the interference pattern.

  • 4. 
    You can build an interferometer yourself if you use the following components:
    • A. 

      A light source, a detector screen, a partially silvered mirror, a flat mirror, and a glass plate.

    • B. 

      A light source, a detector screen, two partially silvered mirrors, and a glass plate.

    • C. 

      A light source, a detector screen, two partially silvered mirrors, a flat mirror, and a glass plate.

    • D. 

      A light source, a detector screen, a partially silvered mirror, two flat mirrors, and a glass plate.

  • 5. 
    The theory of special relativity
    • A. 

      Is based on a complex mathematical analysis.

    • B. 

      Has not been verified by experiment.

    • C. 

      Does not agree with Newtonian mechanics.

    • D. 

      Does not agree with electromagnetic theory.

  • 6. 
    One of Einstein's postulates in formulating the special theory of relativity was that the laws of physics are the same in reference frames that
    • A. 

      Accelerate.

    • B. 

      Move at constant velocity with respect to an inertial frame.

    • C. 

      Oscillate.

    • D. 

      Are stationary, but not in moving frames.

  • 7. 
    If you were to measure your pulse rate while in a spaceship moving away from the Sun at a speed close to the speed of light, you would find that it was
    • A. 

      Much faster than normal.

    • B. 

      Much slower than normal.

    • C. 

      The same as it was here on Earth.

  • 8. 
    Relative to a stationary observer, a moving clock
    • A. 

      Always runs slower than normal.

    • B. 

      Always runs faster than normal.

    • C. 

      Keeps its normal time.

    • D. 

      Can do any of the above. It depends on the relative velocity between the observer and the clock.

  • 9. 
    Suppose one twin takes a ride in a space ship traveling at a very high speed to a distant star and back again, while the other twin remains on Earth. The twin that remained on Earth predicts that the astronaut twin is
    • A. 

      Younger.

    • B. 

      The same age.

    • C. 

      Older.

    • D. 

      Cannot be determined from the given information

  • 10. 
    Relative to a stationary observer, a moving object
    • A. 

      Appears shorter than normal.

    • B. 

      Appears longer than normal.

    • C. 

      Keeps its same length time.

    • D. 

      Can do any of the above. It depends on the relative velocity between the observer and the object.

  • 11. 
    An object moves in a direction parallel to its length with a velocity that approaches the velocity of light. The width of this object, as measured by a stationary observer,
    • A. 

      Approaches infinity.

    • B. 

      Approaches zero.

    • C. 

      Increases slightly.

    • D. 

      Does not change.

  • 12. 
    An object moves in a direction parallel to its length with a velocity that approaches the velocity of light. The length of this object, as measured by a stationary observer,
    • A. 

      Approaches infinity.

    • B. 

      Approaches zero.

    • C. 

      Increases slightly.

    • D. 

      Does not change.

  • 13. 
    As the speed of a particle approaches the speed of light, the mass of the particle
    • A. 

      Increases.

    • B. 

      Decreases.

    • C. 

      Remains the same.

    • D. 

      Approaches zero.

  • 14. 
    As the speed of a particle approaches the speed of light, the momentum of the particle
    • A. 

      Increases.

    • B. 

      Decreases.

    • C. 

      Remains the same.

    • D. 

      Approaches zero.

  • 15. 
    A spear is thrown by you at a very high speed. As it passes, you measure its length at one-half its normal length. From this measurement, you conclude that the moving spear's mass must be
    • A. 

      One-half its rest mass.

    • B. 

      Twice its rest mass.

    • C. 

      Four times its rest mass.

    • D. 

      None of the given answers

  • 16. 
    What happens to the kinetic energy of a speedy proton when its relativistic mass doubles?
    • A. 

      It doubles.

    • B. 

      It more than doubles.

    • C. 

      It less than doubles.

    • D. 

      It must increase, but it is impossible to say by how much.

  • 17. 
    What happens to the total relativistic energy of a speedy proton when its relativistic mass doubles?
    • A. 

      It doubles.

    • B. 

      It more than doubles.

    • C. 

      It less than doubles.

    • D. 

      It must increase, but it is impossible to say by how much.

  • 18. 
    Consider two spaceships, each traveling at 0.50c in a straight line. Ship A is moving directly away from the Sun and ship B is approaching the Sun. The science officers on each ship measure the velocity of light coming from the Sun. What do they measure for this velocity?
    • A. 

      Ship A measures it as less than c, and ship B measures it as greater than c.

    • B. 

      Ship B measures it as less than c, and ship A measures it as greater than c.

    • C. 

      On both ships it is measured to be less than c.

    • D. 

      On both ships it is measured to be exactly c.

  • 19. 
    Which of the following depends on the observer's frame of reference?
    • A. 

      The mass of the proton

    • B. 

      The length of a meter stick

    • C. 

      The half-life of a muon

    • D. 

      All of the given answers

  • 20. 
    As the velocity of your spaceship increases, you would observe
    • A. 

      That your precision clock runs slower than normal.

    • B. 

      That the length of your spaceship has decreased.

    • C. 

      That your mass has increased.

    • D. 

      All of the given answers

    • E. 

      None of the given answers

  • 21. 
    A boat can travel 4.0 m/s in still water. With what speed, relative to the shore, does it move in a river that is flowing at 1.0 m/s if the boat is heading upstream?
    • A. 

      3.0 m/s

    • B. 

      4.1 m/s

    • C. 

      4.8 m/s

    • D. 

      5.0 m/s

  • 22. 
    A boat can travel 4.0 m/s in still water. With what speed, relative to the shore, does it move in a river that is flowing at 1.0 m/s if the boat is heading downstream?
    • A. 

      3.0 m/s

    • B. 

      4.1 m/s

    • C. 

      4.8 m/s

    • D. 

      5.0 m/s

  • 23. 
    A boat can travel 4.0 m/s in still water. With what speed, relative to the shore, does it move in a river that is flowing at 1.0 m/s if the boat is heading straight across the river?
    • A. 

      3.0 m/s

    • B. 

      4.1 m/s

    • C. 

      4.8 m/s

    • D. 

      5.0 m/s

  • 24. 
    How fast should a moving clock travel if it is to be observed by a stationary observer as running at one-half its normal rate?
    • A. 

      0.50c

    • B. 

      0.65c

    • C. 

      0.78c

    • D. 

      0.87c

  • 25. 
    A spaceship takes a nonstop journey to a planet and returns in 10 hours according to a clock on the spaceship. If the speed of the spaceship is 0.80c, how much time has elapsed on the Earth?
    • A. 

      3.2 h

    • B. 

      7.0 h

    • C. 

      15 h

    • D. 

      17 h

  • 26. 
    • A. 

      10 years

    • B. 

      12 years

    • C. 

      18 years

    • D. 

      20 years

  • 27. 
    One 20-year-old twin brother takes a space trip with a speed of 0.80c for 30 years according to a clock on the spaceship. Upon returning to the Earth, what is his own age and the age of the Earth-based twin brother?
    • A. 

      20; 30

    • B. 

      30; 50

    • C. 

      50; 70

    • D. 

      70; 90

  • 28. 
    A meter stick is moving toward you with a speed of 0.80c. What is its length?
    • A. 

      Zero

    • B. 

      0.40 m

    • C. 

      0.60 m

    • D. 

      1.0 m

  • 29. 
    How fast would a rocket ship have to move to contract to half of its proper length (as observed by a stationary object)?
    • A. 

      0.50c

    • B. 

      0.65c

    • C. 

      0.78c

    • D. 

      0.87c

  • 30. 
    The length of a spaceship is 10 m when it is at rest. If the spaceship travels by you with a speed of 0.70c, what length does it appear to you?
    • A. 

      5.5 m

    • B. 

      7.1 m

    • C. 

      12 m

    • D. 

      18 m

  • 31. 
    • A. 

      2.58 ly

    • B. 

      3.52 ly

    • C. 

      4.12 ly

    • D. 

      4.30 ly

  • 32. 
    The closest star to our solar system is Alpha Centauri, which is 4.30 light years away. A spaceship with a constant speed of 0.800c relative to the Earth travels toward the star. How much time would elapse on a clock on board the spaceship?
    • A. 

      3.23 y

    • B. 

      4.40 y

    • C. 

      5.15 y

    • D. 

      5.38 y

  • 33. 
    The closest star to our solar system is Alpha Centauri, which is 4.30 light years away. A spaceship with a constant speed of 0.800c relative to the Earth travels toward the star. How much time would elapse on a clock on the Earth?
    • A. 

      3.23 y

    • B. 

      4.40 y

    • C. 

      5.15 y

    • D. 

      5.38 y

  • 34. 
    An electron is traveling at 0.85c. What is its mass? (The rest mass is 9.11 * 10^(-31) kg.)
    • A. 

      1.4 * 10^(-29) kg

    • B. 

      7.2 * 10^(-30) kg

    • C. 

      1.7 * 10^(-30) kg

    • D. 

      2.4 * 10^(-30) kg

  • 35. 
    What is the speed of a proton if its mass is twice its rest mass?
    • A. 

      0.50c

    • B. 

      0.68c

    • C. 

      0.73c

    • D. 

      0.87c

  • 36. 
    If the velocity of your spaceship goes from 0.3 c to 0.6 c, then your mass will increase by
    • A. 

      19%.

    • B. 

      38%.

    • C. 

      100%.

    • D. 

      200%.

  • 37. 
    What is the momentum in kg*m/s of a proton when it is moving with a speed of 0.60c?
    • A. 

      1.2 * 10^(-19) kg*m/s

    • B. 

      1.5 * 10^(-19) kg*m/s

    • C. 

      3.0 * 10^(-19) kg*m/s

    • D. 

      3.8 * 10^(-19) kg*m/s

  • 38. 
    During a reaction, an element loses 4.8 * 10^(-28) kg of mass. How much energy (in Joules) is released?
    • A. 

      4.3 * 10^(-11) J

    • B. 

      1.4 * 10^(-19) J

    • C. 

      1.6 * 10^(-36) J

    • D. 

      5.3 * 10^(-45) J

  • 39. 
    During a reaction, 1.7 * 10^(-4) J of energy is released. What change of mass would cause this?
    • A. 

      5.1 * 10^(-4) kg

    • B. 

      1.5 * 10^(-13) kg

    • C. 

      4.8 * 10^(-18) kg

    • D. 

      1.9 * 10^(-21) kg

  • 40. 
    How much energy would be released if 2.0 kg of material was lost during a reaction?
    • A. 

      1.8 * 10^17 J

    • B. 

      1.5 * 10^16 J

    • C. 

      6.0 * 10^8 J

    • D. 

      4.7 * 10^(-8) J

  • 41. 
    The amount of energy equivalent to two kilogram of mass at rest is
    • A. 

      18 * 10^16 J.

    • B. 

      3.0 * 10^8 J.

    • C. 

      9.0 * 10^16 J.

    • D. 

      None of the given answers

  • 42. 
    The atomic bomb that was dropped on Nagasaki in 1945 killed 140,000 people, helping to end World War II on the next day. It released energy equivalent to that of 20,000 tons of TNT explosive. How much mass was converted to energy when this took place? (1000 tons of TNT = 4.3 * 10^12 J) Incidentally, modern H-bombs have energy yields 1000 times as much!
    • A. 

      1 g

    • B. 

      10 g

    • C. 

      100 g

    • D. 

      1 kg

  • 43. 
    The kinetic energy of a proton is 80% of its total energy. What is the speed of the proton?
    • A. 

      0.02c

    • B. 

      0.87c

    • C. 

      0.98c

    • D. 

      1.0c

  • 44. 
    The kinetic energy of a proton is 80% of its total energy. What is the momentum in kg*m/s of the proton?
    • A. 

      5.0 * 10^(-19) kg*m/s

    • B. 

      2.5 * 10^(-19) kg*m/s

    • C. 

      5.0 * 10^(-18) kg*m/s

    • D. 

      2.5 * 10^(-18) kg*m/s

  • 45. 
    What energy is released (in MeV) during a reaction in which 1.67 * 10^(-25) kg of material is converted to energy?
    • A. 

      5.0 * 10^(-14) MeV

    • B. 

      4.1 * 10^(-7) MeV

    • C. 

      3.1 * 10^(-4) MeV

    • D. 

      9.4 * 10^4 MeV

  • 46. 
    How much mass is lost during a reaction in which 1.7 * 10^8 MeV of energy is released?
    • A. 

      1.8 * 10^(-8) kg

    • B. 

      5.7 * 10^(-9) kg

    • C. 

      1.9 * 10^(-17) kg

    • D. 

      3.0 * 10^(-22) kg

  • 47. 
    What is the total energy of an electron moving with a speed of 0.95c?
    • A. 

      2.6 * 10^(-13) J

    • B. 

      8.2 * 10^(-14) J

    • C. 

      1.1 * 10^(-13) J

    • D. 

      1.2 * 10^(-14) J

  • 48. 
    How many joules of energy are required to accelerate one kilogram of mass from rest to a velocity of 0.866 c?
    • A. 

      1.8 * 10^17 J

    • B. 

      9.0 * 10^16 J

    • C. 

      3.0 * 10^3 J

    • D. 

      None of the given answers

  • 49. 
    In a nuclear plant, 10^17 J of energy is available from mass conversion. How much mass was lost?
    • A. 

      0.1 kg

    • B. 

      1 kg

    • C. 

      10 kg

    • D. 

      100 kg

  • 50. 
    An electron is accelerated through 100 kV. By what factor has its mass increased with respect to its rest mass?
    • A. 

      1.20

    • B. 

      1.55

    • C. 

      4.25

    • D. 

      8.00

  • 51. 
    You are in a rocket traveling away from the Sun at 0.95c. You measure the speed of light from the Sun to be
    • A. 

      0.05c.

    • B. 

      0.95c.

    • C. 

      1.0c.

    • D. 

      Cannot be determined without knowing the frequency of the light

  • 52. 
    Two spaceships are traveling through space at 0.60 c relative to the Earth. If the ships are headed directly toward each other, what is their approach velocity, as measured by a person on either craft?
    • A. 

      1.2c

    • B. 

      C

    • C. 

      0.60c

    • D. 

      None of the given answers

  • 53. 
    A fast spaceship is traveling with a speed of 0.80c. How fast would light travel from the headlights of the ship relative to a stationary observer?
    • A. 

      0.20c

    • B. 

      0.80c

    • C. 

      1.0c

    • D. 

      1.8c

  • 54. 
    A spaceship moves away from the Earth with a speed of 0.80c. The spaceship then fires a missile with a speed of 0.50c relative to the spaceship. What is the velocity of the missile measured by observers on the Earth if the missile is fired away from the Earth?
    • A. 

      0.30c

    • B. 

      0.50c

    • C. 

      0.93c

    • D. 

      1.3c

  • 55. 
    A spaceship moves away from the Earth with a speed of 0.80c. The spaceship then fires a missile with a speed of 0.50c relative to the spaceship. What is the velocity of the missile measured by observers on the Earth if the missile is fired toward the Earth?
    • A. 

      0.30c

    • B. 

      0.50c

    • C. 

      0.93c

    • D. 

      1.3c