Ch26 Exam Questions Relativity

Physics, 9e (Giambattista)

Chapter 26 Relativity

1) Which of the following is a postulate of special relativity?

A) E0 = mc2.

B) Energy is conserved.

C) Momentum is conserved.

D) The laws of physics are the same in all inertial reference frames.

2) An astronaut in a rocket moving with a speed v = 0.6c relative to Earth performs a collision experiment with two small steel balls and concludes the both momentum and energy are conserved. What would an Earth observer conclude?

A) Only momentum is conserved.

B) Only energy is conserved.

C) Neither energy nor momentum is conserved.

D) Both energy and momentum are conserved.

E) The collision never happened because the two balls are never in the same place at the same time.

3) The principle of relativity states that

A) momentum is conserved in all reference frames.

B) the Earth is a noninertial reference frame.

C) the speed of light in vacuum is constant.

D) the laws of physics are the same in all inertial reference frames.

E) Newton's second law does not hold at high speeds.

4) The conclusion of the Michelson-Morley experiments was that

A) interference of EM-waves does not happen.

B) the ether doesn't exist.

C) Galilean relativity holds.

D) light has momentum.

E) light has no momentum.

5) According to special relativity, what is the speed of light measured in a spaceship traveling at 0.40 c?

A) 0.60 c

B) 1.4 c

C) 0.86 c

D) 1.0 c

E) None of these choices are correct.

6) A conclusion from special relativity is that events that are simultaneous in one inertial frame

A) are simultaneous in all inertial reference frames.

B) are simultaneous in all inertial frames moving at the same speed.

C) may not be simultaneous in another inertial reference frame.

D) are simultaneous in inertial reference frames moving in the same direction.

E) are simultaneous in inertial reference frames moving in the opposite direction.

7) What is the Lorentz factor γ for a speed of 0.800 c?

A) 0.800

B) 1.67

C) 0.600

D) 0.360

E) 1.25

8) What are the minimum and maximum values for the Lorentz factor γ, respectively?

A) 0, 1

B) 1, no maximum

C) no minimum, 1

D) 1, 2

E) None of these choices are correct.

9) Which of the following is the best definition of inertial frame?

A) a frame of reference in which Newtonian mechanics holds true, but relativistic mechanics does not

B) a frame of reference in which relativistic mechanics holds true, but Newtonian mechanics does not

C) a frame of reference in which there are no accelerations without applied forces

D) a frame of reference in which Newton's second and third laws hold, but not the first

E) None of these choices are correct.

10) Which best describes the proper time interval between two events?

A) the longest interval measured by any inertial observer

B) the interval measured in the inertial reference frame in which the two events occur a maximum distance from each other

C) the interval measured in an inertial reference frame in which the two events are simultaneous

D) the interval measured in an inertial reference frame in which the two events occur at the same place

E) None of these choices are correct

11) At what speed would a clock be moving if time dilation caused it to run slow by 50%?

A) 0.500 c

B) 0.750 c

C) 0.250 c

D) 0.414 c

E) 0.866 c

12) A spaceship is observed from the Earth to be moving toward a star at a speed of 0.80 c. If the distance from the spaceship to the star is 1.6 ly as measured from Earth, how long does an observer on Earth find that it takes for the spaceship to reach the star?

A) 2.0 y

B) 2.1 y

C) 1.6 y

D) 1.2 y

E) 0.96 y

13) A spaceship is observed from the Earth to be moving toward a star at a speed of 0.80 c. If the distance from the spaceship to the star is 1.6 ly as measured from Earth, how much time passes on the spaceship while traveling to the star?

A) 3.3 y

B) 2.0 y

C) 1.3 y

D) 1.2 y

E) 0.96 y

14) Radioactive particles moving at 0.80 c are measured to have a half-life of 4.3 × 10-8 s. What is their half-life when at rest?

A) 7.2 × 10-8 s

B) 2.6 × 10-8 s

C) 3.4 × 10-8 s

D) 1.6 × 10-8 s

E) 1.7 × 10-7 s

15) The mean lifetime of muons is 2.2 μs. How fast are they moving if their measured mean lifetime is 1.1 μs?

A) 0.50 c

B) 0.87 c

C) 0.56 c

D) 0.94 c

E) This cannot happen.

16) Protons are sent at 0.900 c down a tube of length 27.0 m. How long does it take for the protons to travel this distance as measured in the lab?

A) 100 ns

B) 43.6 ns

C) 229 ns

D) 150 ns

E) 90.0 ns

17) A passenger is on a spaceship traveling at 0.8 c. The passenger observes that her watch

A) is running slow.

B) is running fast.

C) is keeping time as usual.

D) is running slow if the ship is traveling in the positive direction.

E) is running slow if the ship is traveling in the negative direction.

18) At what speed would an astronaut need to travel so that he would age 4.20 years while traveling a distance (as measured by an Earth observer) of 4.20 ly?

A) 1.00 c

B) This cannot be done.

C) 0.50 c

D) 0.707 c

E) 0.750 c

19) 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) Any of these choices could be correct depending on the relative velocity.

20) A pion has a mean lifetime of 25 ns in its own rest frame. A beam of pions traveling through the laboratory at a speed of 0.60 c is measured to have a mean lifetime of

A) 21 µs.

B) 20 ns.

C) 31 ns.

D) 31 µs.

21) The front of a spacecraft forms a point (like the tip of a cone) with an interior opening angle of 60°. As the spacecraft increases speed relative to Earth, what happens to this angle as observed in the Earth frame?

A) It stays the same.

B) It decreases.

C) It increases.

D) It decreases only if the spacecraft is going to the left.

E) It decreases only if the spacecraft is going to the right.

22) What speed is required for a length to contract to 80% of its proper length?

A) 0.80 c

B) 0.60 c

C) 0.40 c

D) 0.20 c

E) 0.50 c

23) If a spaceship of proper length 40 m is measured to have a length 30 m, how fast is it moving?

A) 0.50 c

B) 0.81 c

C) 0.75 c

D) 0.66 c

E) 0.43 c

24) A spaceship is observed from the Earth to be moving toward a star at a speed of 0.80 c. If the distance from the spaceship to the star is 1.6 ly as measured from Earth, how far is the star as measured from the moving spaceship?

A) 2.7 ly

B) 1.9 ly

C) 1.6 ly

D) 1.2 ly

E) 0.96 ly

25) A spaceship is 25 m wide and 100 m long. When traveling at 0.80 c (in a direction parallel to its length), what is its observed width?

A) 42 m

B) 25 m

C) 16 m

D) 15 m

E) 20 m

26) A spear is thrown at a very high speed. As it passes, you measure its length to be half its normal length. From this you conclude that the spear must be moving at

A) 1.00 c

B) 0.866 c

C) 0.707 c

D) 0.500 c

E) Not enough information

27) Two cars are traveling down the highway in the same direction. Car A is traveling at 30.0 m/s and car B is passing car A at a relative speed of 3.0 m/s. What is the speed of car B with respect to the highway?

A) 27.0 m/s

B) 30.0 m/s

C) 33.0 m/s

D) 32.9 m/s

E) 33.1 m/s

28) Two cars are traveling down the highway in the same direction. Car A is traveling at 30.0 m/s and car B is passing car A at a relative speed of 3.0 m/s. Using Galilean relativity to calculate the speed of car B relative to the highway results in an answer that is incorrect by how much?

A) 3.3 × 10-2 m/s

B) 3.3 × 10-5 m/s

C) 3.3 × 10-8 m/s

D) 3.3 × 10-11 m/s

E) 3.3 × 10-14 m/s

29) Spaceships A and B are moving in the same direction. Spaceship A is moving at 0.80 c relative to a stationary observer, and spaceship B is moving at 0.80 c relative to spaceship A. What does the stationary observer find for the speed of spaceship B?

A) 1.6 c

B) 1.3 c

C) 1.0 c

D) 0.78 c

E) 0.98 c

30) A spaceship is observed by a stationary observer to be moving at 0.600 c. A laser beam is directed straight ahead from the front of the spaceship. How fast does the laser beam travel relative to the stationary observer?

A) 4.00 c

B) 1.60 c

C) 1.00 c

D) 0.750 c

E) 0.480 c

31) In the lab, charged particles are directed toward one another, each at speed 0.500 c. What is the speed of the particles moving one way with respect to the particles moving the other way?

A) 1.25 c

B) 1.00 c

C) 0.800 c

D) 0.500 c

E) 0

32) Event 2 occurs a time Δt after event 1. If event 2 is caused by event 1, which of the following is true?

A) The distance between event 1 and event 2 can be anything.

B) The distance between event 1 and event 2 is not more than c Δt.

C) There are frames of reference in which event 2 occurs before event 1.

D) There are frames of reference in which event 1 and event 2 are simultaneous.

E) None of these choices are correct.

33) If two protons are heading toward one another at 0.800 c in the laboratory frame, what is the kinetic energy of one proton in the frame of reference of the other proton? The mass of a proton is 938 MeV/c2.

A) 3.13 GeV

B) 5.56 GeV

C) 1.56 GeV

D) 2.50 GeV

E) 3.34 GeV

34) In a colliding-beam experiment, protons moving at 0.800 c in opposite directions strike one another. What is the speed of the incoming proton as viewed by the proton about to be hit?

A) 1.60 c

B) 0.00

C) 0.640 c

D) 0.976 c

E) 0.960 c

35) What is the magnitude of the momentum of a proton moving at 0.95 c? (mp = 1.67 × 10-27 kg)

A) 5.0 × 10-18 kg·m/s

B) 4.8 × 10-18 kg·m/s

C) 1.5 × 10-18 kg·m/s

D) 9.5 × 10-18 kg·m/s

E) 4.4 × 10-18 kg·m/s

36) What is the rest energy of a proton? (mp = 1.67 × 10-27 kg)

A) 1.5 × 10-10 J

B) 5.0 × 10-13 J

C) 1.6 × 10-13 J

D) 1.6 × 10-19 J

E) 0.0

37) If a proton has a kinetic energy of 1.000 GeV, what is its momentum? (mp = 938.3 MeV/c2)

A) 1.938 GeV/c

B) 1.000 GeV/c

C) 938.0 GeV/c

D) 2.872 GeV/c

E) 1.696 GeV/c

38) What error is made calculating the momentum of a particle moving at 0.80 c using classical mechanics rather than relativistic mechanics?

A) less than 1%

B) the classical value is 67% too high

C) the classical value is 67% too low

D) the classical value is 40% too high

E) the classical value is 40% too low

39) If an object has its speed doubled, what happens to its relativistic momentum?

A) Nothing happens.

B) The momentum doubles.

C) The momentum halves.

D) The momentum more than doubles.

E) The momentum increases a little less than double.

40) If an object increases its speed such that its total energy is doubled, what happens to its relativistic momentum?

A) The momentum is doubled.

B) The momentum is more than doubled.

C) The momentum is less than doubled.

D) The momentum is quadrupled.

E) Nothing happens to the momentum.

41) What is the ratio of the relativistic momentum to the classical momentum?

A) γ

B) γ − 1

C) γ + 1

D) γ−1

E) (γ − 1)−1

42) At what speed is the relativistic momentum five times the value calculated classically?

A) 0.99 c

B) 0.98 c

C) 0.96 c

D) 0.80 c

E) 0.20 c

43) A megaton explosion releases 4.2 × 1015 J of energy. Approximately how much mass is converted into energy in this process?

A) None, if it is the result of a chemical reaction.

B) None, since mass is conserved.

C) 50 kg

D) 50 g

E) 109 kg

44) How much mass must be converted to energy to release one million kilowatt-hours?

A) 3.6 × 10-6 g

B) 40 μg

C) 4.0 g

D) 3.6 × 10-12 g

E) 40 pg

45) Which of the following is (or are) invariant?

A) mass

B) momentum

C) energy

D) the speed of light

E) mass and the speed of light

F) energy and momentum

G) All of these are invariant.

46) Tritium (3H) decays to 3He releasing 18.6 keV of energy. How much mass is converted into energy during this process?

A) 2.07 × 10-13 kg

B) 2.07 × 10-10 kg

C) 2.07 × 10-16 kg

D) 3.31 × 10-29 kg

E) 3.31 × 10-32 kg

47) A star like the Sun has a luminosity (energy emitted per unit time) of 3.8 × 1026 W. How much mass must be turned into energy each second to produce this power?

A) 1.3 × 1018 kg

B) 4.2 × 109 kg

C) 5.6 × 105 kg

D) 5.8 × 106 kg

E) 1.5 × 1011 kg

48) How much energy is released in a nuclear reactor if the total mass of the fuel decreases by 1.0 g?

A) 9.0 × 1013 J

B) 3.0 × 1011 J

C) 9.0 × 1014 J

D) 3.0 × 1014 J

49) The Sun radiates energy at a rate of 3.8 × 1026 W. Assuming that rate is constant, approximately how long does it take for the Sun to lose an amount of mass equal to the mass of the Earth (6.0 × 1024 kg)?

A) 63 seconds

B) 600 years

C) 4.5 × 107 years

D) 1.8 × 1011 years

E) 1.4 × 1015 years

50) What is the kinetic energy of a particle of mass m that has a total energy four times its rest energy?

A) 5 mc2

B) 4 mc2

C) 3 mc2

D) 2 mc2

E) 1 mc2

51) How fast is a particle moving if its kinetic energy is equal to its rest energy?

A) 0.00

B) 0.57 c

C) 0.75 c

D) 0.87 c

E) 0.50 c

52) In a radioactive decay, 2.37 × 10-3 u are converted into kinetic energy. How much kinetic energy is this? (1 u = 1.66 × 10-27 kg)

A) 2.13 × 1014 J

B) 9.31 × 108 J

C) 3.54 × 10-13 J

D) 3.93 × 10-30 J

E) 1.60 × 10-13 J

53) An electron has a rest energy of 0.511 MeV. At what speed would its kinetic energy equal 1.022 MeV?

A) 0.866 c

B) 0.943 c

C) 0.888 c

D) 0.971 c

E) 0.500 c

54) If a proton has a kinetic energy of 1.000 GeV, what is its speed? (mp = 938 MeV/c2)

A) 0.935 c

B) 0.875 c

C) 0.766 c

D) 0.586 c

E) 0.343 c

55) What is the momentum of an electron moving at a speed of 0.90 c? (me = 0.511 MeV/c2 = 9.11 × 10-31 kg)

A) 3.1 × 10-22 kg·m/s

B) 2.5 × 10-22 kg·m/s

C) 5.6 × 10-22 kg·m/s

D) 4.4 × 10-22 kg·m/s

E) 2.5 × 10-23 kg·m/s

56) If the momentum of an electron is 1.53 MeV/c, what is its kinetic energy? The rest energy of an electron is 511 keV.

A) 1.53 MeV

B) 1.02 MeV

C) 1.44 MeV

D) 1.10 MeV

E) 2.59 MeV

57) What is the kinetic energy of a proton moving at 0.800 c? The rest energy of a proton is 938 MeV.

A) 1560 MeV

B) 1250 MeV

C) 938 MeV

D) 2500 MeV

E) 625 MeV

58) An electron is accelerated from rest through a potential difference of 1.0 MV. If the rest energy of the electron is 0.511 MeV, how fast is the electron moving?

A) 0.57 c

B) 0.30 c

C) 0.67 c

D) 0.90 c

E) 0.94 c

59) How does the kinetic energy of a proton change when its total energy doubles?

A) It doubles.

B) It more than doubles.

C) It less than doubles.

D) It must increase but it is not possible to say how much.

60) Two observers will always agree on 

A) the speed of light.

B) the speed of sound.

C) the lengths of objects.

D) the lifetime of cosmic ray muons.

61) A pair of observers moving relative to one another will always agree upon all but which of the following?

A) the speed of light

B) their respective masses

C) whether two events are simultaneous

D) their relative velocity

E) the relativistic factor gamma that links their reference frames

62) A pair of observers moving relative to each other will

A) always agree on the ordering in time of two events

B) sometimes disagree about whether two events are simultaneous

C) always disagree about the ordering in time of two events

D) always agree about whether two events are simultaneous

63) How tall is Mount Everest from the perspective of a cosmic ray muon traveling straight down toward the Earth at 0.99c? Observers at rest relative to the ground measure the height of Mt. Everest to be 8848 m.

A) 885 m

B) 6.29 km

C) 1.25 km

D) 176 m

64) A rocket speeding by the Earth at 0.917c is roughly cylindrical in shape and oriented such that its axis is parallel to its velocity. At rest, it is measured to have a radius of 15 m and a length of 150 m. When speeding by, what is its volume as measured by observers on Earth?

A) 6.78 × 103 m3

B) 1.70 × 104 m3

C) 4.23 × 104 m3

D) 1.35 × 104 m3

E) 1.06 × 105 m3

65) A rocket speeding by the Earth is roughly cylindrical in shape and oriented such that its axis is parallel to its velocity. At rest, it is measured to have a radius of 15 m and a length of 150 m. When speeding by, its volume is measured to be 4.24 × 104 m3. What is its speed?

A) 0.917 c

B) 0.774 c

C) 0.678 c

D) Insufficient information is given.

66) The time of flight (TOF) technique is routinely used to distinguish between different particle species in a particle detector. Calculate the difference in time interval required for a proton (mass 938 MeV/c2) and a muon (mass 106 MeV/c2) to travel 2.5 m, assuming each particle has a momentum of 255 MeV/c.

A) 8.3 ns

B) 15 ns

C) 23 ns

D) 27 ns

67) If the velocity of a nonrelativistic object is doubled, its energy is quadrupled. This is only true for velocities that are very small compared with the speed of light. At what velocity would a doubling of velocity result in a doubling of energy?

A) 0.45c

B) 0.33c

C) 0.11c

D) 0.20c

E) 0.50c

68) Calculate the speed of a beam of neutrons with kinetic energies of 1.0 MeV. The mass of a neutron is 940 MeV/c2.

A) 799 m/s

B) 640 km/s

C) 9.8 × 106 m/s

D) 1.4 × 107 m/s

69) The expression used for momentum, p=mv,

A) is a good low-velocity approximation.

B) is a good high-velocity approximation.

C) is correct, provided we properly understand v.

D) always gives too high a value for p.

70) In relativistic mechanics, what law or principle does not apply?

A) principle of relativity

B) conservation of momentum

C) conservation of energy

D) Gauss's Law

E) All these choices still apply under relativistic conditions.