Deck 26: Relativity

Question 1

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

Answer 1

100 ns

Question 2

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.

Answer 2

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

Question 3

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.

Answer 3

31 ns.

Question 4

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.

Question 5

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.

Question 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.

Question 7

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

Question 8

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

Question 9

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.

Question 10

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

Question 11

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

Question 12

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

Question 13

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.

Question 14

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.

Question 15

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

Question 16

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

Question 17

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.

Question 18

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.

Question 19

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.

Question 20

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.

Question 21

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

Question 22

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

Question 23

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.

Question 24

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

Question 25

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

Question 26

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

Question 27

What is the rest energy of a proton? (m_p = 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

Question 28

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

Question 29

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

Question 30

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

Question 31

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

Question 32

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.

Question 33

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

Question 34

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

Question 35

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

Question 36

If a proton has a kinetic energy of 1.000 GeV, what is its momentum? (m_p = 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

Question 37

What is the magnitude of the momentum of a proton moving at 0.95 c? (m_p = 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

Question 38

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.

Question 39

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.

Question 40

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

Question 41

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

A) 0.935 c
B) 0.875 c
C) 0.766 c
D) 0.586 c
E) 0.343 c

Question 42

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

Question 43

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

Question 44

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

Question 45

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

Question 46

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

Question 47

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

Question 48

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

Question 49

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

Question 50

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.

Question 51

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

Question 52

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

Question 53

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

Question 54

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

Question 55

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

Question 56

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

Question 57

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

Question 58

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.

Question 59

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

Question 60

What is the momentum of an electron moving at a speed of 0.90 c? (m_e = 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

Question 61

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

Question 62

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.

Question 63

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.

Question 64

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.

Question 65

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

Question 66

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

Question 67

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

Question 68

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

Question 69

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