Question 1

Complete the following statement: The Michelson-Morley experiment

Accepted Answer

A) confirmed that time dilation occurs. 
B) proved that length contraction occurs. 
C) verified the conservation of momentum in inertial reference frames. 
D) supported the relationship between mass and energy. 
E) indicated that the speed of light is the same in all inertial reference frames. 
A) confirmed that time dilation occurs. 
B) proved that length contraction occurs. 
C) verified the conservation of momentum in inertial reference frames. 
D) supported the relationship between mass and energy. 
E) indicated that the speed of light is the same in all inertial reference frames.

Question 2

Spaceship A travels at 0.400c relative to an earth observer. According to the same observer, spaceship A overtakes a slower moving spaceship B that moves in the same direction. The captain of B sees A pass her ship at 0.114c. Determine the speed of B relative to the earth observer.

Accepted Answer

A) 0.100c 
B) 0.214c 
C) 0.300c 
D) 0.625c 
E) 0.700c 
A) 0.100c 
B) 0.214c 
C) 0.300c 
D) 0.625c 
E) 0.700c

Question 3

Which one of the following is a consequence of the postulates of special relativity?

Accepted Answer

A) There is no such thing as an inertial reference frame. 
B) Newton's laws of motion apply in every reference frame. 
C) Coulomb's law of electrostatics applies in any reference frame. 
D) The question of whether an object is at rest in the universe is meaningless. 
E) The value of every physical quantity depends on the reference frame in which it is measured. 
A) There is no such thing as an inertial reference frame. 
B) Newton's laws of motion apply in every reference frame. 
C) Coulomb's law of electrostatics applies in any reference frame. 
D) The question of whether an object is at rest in the universe is meaningless. 
E) The value of every physical quantity depends on the reference frame in which it is measured.

Question 4

Astronomers on Earth, an inertial reference frame, observe galaxies A and B that are moving away from the Earth as shown. The speeds indicated are those measured by the astronomers on Earth. What is the speed of galaxy B as measured by an observer in galaxy A?

Accepted Answer

A) 0.22c 
B) 0.60c 
C) 0.71c 
D) 0.95c 
E) 1.42c 
A) 0.22c 
B) 0.60c 
C) 0.71c 
D) 0.95c 
E) 1.42c

Question 5

A subatomic particle X spontaneously decays into two particles, A and B, each of rest energy 1.40 × 10S1U1P12S1S1P0 MeV. The particles fly off in opposite directions, each with speed 0.827c relative to an inertial reference frame S.
-Use energy conservation to determine the rest energy of particle X.

Accepted Answer

A) 206 MeV 
B) 249 MeV 
C) 280 MeV 
D) 392 MeV 
E) 498 MeV 
A) 206 MeV 
B) 249 MeV 
C) 280 MeV 
D) 392 MeV 
E) 498 MeV

Question 6

A spaceship traveling at 0.7370c relative to the Earth monitors a motorcycle drag race on Earth. The space travelers measure the time from the start to the finish of the race to be 15.25 s. What is the proper time interval for the motorcycle race?

Accepted Answer

A) 7.012 s 
B) 8.577 s 
C) 10.31 s 
D) 12.53 s 
E) 15.02 s 
A) 7.012 s 
B) 8.577 s 
C) 10.31 s 
D) 12.53 s 
E) 15.02 s

Question 7

A subatomic particle X spontaneously decays into two particles, A and B, each of rest energy 1.40 × 10S1U1P12S1S1P0 MeV. The particles fly off in opposite directions, each with speed 0.827c relative to an inertial reference frame S.
-Determine the total energy of particle A.

Accepted Answer

A) 109 MeV 
B) 140 MeV 
C) 200 MeV 
D) 249 MeV 
E) 314 MeV 
A) 109 MeV 
B) 140 MeV 
C) 200 MeV 
D) 249 MeV 
E) 314 MeV

Question 8

How much energy would be released if 1.0 g of material were completely converted into energy?

Accepted Answer

A) 9 × 108 J 
B) 9 × 109 J 
C) 9 × 1011 J 
D) 9 × 1013 J 
E) 9 × 1016 J 
A) 9 × 108 J 
B) 9 × 109 J 
C) 9 × 1011 J 
D) 9 × 1013 J 
E) 9 × 1016 J

Question 9

The proper mean lifetime of a muon is 2.2 × 10-6 s. A beam of muons is moving with speed 0.6c relative to an inertial observer. Approximately how far will a muon in the beam travel, on average, before it decays?

Accepted Answer

A) 288 m 
B) 360 m 
C) 500 m 
D) 600 m 
E) 800 m 
A) 288 m 
B) 360 m 
C) 500 m 
D) 600 m 
E) 800 m

Question 10

The figure shows a side view of a galaxy that is 50.0 light years in diameter. This value for the diameter is its proper length. A spaceship enters the galactic plane with speed 0.995c relative to the galaxy. Assume that the galaxy can be treated as an inertial reference frame. Note: A light year is the distance that light travels through vacuum in one year; that is, 1 light year = c × (1 year).  
-How long does it take the spaceship to cross the galaxy according to an observer at rest in the galaxy?

Accepted Answer

A) 5.00 years 
B) 12.5 years 
C) 49.8 years 
D) 50.3 years 
E) 90.0 years 
A) 5.00 years 
B) 12.5 years 
C) 49.8 years 
D) 50.3 years 
E) 90.0 years

Question 11

The power capacity of all nuclear power plants in the United States is 1.01 × 105 MW. In one hour, what is the total change in the mass of the nuclear fuel at these power plants due to the energy being taken from the reactors? Assume 100% efficiency.

Accepted Answer

A) 1.12 × 10-6 kg 
B) 7.59 × 10-5 kg 
C) 5.11 × 10-4 kg 
D) 4.04 × 10-3 kg 
E) 3.62 kg 
A) 1.12 × 10-6 kg 
B) 7.59 × 10-5 kg 
C) 5.11 × 10-4 kg 
D) 4.04 × 10-3 kg 
E) 3.62 kg

Question 12

Two spaceships are observed from earth to be approaching each other along a straight line. Ship A moves at 0.40c relative to the earth observer, while ship B moves at 0.60c relative to the same observer. What speed does the captain of ship A report for the speed of ship B?

Accepted Answer

A) 0.19c 
B) 0.75c 
C) 0.81c 
D) 0.92c 
E) 0.96c 
A) 0.19c 
B) 0.75c 
C) 0.81c 
D) 0.92c 
E) 0.96c

Question 13

Calculate the ratio of the relativistic kinetic energy to the classical kinetic energy, KErel/KEclass, for an electron (mass = 9.109 × 10-31 kg) moving with a constant speed of 0.75c.

Accepted Answer

A) 1.8 
B) 1.6 
C) 1.4 
D) 0.74 
E) 0.56 
A) 1.8 
B) 1.6 
C) 1.4 
D) 0.74 
E) 0.56

Question 14

A muon has rest energy 105 MeV. What is a muon's kinetic energy when its speed is 0.95c?

Accepted Answer

A) 37 MeV 
B) 47 MeV 
C) 231 MeV 
D) 441 MeV 
E) 741 MeV 
A) 37 MeV 
B) 47 MeV 
C) 231 MeV 
D) 441 MeV 
E) 741 MeV

Question 15

Complete the following statement: The results of special relativity indicate that

Accepted Answer

A) Newtonian mechanics is a valid approximation at low speeds (v << c). 
B) the laws of electromagnetism are invalid at speeds that are comparable to that of light. 
C) Newtonian mechanics is an incorrect theory. 
D) moving clocks run fast compared to when they are at rest. 
E) moving objects appear to be longer than when they are at rest. 
A) Newtonian mechanics is a valid approximation at low speeds (v << c). 
B) the laws of electromagnetism are invalid at speeds that are comparable to that of light. 
C) Newtonian mechanics is an incorrect theory. 
D) moving clocks run fast compared to when they are at rest. 
E) moving objects appear to be longer than when they are at rest.

Question 16

A proton has a mass of 1.673 × 10-27 kg. If the proton is accelerated to a speed of 0.96c, what is the magnitude of the relativistic momentum of the proton?

Accepted Answer

A) 6.2 × 10-17 kg . m/s 
B) 1.4 × 10-19 kg . m/s 
C) 4.7 × 10-19 kg . m/s 
D) 5.9 × 10-24 kg . m/s 
E) 1.8 × 10-18 kg . m/s 
A) 6.2 × 10-17 kg . m/s 
B) 1.4 × 10-19 kg . m/s 
C) 4.7 × 10-19 kg . m/s 
D) 5.9 × 10-24 kg . m/s 
E) 1.8 × 10-18 kg . m/s

Question 17

Which one of the following statements concerning the proper length of a meter stick is true?

Accepted Answer

A) The proper length is always one meter. 
B) The proper length depends upon the speed of the observer. 
C) The proper length depends upon the acceleration of the observer. 
D) The proper length depends upon the reference frame in which it is measured. 
E) The proper length is the length measured by an observer who is moving with respect to the meter stick. 
A) The proper length is always one meter. 
B) The proper length depends upon the speed of the observer. 
C) The proper length depends upon the acceleration of the observer. 
D) The proper length depends upon the reference frame in which it is measured. 
E) The proper length is the length measured by an observer who is moving with respect to the meter stick.

Question 18

Which one of the following statements concerning time dilation is true?

Accepted Answer

A) Time dilation is predicted by special relativity, but has never been observed. 
B) Time dilation has been observed only in experiments involving radioactive decay processes. 
C) Time dilation has been observed in experiments involving both atomic clocks and radioactive decay processes. 
D) Time dilation was demonstrated by the Michelson-Morley experiment. 
E) Time dilation has been disproved in experiments with atomic clocks. 
A) Time dilation is predicted by special relativity, but has never been observed. 
B) Time dilation has been observed only in experiments involving radioactive decay processes. 
C) Time dilation has been observed in experiments involving both atomic clocks and radioactive decay processes. 
D) Time dilation was demonstrated by the Michelson-Morley experiment. 
E) Time dilation has been disproved in experiments with atomic clocks.

Question 19

The starship Enterprise approaches the Klingon home world with speed 0.6c relative to the planet. To announce its arrival, the Enterprise sends a message in a projectile that travels toward the planet with speed 0.4c relative to the Enterprise. At what speed does a Klingon at the surface of the planet see the projectile approach?

Accepted Answer

A) 0.2c 
B) 0.4c 
C) 0.5c 
D) 0.6c 
E) 0.8c 
A) 0.2c 
B) 0.4c 
C) 0.5c 
D) 0.6c 
E) 0.8c

Question 20

An earth observer sees an alien ship pass overhead at 0.3c. The ion gun of the alien ship shoots ions straight ahead of the ship at a speed 0.4c relative to the ship. What is the speed of the ions relative to the earth observer?

Accepted Answer

A) 0.40c 
B) 0.63c 
C) 0.70c 
D) 0.79c 
E) 0.99c 
A) 0.40c 
B) 0.63c 
C) 0.70c 
D) 0.79c 
E) 0.99c

Exam 28: Special Relativity

Complete the following statement: The Michelson-Morley experiment

Spaceship A travels at 0.400c relative to an earth observer. According to the same observer, spaceship A overtakes a slower moving spaceship B that moves in the same direction. The captain of B sees A pass her ship at 0.114c. Determine the speed of B relative to the earth observer.

Which one of the following is a consequence of the postulates of special relativity?

Astronomers on Earth, an inertial reference frame, observe galaxies A and B that are moving away from the Earth as shown. The speeds indicated are those measured by the astronomers on Earth. What is the speed of galaxy B as measured by an observer in galaxy A?

A subatomic particle X spontaneously decays into two particles, A and B, each of rest energy 1.40 × 102 MeV. The particles fly off in opposite directions, each with speed 0.827c relative to an inertial reference frame S. -Use energy conservation to determine the rest energy of particle X.

A spaceship traveling at 0.7370c relative to the Earth monitors a motorcycle drag race on Earth. The space travelers measure the time from the start to the finish of the race to be 15.25 s. What is the proper time interval for the motorcycle race?

A subatomic particle X spontaneously decays into two particles, A and B, each of rest energy 1.40 × 102 MeV. The particles fly off in opposite directions, each with speed 0.827c relative to an inertial reference frame S. -Determine the total energy of particle A.

How much energy would be released if 1.0 g of material were completely converted into energy?

The proper mean lifetime of a muon is 2.2 × 10-6 s. A beam of muons is moving with speed 0.6c relative to an inertial observer. Approximately how far will a muon in the beam travel, on average, before it decays?

The power capacity of all nuclear power plants in the United States is 1.01 × 105 MW. In one hour, what is the total change in the mass of the nuclear fuel at these power plants due to the energy being taken from the reactors? Assume 100% efficiency.

Two spaceships are observed from earth to be approaching each other along a straight line. Ship A moves at 0.40c relative to the earth observer, while ship B moves at 0.60c relative to the same observer. What speed does the captain of ship A report for the speed of ship B?

Calculate the ratio of the relativistic kinetic energy to the classical kinetic energy, KErel/KEclass, for an electron (mass = 9.109 × 10-31 kg) moving with a constant speed of 0.75c.

A muon has rest energy 105 MeV. What is a muon's kinetic energy when its speed is 0.95c?

Complete the following statement: The results of special relativity indicate that

A proton has a mass of 1.673 × 10-27 kg. If the proton is accelerated to a speed of 0.96c, what is the magnitude of the relativistic momentum of the proton?

Which one of the following statements concerning the proper length of a meter stick is true?

Which one of the following statements concerning time dilation is true?

An earth observer sees an alien ship pass overhead at 0.3c. The ion gun of the alien ship shoots ions straight ahead of the ship at a speed 0.4c relative to the ship. What is the speed of the ions relative to the earth observer?

Introduction and Mathematical Concepts

Kinematics in One Dimension

Kinematics in Two Dimensions

Forces and Newtons Laws of Motion

Dynamics of Uniform Circular Motion

Work and Energy

Impulse and Momentum

Rotational Kinematics

Rotational Dynamics

Simple Harmonic Motion and Elasticity

Fluids

Temperature and Heat

The Transfer of Heat

The Ideal Gas Law and Kinetic Theory

Thermodynamics

Waves and Sound

The Principle of Linear Superposition and Interference Phenomena

Electric Forces and Electric Fields

Electric Potential Energy and the Electric Potential

Electric Circuits

Magnetic Forces and Magnetic Fields

Electromagnetic Induction

Alternating Current Circuits

Electromagnetic Waves

The Refl Ection of Light: Mirrors

The Refraction of Light: Lenses and Optical Instruments

Interference and the Wave Nature of Light

Particles and Waves

The Nature of the Atom

Nuclear Physics and Radioactivity

Ionizing Radiation, Nuclear Energy, and Elementary Particles

Filters

A subatomic particle X spontaneously decays into two particles, A and B, each of rest energy 1.40 × 10² MeV. The particles fly off in opposite directions, each with speed 0.827c relative to an inertial reference frame S. -Use energy conservation to determine the rest energy of particle X.

A subatomic particle X spontaneously decays into two particles, A and B, each of rest energy 1.40 × 10² MeV. The particles fly off in opposite directions, each with speed 0.827c relative to an inertial reference frame S. -Determine the total energy of particle A.

The proper mean lifetime of a muon is 2.2 × 10^-⁶ s. A beam of muons is moving with speed 0.6c relative to an inertial observer. Approximately how far will a muon in the beam travel, on average, before it decays?

The power capacity of all nuclear power plants in the United States is 1.01 × 10⁵ MW. In one hour, what is the total change in the mass of the nuclear fuel at these power plants due to the energy being taken from the reactors? Assume 100% efficiency.

Calculate the ratio of the relativistic kinetic energy to the classical kinetic energy, KE_rel/KE_class, for an electron (mass = 9.109 × 10^-³¹ kg) moving with a constant speed of 0.75c.

A proton has a mass of 1.673 × 10^-²⁷ kg. If the proton is accelerated to a speed of 0.96c, what is the magnitude of the relativistic momentum of the proton?