Deck 36: Special Theory of Relativity

Question 1

An observer sees two spaceships, S₁ and S₂, each having the same length in its own rest frame, traveling toward each other along parallel lines from opposite directions, with equal speeds relative to the observer. As seen by this observer, the two spaceships have the same length and, when they are next to each other, the nose of one coincides with the tail of the other, and vice-versa. However, as seen by passengers on either one of the spaceships, the other spaceship is shorter than their own, so if the tail of the other spaceship is in line with the nose of their spaceship, the nose of the other spaceship cannot be lined up with the tail of theirs. How can you explain this discrepancy?

Answer 1

Events that are simultaneous in one frame of reference are not simultaneous in a reference frame that is moving relative to the first. If we call the event A the coincidence of the nose of S₁ and the tail of S₂, and event B the coincidence of the nose of S₂ and the tail of S₁, then, according to the passengers in S₁, A occurs before B, while according to the passengers in S₂, B precedes A. Finally, the observer who saw them traveling towards each other sees the two events as simultaneous.

Question 2

State the second postulate of the special theory of relativity (constancy of the speed of light).

Answer 2

Light propagates through empty space with a definite speed c independent of the speed of the source or observer.

Question 3

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.
E)can do any of the above. It depends on the relative energy between the observer and the clock.

Answer 3

always runs slower than normal.

Question 4

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.

Question 5

Einstein's theory of general relativity applies to gravitation.

Question 6

Observers in different inertial frames can disagree about the location of an event.

Question 7

Which of the following is not an inertial reference frame?

A)a reference frame that is rotating at a constant rate
B)a reference frame that is moving downward at a constant speed
C)a reference frame that is moving westward at 10 km/s
D)a reference frame that is motionless
E)a reference frame that is moving upward at a constant speed

Question 8

Events that are simultaneous in one inertial reference frame are simultaneous in all inertial reference frames.

Question 9

State the three unprovable assumptions of Galilean-Newtonian relativity.

Question 10

The Michelson-Morley experiment was designed to measure

A)the relativistic mass of the electron.
B)the relativistic momentum of the electron.
C)the relativistic energy of the electron.
D)the velocity of the Earth relative to the ether.
E)the acceleration of gravity on the Earth's surface.

Question 11

State the first postulate of the special theory of relativity (relativity principle).

Question 12

In his theory of relativity, Einstein revealed that the behavior we experience at low speeds could not be assumed to hold for high speeds.

Question 13

According to Einstein's theory of general relativity, it is impossible to perform an experiment in a local environment that will enable us to decide whether we are accelerating or in a gravitational field.

Question 14

You are a passenger on a spaceship. As the speed of the spaceship increases, you would observe

A)your watch slowing down.
B)your watch speeding up.
C)your watch losing time.
D)your watch gaining time.
E)nothing unusual about your watch.

Question 15

Special relativity tells us that

A)the speed of light is variable.
B)light moves faster if emitted by a source moving in the direction of emission.
C)light moves faster if emitted by a source moving in the direction of emission and light moves slower if emitted by a source moving in the direction opposite the emission.
D)light moves slower if emitted by a source moving in the direction opposite the emission.
E)light moves at the same speed independent of the motion of the source.

Question 16

According to Einstein's theory of general relativity, a ray of light bends in a gravitational field.

Question 17

Observers in different inertial frames can disagree about the time separating two events.

Question 18

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

Question 19

Einstein's theory of general relativity applies to accelerated frames of reference.

Question 20

According to Einstein's theory of general relativity, a ray of light bends in an accelerated frame of reference.

Question 21

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.
E)approaches infinity.

Question 22

A spaceship carrying a light clock moves at a speed of 0.96 c relative to an observer on Earth. Relative to a frame of reference that is fixed with respect to the earth, how long does it take the clock to advance 1 s?

A)5.83 s
B)3.57 s
C)0.96 s
D)1.22 s
E)2.59 s

Question 23

A spaceship approaches the earth with a speed 0.50 c. A passenger in the spaceship measures his heartbeat as 70 beats per minute. What is his heartbeat rate according to an observer that is at rest relative to the earth?

A)69 beats per minute
B)73 beats per minute
C)65 beats per minute
D)61 beats per minute
E)80 beats per minute

Question 24

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)decreases slightly.
E)does not change.

Question 25

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)40; 60
D)50; 70
E)70; 90

Question 26

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)0.25c
B)0.50c
C)0.65c
D)0.78c
E)0.87c

Question 27

A set of twins, Andrea and Courtney, are initially 10 years old. While Courtney remains on Earth, Andrea rides on a space ship which travels away from Earth at a speed of 0.6c for five years (as measured by Courtney), then turns around and comes back at 0.6c. When Andrea returns, Courtney is 20 years old. How old is Andrea upon her return?

A)10 years
B)12 years
C)15 years
D)18 years
E)20 years

Question 28

An astronaut leaves Earth in a spaceship at a speed of 0.96 c relative to an observer on Earth. The astronaut's destination is a star system 14.4 light-years away (one light-year is the distance light travels in one year.) According to the astronaut, how long does the trip take?

A)14.4 years
B)22.7 years
C)9.34 years
D)15.0 years
E)4.20 years

Question 29

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.
(a) What is the velocity of the missile measured by observers on the Earth if the missile is fired away from the Earth?
(b) What is the velocity of the missile measured by observers on the Earth if the missile is fired toward the Earth?

Question 30

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

Question 31

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

Question 32

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)decreases slightly.
E)does not change.

Question 33

Relative to a stationary observer, a moving object

A)appears shorter than normal.
B)appears longer than normal.
C)keeps its same length.
D)can do any of the above. It depends on the relative velocity between the observer and the object.
E)can do any of the above. It depends on the relative energy between the observer and the object.

Question 34

The redshift due to the Doppler effect is caused by

A)sources of light moving toward the Solar System.
B)sources of light moving away from the Solar System.
C)sources of light obscured by interstellar dust.
D)sources of light moving at right angles to the Solar System.
E)an effect not yet believed to be understood.

Question 35

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.

Question 36

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.
E)approaches infinity.

Question 37

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
E)19 h

Question 38

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.
(a) How much time would elapse on a clock on board the spaceship?
(b) How much time would elapse on a clock on the Earth?

Question 39

You are a passenger on a spaceship. As the speed of the spaceship increases, you would observe

A)the length of your spaceship getting shorter.
B)the length of your spaceship getting longer.
C)the length of your spaceship varying erratically.
D)nothing unusual about the length of your spaceship.
E)cannot be determined from the given information

Question 40

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.

Question 41

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 × 10¹² J) Incidentally, modern H-bombs have energy yields 1000 times as much!

A)1 g
B)10 g
C)100 g
D)1 kg
E)10 kg

Question 42

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
E)4.2 × 10^-30 kg

Question 43

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

A)0.25c
B)0.50c
C)0.65c
D)0.78c
E)0.87c

Question 44

With respect to the earth, object 1 is moving at speed 0.90 c to the right. Object 2 is moving in the same direction at speed 0.70 c with respect to object 1. How fast is object 2 moving with respect to the earth?

A)0.64 c
B)1.6 c
C)0.16 c
D)0.80 c
E)0.98 c

Question 45

With respect to the earth, object 1 is moving at speed 0.90 c to the right. Object 2 is moving to the left at speed 0.70 c with respect to object 1. How fast is object 2 moving with respect to the earth?

A)0.12 c
B)-0.20 c
C)0.54 c
D)0.20 c
E)1.6 c

Question 46

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
E)1.5 × 10^-19 kg∙m/s

Question 47

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)4.3 × 10^-11 kg
C)1.5 × 10^-13 kg
D)4.8 × 10^-18 kg
E)1.9 × 10^-21 kg

Question 48

A beam of light is moving in the same direction as an object is traveling. If the object is moving at speed 0.70 c, how fast is the light moving as it passes the object?

A)c
B)1.35 c
C)1.40 c
D)0.3 c
E)1.70 c

Question 49

What is the speed of a proton if its mass is twice its rest mass?

A)0.25c
B)0.50c
C)0.68c
D)0.73c
E)0.87c

Question 50

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)1.3 × 10^-19 kg∙m/s
C)1.5 × 10^-19 kg∙m/s
D)3.0 × 10^-19 kg∙m/s
E)3.8 × 10^-19 kg∙m/s

Question 51

With respect to the earth, object 1 is moving at speed 0.80 c to the right. Object 2 is moving in the same direction at speed 0.80 c with respect to object 1. How fast is object 2 moving with respect to the earth?

A)0.64 c
B)0.98 c
C)0.16 c
D)1.6 c
E)0.80 c

Question 52

The amount of energy equivalent to two kilogram of mass at rest is

A)18 × 10¹⁶ J.
B)9.0 × 10¹⁶ J.
C)3.0 × 10⁸ J.
D)6.0 × 10⁸ J.
E)none of the given answers

Question 53

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)2.1 × 10^-40 J
E)5.3 × 10^-45 J

Question 54

At what speed, relative to the frame of the observer making the measurement, is the length of a meter stick 0.60 m?

A)0.80c
B)0.60c
C)0.50c
D)0.70c
E)0.90c

Question 55

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

A)1.8 × 10¹⁷ J
B)1.5 × 10¹⁶ J
C)2.4 × 10^-17 J
D)6.0 × 10⁸ J
E)4.7 × 10^-8 J

Question 56

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)0.92c.
D)0.98c
E)1.0c

Question 57

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)74%.
D)100%.
E)200%.

Question 58

The length of a spaceship is 14 m when it is at rest. If the spaceship travels by you with a speed of 0.80c, what length does it appear to you?

A)6.3 m
B)8.4 m
C)18 m
D)20 m
E)22 m

Question 59

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. What distance does the space ship travel according to a passenger on the ship?

A)2.58 ly
B)3.52 ly
C)4.12 ly
D)4.30 ly
E)6.16 ly

Question 60

A meter stick is moving toward you with a speed of 0.85c. What is its length?

A)zero
B)0.47 m
C)0.53 m
D)0.74 m
E)1.0 m

Question 61

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)0.50c.
C)0.95c.
D)1.0c.
E)cannot be determined without knowing the frequency of the light

Question 62

In a nuclear plant, 10¹⁷ 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
E)1000 kg

Question 63

How much mass is lost during a reaction in which 1.7 × 10⁸ 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
E)6.2 × 10^-28 kg

Question 64

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 × 10¹⁷ J
B)9.0 × 10¹⁶ J
C)4.5 × 109 J
D)3.0 × 10³ J
E)none of the given answers

Question 65

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)6.7 × 10⁷ MeV
D)3.1 × 10^-4 MeV
E)9.4 × 10⁴ MeV

Question 66

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)4.2c
B)1.2c
C)c
D)0.60c
E)none of the given answers

Question 67

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)1.2c
E)1.8c

Question 68

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)6.50
E)8.00

Question 69

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
E)2.2 × 10^-14 J