Deck 29: Relativity

Question 1

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.

Answer 1

True

Question 2

Relativistic time dilation does apply to biological processes.

Answer 2

True

Question 3

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

Answer 3

True

Question 4

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?

Question 5

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 6

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

Question 7

What is meant by proper time?

Question 8

When a spring is compressed, its mass increases.

Question 9

When a spring is stretched, its mass decreases.

Question 10

What is meant by proper length?

Question 11

State the Equivalence of Physical Laws postulate of special relativity.

Question 12

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

Question 13

Einstein's theory of general relativity applies to gravitation.

Question 14

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

Question 15

A black hole is a star whose gravitational field is so strong that light cannot escape from it.

Question 16

State the Constancy fo the Speed of Light postulate of special relativity.

Question 17

In order to see a distant star during a total eclipse of the Sun you must look for it in a direction that is farther from the Sun than the direction you would normally look for the star.

Question 18

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

Question 19

A spaceship traveling at constant speed away from the Sun crosses the orbit of Earth and later crosses the orbit of Mars. What is the distance between these two events in the spaceship frame of reference?
The radius of Earth's orbit is 150 × 10⁹ m and that of Mars is 228 × 10⁹ m.

Question 20

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

Question 21

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?

Question 22

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 23

The principle of equivalence states that

A) the laws of physics are the same in all inertial frames of reference.
B) the speed of light is the same in any frame of reference.
C) clocks that move relative to one another keep time at different rates.
D) the length of an object depends on its speed relative to a given observer.
E) all physical experiments conducted in a uniform gravitational field and in an accelerated frame of reference give identical results.

Question 24

Which of the following results shows the validity of the relativistic effect of time dilation?

A) the detection of gravity waves
B) bending of light near the Sun
C) the decay of muons
D) red shift in distant galaxies
E) blue shift in distant galaxies

Question 25

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 26

A 30-year-old astronaut goes off on a long term mission in a spacecraft that travels at speeds close to that of light. The mission lasts exactly 20 years as measured on Earth. Biologically speaking, the astronaut's age would be

A) more than 50 years.
B) exactly 50 years.
C) less than 50 years.
D) exactly 30 years.
E) exactly 25 years.

Question 27

Observer A sees a pendulum oscillating back and forth in a relativistic train and measures its period to be T_A. Observer B moves together with the train and measures the period of the pendulum to be T_B. These two results will be such that

A) T_A > T_B.
B) T_A = T_B.
C) T_A < T_B.
D) T_A could be greater or smaller than T_B depending on the direction of the motion.

Question 28

As the velocity of an inertial frame of reference increases with respect to a stationary observer, Einstein's theory of special relativity predicts that the length of an object, measured in the dimension parallel to the motion of the reference frame, will

A) decrease.
B) remain unchanged.
C) increase.
D) increase at first but start to decrease when the speed of the reference frame equals half the speed of light.
E) decrease at first but start to increase when the speed of the reference frame equals half the speed of light.

Question 29

A spaceship visits Alpha Centauri and returns to Earth. Alpha Centauri is 4.5 light-years from Earth (our second closest star). The spaceship travels at one-half the speed of light for essentially all of its expedition.
(a) How long was the ship gone according to an observer on the Earth?
(b) How long was the ship gone according to an observer on the spaceship?

Question 30

Observer A sees a ruler moving by in a relativistic train and measures its length to be L_A. Observer B moves together with the train and measures the length of the ruler to be L_B. These two results will be such that

A) L_A > L_B.
B) L_A = L_B.
C) L_A < L_B.
D) L_A could be greater or smaller than L_B depending on the direction of the motion.

Question 31

The special theory of relativity sets a limit on speed. Does it set a limit on momentum?

A) Yes
B) No

Question 32

A spaceship traveling at constant speed passes by Earth and later passes by Mars. In which frame of reference is the amount of time separating these two events the proper time?

A) the Earth frame of reference
B) the Mars frame of reference
C) the spaceship frame of reference
D) any inertial frame of reference
E) any frame of reference, inertial or not

Question 33

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

A) your mass increasing.
B) your mass decreasing.
C) your mass varying erratically.
D) nothing unusual about your mass.

Question 34

FIGURE 29-1
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 35

FIGURE 29-1
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 36

The special theory of relativity sets a limit on speed. Does it set a limit on energy?

A) Yes
B) No

Question 37

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.

Question 38

A moving object's mass is twice its rest mass. Its length (in the direction of travel) must therefore be

A) one-half its proper length.
B) twice its proper length.
C) one-fourth its proper length.
D) four times its proper length.
E) times its proper length.

Question 39

FIGURE 29-1
An astronaut is resting on a bed inclined at an angle above the floor of a spaceship, as shown in Figure 29-1. From the point of view of an observer who sees the spaceship moving to the right with a speed approaching c, the angle the bed makes with the floor

A) is greater than the angle observed by the astronaut.
B) is the same as the angle observed by the astronaut.
C) is smaller than the angle observed by the astronaut.
D) could be greater or smaller than the angle observed by the astronaut depending on the actual speed of the craft.

Question 40

When a current flows through an inductor, its mass

A) decreases.
B) increases.
C) stays the same.
D) oscillates.

Question 41

You are moving at a speed (2/3)c relative to Randy, and Randy shines a light toward you. At what speed do you see the light passing you by?

A) (1/3)c
B) (2/3)c
C) (4/3)c
D) c
E) It depends on whether you are moving towards or away from Randy.

Question 42

A muon at rest decays in 2.2 μs. Moving at 99.% the speed of light, it would be seen to "live" for how long?

Question 43

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 ⇔ 4.3 × 10¹² J) (Incidentally, modern H-bombs have energy yields 1000 times as much!)

Question 44

An alpha particle (6.70 × 10^-27 kg, 3.2 × 10^-19 Coulomb) travels at 0.965c. What is its:
(a) rest energy (in eV)?
(b) total energy (in eV)?
(c) kinetic energy (in eV)?

Question 45

A starship is built to plans that state it is to be constructed 100. meters long. It is launched and as it coasts by the Earth, it is seen to be shortened to 5.48 meters long.
(a) How fast is it moving?
(b) The ship's crew measure the length of the ship to be how long?

Question 46

Two spaceships approach each other along a straight line at a constant velocity of 0.988c as measured by the captain of one of the ships. An observer on Earth is able to measure the speed of only one of the ships as 0.900c. From the point of view of the observer on Earth, what is the speed of the other ship?

Question 47

Two spaceships are traveling through space at velocities of 0.600c and 0.900c, respectively, with respect to Earth. If they are headed directly toward each other, what is their approach velocity, as measured by the captain of either ship?

Question 48

A stretch of land is 12.5 km long on a map.
(a) What would be its length to an observer moving by, parallel to the stretch, at 0.95c?
(b) Which length is the proper length?
(c) How fast must the observer move for the land to appear 6.50 km long?

Question 49

Consider a student whose mass is 70. kg (he weighs 154. lb). If all his mass were converted to energy, this energy could light a 100. watt lamp for how long?

Question 50

You are moving past the Earth at 0.99c and notice your heart beating 88. times/minute.
(a) Your doctor on Earth observes your heart rate to be what?
(b) If you had been moving 99.99% the speed of light, you would have observed your heart to be beating how fast?

Question 51

How fast must something be traveling if its mass increases by 10%?

Question 52

From the Earth, they see the Enterprise approaching at 0.800c and the Klingons approaching from the opposite direction at 0.900c. From the Enterprise, the crew sees the Klingon ship approaching at what speed?

Question 53

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

Question 54

An electron-volt is the energy required to move an electron through a potential difference of one volt. Because of the connection between mass and energy, an electron-volt can also be regarded as a unit of mass. What is the equivalent to an electron-volt in kilograms?
The charge on an electron is 1.602 × 10^-19 C.

Question 55

An electron has a relativistic momentum of 1.1 × 10^-21 kg-m/s. What fraction of its total energy is its kinetic energy?

Question 56

An electron slowing from 0.998c to 0.500c loses how much momentum?
Express the answer in MeV/c as well as N-s.

Question 57

A spaceship carrying a light clock moves at a speed of 0.960c relative to an observer on Earth. Relative to a frame of reference that is fixed with respect to Earth, how long does it take the clock on the ship to advance 1.00 s?

A) 0.960 s
B) 1.22 s
C) 2.59 s
D) 3.57 s
E) 5.83 s

Question 58

Aliens on Krypton build a spacecraft 472. teef long. In their units the speed of light is 22.2 million teef/ces. How fast (teef/ces) must it travel to appear to be 66.6 teefs long?

Question 59

A person in a rocket ship traveling past the earth at a speed of 0.500c fires a laser gun in the forward direction. With what speed does an observer on Earth see the light pulse travel?

Question 60

Astronaut Rob leaves Earth in a spaceship at a speed of 0.960c relative to an observer on Earth. Rob's destination is a star system 14.4 light-years away (one light-year is the distance light travels in one year). Relative to a frame of reference that is fixed with respect to Earth, how long does it take Rob to complete the trip?

A) 14.4 years
B) 15.0 years
C) 10.8 years
D) 4.20 years
E) 22.7 years

Question 61

A spaceship enters the solar system moving toward the Sun at a constant speed relative to the Sun. By its own clock, the time elapsed between the time it crosses the orbit of Jupiter and the time it crosses the orbit of Mars is 50.0 minutes. As measured in the coordinate system of the Sun, how long did it take for the spaceship to travel that distance? The radius of the orbit of Jupiter is 778 × 10⁹ m, and that of the orbit of Mars is 228 × 10⁹ m.

A) 30.0 minutes
B) 43.6 minutes
C) 58.6 minutes
D) 69.8 minutes
E) 95.8 minutes

Question 62

Two spaceships, each 100 m long in its own rest frame, approach Earth from opposite directions, each with a speed 0.50c relative to Earth. As measured by a passenger in one of the spaceships, how long is the other spaceship?

A) 50 m
B) 60 m
C) 70 m
D) 80 m
E) 90 m

Question 63

A muon is an unstable particle that has an average lifetime of 1.52 × 10^-6 s. This is the time interval between its creation in a nuclear process and its extinction into decay products, as measured in a frame of reference at rest with respect to the muon. An "average" muon is observed by a scientist on Earth to travel 342 m in its lifetime. What is the speed of the muon relative to Earth?

A) 0.821c
B) 0.681c
C) 0.601c
D) 0.551c
E) 0.335c

Question 64

How fast would you have to travel in order to reach a star that is 50 light-years away from Earth when you are 40 years older than you were when you left Earth? One light-year is the distance light travels in one year.

A) 0.58c
B) 0.68c
C) 0.78c
D) 0.88c
E) 0.96c

Question 65

A spaceship approaches Earth with a speed 0.38c. A passenger in the spaceship measures his heartbeat as 72 beats per minute. How many beats per minute are observed in the telemetry radio signals received on Earth? Note that, in addition to time dilation, one must take into account that the signals of successive heartbeats have to travel shorter distances because the spaceship is moving closer (Doppler Effect).

A) 75
B) 107
C) 48
D) 100
E) 67

Question 66

A spaceship, traveling at 0.560c towards a stationary enemy station, shoots a projectile towards the station with a speed of 0.100c relative to the spaceship. What is the speed of the projectile relative to the station?

A) 0.460c
B) 0.575c
C) 0.600c
D) 0.625c
E) 0.660c

Question 67

Astronaut Brian leaves Earth in a spaceship at a speed of 0.280c relative to an observer on Earth. Brian is holding a pencil at an angle of 30.0° with the direction of travel, as seen by Brian. What angle does the pencil make with the direction of travel, as seen in the frame of reference of the observer?

A) 29.0°
B) 30.0°
C) 31.0°
D) 32.0°
E) 33.0°

Question 68

A pion is an unstable particle that has an average lifetime of 2.55 × 10^-8 s. This is the time interval between its creation in a nuclear process and its extinction into decay products, as measured in a frame of reference at rest with respect to the pion. An "average" pion is traveling at 0.230c relative to Earth. How far does it travel in its lifetime, relative to Earth?

A) 2.07 m
B) 1.81 m
C) 2.23 m
D) 3.22 m
E) 3.50 m

Question 69

Two spaceships approach Earth from the same direction. One has a speed of 0.21c and the other a speed of 0.34c, both relative to Earth. What is the speed of one spaceship relative to the other?

A) 0.13c
B) 0.14c
C) 0.15c
D) 0.16c
E) 0.18c

Question 70

A spaceship enters the solar system moving toward the Sun at a constant speed relative to the Sun. By its own clock, the time elapsed between the time it crosses the orbit of Jupiter and the time it crosses the orbit of Mars is 50.0 minutes. How fast is the spaceship traveling towards the Sun? The radius of the orbit of Jupiter is 778 × 10⁹ m, and that of the orbit of Mars is 228 × 10⁹ m.

A) 0.319c
B) 0.438c
C) 0.522c
D) 0.671c
E) 0.982c

Question 71

A spaceship is going away from Earth with a speed 0.28c. A passenger in the spaceship measures his heartbeat as 72 beats per minute. How many beats per minute are observed in the telemetry radio signals received on Earth? Note that, in addition to time dilation, one must take into account that the signals of successive heartbeats have to travel longer distances because the spaceship is moving away (Doppler Effect).

A) 75
B) 96
C) 54
D) 69
E) 100

Question 72

Astronaut Sarah leaves Earth in a spaceship at a speed of 0.280c relative to Earth. Sarah's destination is a star system 12.5 light-years away (one light-year is the distance light travels in one year). According to Sarah, how far did she travel during the trip?

A) 13.0 light-years
B) 12.5 light-years
C) 12.0 light-years
D) 11.5 light-years
E) 11.0 light-years

Question 73

Two spaceships approach Earth from opposite directions. One has a speed of 0.21c and the other a speed of 0.34c, both relative to Earth. What is the speed of one spaceship relative to the other?

A) 0.51c
B) 0.55c
C) 0.58c
D) 0.61c
E) 0.64c

Question 74

Astronaut Jill leaves Earth in a spaceship and is now traveling at a speed of 0.280c relative to an observer on Earth. When Jill left Earth, the spaceship was equipped with all kinds of scientific instruments, including a meter stick. Now that Jill is underway, how long does she measure the meter stick to be?

A) 1.00 m
B) 0.960 m
C) 1.04 m
D) 0.280 m
E) 1.28 m

Question 75

Hydrogen emits light at certain discrete frequencies. One particular emission has a frequency of 4.57 × 10¹⁵ s^-1, as measured in the frame of reference of the hydrogen atom. Light from this emission is observed coming from a star that is moving away from Earth at 0.900c. What is the observed frequency? Note that, in addition to time dilation, one must take into account that successive wavefronts have to travel longer distances because the star is moving away (Doppler Effect).

A) 1.99 × 10¹⁵ s^-1
B) 7.62 × 10¹⁵ s^-1
C) 1.99 × 10¹⁶ s^-1
D) 1.05 × 10¹⁵ s^-1
E) 0.90 × 10¹⁵ s^-1

Question 76

Two spaceships, each 100 m long in its own rest frame, approach Earth from opposite directions, with equal speeds relative to Earth. As measured by a passenger in one of the spaceships, the other spaceship is 96 m long. What is the speed of the spaceships?

A) c/7
B) c/6
C) c/5
D) c/4
E) c/3

Question 77

Astronaut Rachel leaves Earth in a spaceship at a speed of 0.960c relative to an observer on Earth. Rachel's destination is a star system 14.4 light-years away (one light-year is the distance light travels in one year). According to Rachel, how long does the trip take?

A) 14.4 years
B) 15.0 years
C) 10.8 years
D) 4.20 years
E) 22.7 years

Question 78

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

A) 0.40c
B) 0.60c
C) 0.70c
D) 0.80c
E) 0.90c

Question 79

A spaceship, traveling at 0.100c away from a stationary enemy station, shoots a projectile towards the station, with a speed of 0.560c relative to the spaceship. What is the speed of the projectile relative to the station?

A) 0.460c
B) 0.487c
C) 0.492c
D) 0.492c.
E) 0.660c

Question 80

A spaceship approaches Earth with a speed 0.50c. 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 Earth?

A) 61 beats per minute
B) 65 beats per minute
C) 69 beats per minute
D) 73 beats per minute
E) 75 beats per minute