Deck 26: Relativity

Question 1

State the two fundamental postulates of Einstein's Special Relativity.

Answer 1

(1) the constancy of the speed of light;
(2) the laws of nature are the same in all inertial frames.

Question 2

State the Principle of Equivalence.

Answer 2

An inertial reference frame in a uniform gravitational field is physically equivalent to a reference frame that is not in a gravitational field, but that is in uniform linear acceleration.

Question 3

Jennifer is inside her windowless space station laboratory and finds herself increasingly pulled to the floor. What experiment can she perform inside the lab to decide if she is feeling the effect of an acceleration or an effect of gravity?

Answer 3

None. The Equivalence Principle says no experiment performed in a closed system can distinguish between the two effects.

Question 4

Using the Equivalence Principle as a guide, explain how one might cancel out (or make disappear) a gravitational field.

Question 5

Moving clocks are observed to run more slowly than clocks that are at rest in the observer's own frame fo reference.

Question 6

An object's length is largest when measured by an observer at rest with respect to the object.

Question 7

According to Einstein's general theory of relativity, rotating reference frames cannot be distinguished from gravitational acceleration.

Question 8

Albert Michelson is primarily remembered for

A) proving time dilation.
B) proving length contraction.
C) proving that the speed of light is not constant.
D) his theory published in 1916.
E) not being able to detect an "ether".

Question 9

The Michelson-Morley experiment was designed to measure

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

Question 10

Michelson and Morley concluded from the results of their experiment that

A) the experiment was successful in detecting a shift in the interference pattern.
B) the experiment was a failure since they detected a shift in the interference pattern.
C) the result was a surprise since there was no detectable shift in the interference pattern.

Question 11

You can build an interferometer yourself if you use the following components:

A) a light source, a detector screen, a partially silvered mirror, two flat mirrors, and a glass plate.
B) a light source, a detector screen, a partially silvered mirror, a flat mirror, and a glass plate.
C) a light source, a detector screen, two partially silvered mirrors, and a glass plate.
D) a light source, a detector screen, two partially silvered mirrors, a flat mirror, and a glass plate.

Question 12

The theory of special relativity

A) does not agree with Newtonian mechanics.
B) is based on a complex mathematical analysis.
C) does not agree with electromagnetic theory.
D) has not been verified by experiment.

Question 13

You are riding in a spaceship that has no windows or other means for you to observe or measure what is outside. You wish to determine if the ship is stopped or moving at constant velocity. What should you do?

A) You can determine if the ship is moving by checking your precision time piece. If its running slow, the ship is moving.
B) You should give up because you have taken on an impossible task.
C) You can determine if the ship is moving by determining the apparent velocity of light.
D) You can determine if the ship is moving either by determining the apparent velocity of light or by checking your precision time piece. If its running slow, the ship is moving.

Question 14

One consequence of Einstein's theory of special relativity is that

A) absolute velocity of stars can be measured with respect to the ether wind.
B) absolute Earth velocity can be measured.
C) simultaneity is not absolute.
D) relative speed can not be measured.
E) nothing is conserved because it changes.

Question 15

In spite of the fictional exploits of the starship Enterprise, "Relativity" teaches us that the maximum possible speed is what? (hint: warp = v/c)

A) "warp" 10
B) "warp" 1
C) "warp"

D) "warp" infinity
E) "warp" 0

Question 16

The gamma factor is 1 / ² and it

A) can be zero.
B) can be any number greater than or equal to zero.
C) can be any number greater than or equal to one.
D) can be a negative number.
E) cannot equal one.

Question 17

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) increases slightly.
B) approaches infinity.
C) approaches "gamma".
D) does not change.
E) approaches zero.

Question 18

Relative to a stationary observer, a moving clock

A) always runs slower than when at rest.
B) can run faster or slower; it depends on the relative velocity between the observer and the clock.
C) always runs faster than when at rest.
D) keeps its normal time.

Question 19

As the velocity of your spaceship increases, you would observe

A) that your mass has increased.
B) that the length of your spaceship has decreased.
C) that your precision clock runs slower than normal.
D) none of the other answers.

Question 20

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 zero.
B) approaches infinity.
C) does not change.
D) increases slightly.

Question 21

A spear is thrown at you at a very high speed. As it passes, you measure its length as one-half its normal length. From this measurement, you conclude that the moving spear's mass must be

A) twice its rest mass.
B) four times its rest mass.
C) zero.
D) one-half its rest mass.

Question 22

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) the same as it was here on Earth.
B) much slower than normal.
C) much faster than normal.

Question 23

Consider a particle of mass m and rest mass m_o. Which of the following is the correct expression for the kinetic energy of such a particle?

A) m_oc² + m_ov²/2
B) m v²/2
C) mc² - m_oc²
D) 1/2(m c² - m_oc²)
E) m_ov²/2

Question 24

The total energy of a particle at rest is

A) m_oc².
B) (1/2) m_oc².
C) zero.
D) p²/(2m_o) .

Question 25

Which of the following depends on the observer's frame of reference?

A) all of the other answer choices
B) the length of a meter stick
C) the mass of the proton
D) the half-life of a muon

Question 26

What happens to the kinetic energy of a speedy proton when its relativistic mass doubles?

A) It must increase, but it is impossible to say by how much.
B) It less than doubles.
C) It more than doubles.
D) It doubles.

Question 27

George Gamow, the creator of the Big-Bang theory of the origin of the universe, asks you to imagine what would happen if the speed of light was 15. mi/h. If you were on the sidewalk looking at a bicyclist ride down the street, how does she look to you while riding, compared to when she stops?

A) taller, the same mass, but stretched out like a limousine
B) same height, greater mass, and flatter in the direction she is moving
C) shorter, greater mass, but stretched out like a limousine
D) same height, smaller mass, and flatter in the direction she is moving
E) shorter, the same mass, but stretched out like a limousine

Question 28

What happens to the total relativistic energy of a speedy proton when its relativistic mass doubles?

A) It doubles.
B) It less than doubles.
C) It must increase, but it is impossible to say by how much.
D) It more than doubles.

Question 29

An object moves in a direction parallel to its length with a velocity that approaches the velocity of light. The mass of this object as measured by a stationary observer

A) does not change.
B) increases slightly.
C) approaches zero.
D) approaches infinity.

Question 30

Compared to "Special" Relativity, "General" Relativity is more concerned with

A) electromagnetic fields.
B) gravitation.
C) Unified fields.
D) mass-energy.
E) Lorentz transformations.

Question 31

Black holes

A) are the collapsed remnant of stars.
B) cannot be detected in binary star systems.
C) are holes in space, devoid of matter.
D) are predicted by Einstein's special theory of relativity.

Question 32

When star light passes by the sun

A) it is unaffected by the sun.
B) it is absorbed by the sun.
C) it is deflected away from the sun.
D) it is deflected toward the sun.

Question 33

The gravitational red shift is caused by

A) Rayleigh scattering in the atmosphere.
B) rotating black holes.
C) time dilation.
D) gravitational lensing.

Question 34

The Schwarzchild radius of a black hole is that radial distance from the center of a sphere within which not even light can escape. It was first discovered mathematically by Schwarzchild in 1916 after Einstein published his general relativity theory. It can be calculated from a star's mass M as: R = 2GM/c². If the mass of star G is twice as much as the mass of star H, the average density of star G compared to star H will be

A) twice as much.
B) four times as much.
C) half as much.
D) one-fourth as much.

Question 35

Consider two spaceships, each traveling at 0.500c 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) On both ships it is measured to be 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.
E) Ship A measures it as less than c, and ship B measures it as greater than c.

Question 36

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

Question 37

At what speed are lengths contracted to half and times dilated by a factor of 2?

Question 38

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

Question 39

A person of initial mass 70. kg climbs a stairway, rising 6.0 m in elevation. By how much does his mass increase by virtue of his increased potential energy?

Question 40

If the mass of a 1.0 kg book could be entirely converted into electrical energy, how many Kw-h would that generate?

Question 41

Above what speed do the Relativistic and the Newtonian expressions for KINETIC ENERGY disagree by more than 1%?

Question 42

Suppose a 70. kg student were to become (be compressed into) a black hole.
(a) What would be his/her Schwarzshild radius ("size" of the B.H.)?
(b) How does this compare to the size of a proton?

Question 43

A radar operator on Earth sees two spaceships moving straight at each other, each with speed 0.60c. With what speed does the pilot of one ship see the other ship approaching?

Question 44

A person onboard spaceship A sees craft B moving away at 92.2% the speed of light and he sees C approaching at 0.833c (see Figure 26-1)

(a) Spacecraft B sees C approaching with what speed?
(b) Ship C sees B approaching with what speed?
(c) Ship C sees A approaching at what speed?
(d) Spacecraft B determines A to be moving at what speed?

Question 45

Using the velocity transformation formula, calculate the speed in the "rest frame" of a particle which is seen to be moving at c in a "moving frame".

Question 46

Earth observes a rocket move away at 0.370c. The rocket is designed to launch a projectile at 0.505c relative to the rocket.
(a) Fired straight ahead, what is the projectile speed observed from Earth?
(b) Launched to the rear, what is the projectile speed observed from Earth?

Question 47

At what speed would a 100. meter long spaceship appear to be 60. meters long?

A) 24. Mm/s
B) 0.24 m/s
C) 2.4 × 10³ Km/s
D) 2.4 Gm/s
E) 240. Mm/s

Question 48

How fast must a spaceship travel to make the trip to a star 400. LY away in 25.3 years of astronaut travel time?

A) 0.966c
B) 0.987c
C) 0.829c
D) 0.998c
E) 0.992c

Question 49

Suppose one observes cosmic rays creating a new particle high in the atmosphere and the particle moves at 99.7% the speed of light. It is observed to decay in an average 37.0 $\mu$ s. What is the proper lifetime of the particle?

A) 2.86 $\mu$ s
B) 18.1 $\mu$ s
C) 5.33 ms
D) 12.4 $\mu$ s
E) 4.33 $\mu$ s

Question 50

What speed dilates 1.000 second into 70.71 seconds?

A) 0.9999c
B) 0.8777c
C) 0.9777c
D) 0.9888c
E) 0.9666c

Question 51

A stick is moving along the x-axis at 90%c. A person riding with the stick sees it inclined at 45.° with respect to the x-axis. Observers in the rest frame see the stick making what angle with respect to the x-axis?

A) 53.°
B) 66.°
C) 88.°
D) 45.°
E) 79.°

Question 52

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

A) 1.2 × 10⁸ eV.
B) 9.0 × 10¹⁶ J.
C) 4.5 × 10¹⁶ J.
D) 6.0 × 10^-3 eV.
E) 3.0 × 10⁸ J.

Question 53

If one uses the classical expression for kinetic energy (1/2 m v²) for a particle traveling at half the speed of light, the result will be deficient by how many percent?

A) 24%
B) 13%
C) 27%
D) 7%
E) 1%

Question 54

An electron is accelerated through 100 kV. By what factor has its mass increased with respect to its rest mass?

A) 8.00
B) 4.25
C)

D) 1.55
E) 1.20

Question 55

A proton (1.67 × 10^-27 kg) is accelerated to 99.8% the speed of light. How much energy did the accelerator have to impart?

A) 38.9 GeV
B) 7.52 GeV
C) 13.9 GeV
D) 14.8 GeV
E) 223. GeV

Question 56

How much energy would be required to accelerate a 77. kg professor from rest to 90% the speed of light?

A) 2.3 mc²
B) 1.3 mc²
C) 0.30 mc²
D) 0.50 mc²
E) 0.41 mc²

Question 57

How many joules of energy are required to accelerate one kilogram of mass from rest to a velocity of 0.886c?

A) 3.0 × 10³ J
B) 8.1 × 10²¹
C) 1.8 × 10¹⁷ J
D) 3.4 × 10^-7
E) 9.0 × 10¹⁶ J

Question 58

A spaceship leaves Earth at 70.0% the speed of light. How fast must the spacecraft launch a shuttlecraft with respect to the ship so that it appears, from Earth, to be moving 98.7% the speed of light away.

A) 0.911c
B) 0.972c
C) 0.928c
D) 0.987c
E) 0.966c

Question 59

Two spaceships are traveling through space at 0.6c 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) 0
B) c
C) 0.6c
D) 1.2c
E) none of the above

Question 60

A spaceship, traveling at WARP 1/2 away from the Earth, launches a shuttle moving away from the ship at c/2 (c/2 seen from the ship). Classically one expects to see the shuttle moving at c from the Earth, but relativistically what speed do we expect seen from the Earth?

A) 0.9c
B) 0.6c
C) 0.5c
D) 0.8c
E) 0.7c