Deck 39: Relativity

Question 1

What did Michelson conclude from the results of his famous experiment?

A)The ether does not exist.
B)The speed of light is the same in all reference frames.
C)The speed of light is constant relative to the ether.
D)Earth moves relative to the ether.
E)Earth does not move relative to the ether.

Answer 1

Earth does not move relative to the ether.

Question 2

A spaceship travels at a speed of 0.95c to the nearest star,Alpha Centauri,4.3 light-years away.How long does the trip take from the point of view of the passengers on the ship?

A)1.4 y
B)1.0 y
C)4.5 y
D)14 y
E)0.44 y

Answer 2

1.4 y

Question 3

You see a system consisting of a mass oscillating on the end of a spring passed you at a speed u and note that the period of the system is T.Your strange friend,who is moving with the mass-spring system,also measures its period and finds a period that is

A)equal to T.
B)less than T.
C)greater than T.
D)either a or b depending on whether the system was approaching or receding from the first observer.
E)There is not sufficient information to answer the question.

Answer 3

less than T.

Question 4

You stand on a corner as a friend drives past in an automobile.You both note the time interval required for the car to travel one block,and you both measure the distance traveled.The proper time interval is measured by _____,and the proper distance is measured by _____.

A)you; you
B)you; your friend
C)your friend; you
D)your friend; your friend
E)your friend; both of you

Question 5

A standard Canadian football field is 100 m long and 60 m wide.A UFO streaks from one end of the field to the other at a speed of 0.6c relative to the players on the field.An observer in the UFO measures the width of the field to be

A)60 m
B)80 m
C)100 m
D)125 m
E)167 m

Question 6

An induced emf is observed in a coil when a permanent magnet is moved towards the coil,Figure (a).An induced emf is also observed when the coil is moved towards the magnet,Figure (b).Explain how the induced emf in both cases are in accord with Einstein's first postulate.

A)The induced current in (a)is in the clockwise direction whereas it is in the anti-clockwise in (b),indicating the difference in absolute motion.
B)The induced current in (a)is in the anti-clockwise direction whereas it is in the clockwise in (b),indicating the difference in absolute motion.
C)The induced currents are in the clockwise direction for both cases,indicating that absolute motion cannot be detected.
D)The induced currents are in the anti-clockwise direction for both cases,indicating that absolute motion cannot be detected.
E)None of the above statements is correct.

Question 7

The results of the Michelson-Morley experiment can be interpreted to indicate that if an ether exists,

A)light waves and sound waves are the same.
B)light waves and sound waves are not the same.
C)the ether is dragged along by the experiment.
D)the ether is not dragged along by the experiment.
E)the speed of light in the ether is 3 $\times$ 10⁸ m/s.

Question 8

A standard Canadian football field is 100 m long and 60 m wide.A UFO streaks from one end of the field to the other at a speed of 0.6c relative to the players on the field.The aliens in the UFO decide to watch the game on television as they head off toward Jupiter.The game begins at 1:30 p.m.and ends at 4:30 p.m.according to earthbound broadcasters.The elapsed time for the game according to the aliens is

A)1.8 h
B)2.4 h
C)3.0 h
D)3.8 h
E)5.0 h

Question 9

When a meterstick moves past you in the direction of its length,you measure it to be 90 cm long.What is its speed?

A)5.7 $\times$ 10⁷ m/s
B)9.5 $\times$ 10⁷ m/s
C)1.3 $\times$ 10⁸ m/s
D)2.4 $\times$ 10⁸ m/s
E)2.7 $\times$ 10⁸ m/s

Question 10

A standard Canadian football field is 100 m long and 60 m wide.A UFO streaks from one end of the field to the other at a speed of 0.6c relative to the players on the field.An observer in the UFO measures the length of the field to be

A)60 m
B)80 m
C)100 m
D)125 m
E)167 m

Question 11

While astronauts in a spaceship with a speed of 0.6c relative to Earth move outward from Earth toward Jupiter,they observe a cosmic ray shower that contains protons moving toward them.On Earth the speed of these protons is measured as 0.2c toward the spaceship.They measure the speed of the protons to be

A)0.80c
B)0.71c
C)0.95c
D)0.69c
E)0.45c

Question 12

The Michelson-Morley experiment showed

A)a negligible fringe shift indicating an ether drift toward the center of Earth.
B)a negligible fringe shift indicating that,if an ether exists,it is at rest with respect to Earth.
C)a negligible fringe shift indicating that the instrument was not sensitive enough.
D)Earth to be traveling with a speed approaching that of light through space.
E)that light travels too fast to have its velocity measured.

Question 13

Suppose the speed of light is determined experimentally to be 299,796 ± 4 km/s.If the total path length for your interferometer is exactly 11.0 m,how big an error in the time required for the light to travel through the apparatus corresponds to the uncertainty (±4 km/s)in the speed of light?

A)4.9 $\times$ 10^-13 s
B)2.7 $\times$ 10^-3 s
C)3.7 $\times$ 10^-8 s
D)4.9 $\times$ 10^-10 s
E)9.2 $\times$ 10^-12 s

Question 14

The principle of Newtonian relativity predicts that

A)absolute motion can be detected.
B)absolute motion cannot be detected.
C)relative motion can be detected.
D)relative motion cannot be detected.
E)both absolute and relative motion can be detected.

Question 15

A pion lives 26 ns in its rest frame.It travels 15 cm down a beam pipe in a particle accelerator before it decays into other particles.How far is this in the rest frame of the pion?

A)19.026 cm
B)18.465 cm
C)16.123 cm
D)14.997 cm
E)12.886 cm

Question 16

Your space vehicle is traveling directly away from Earth with a speed c/2,where c = 3 $\times$ 10⁸ m/s is the velocity of light.A light signal is sent from Earth.The speed with which this light passes your vehicle,as measured by the crew,would be

A)c/4
B)c/2
C)c
D)3c/4
E)c/(1 - 1/4)^1/2

Question 17

A pion lives 26 ns in its rest frame,but an observer in a laboratory in which the particle moves at a speed of 2.7 $\times$ 10⁸ m/s says the particle lived

A)11 ns
B)15 ns
C)43 ns
D)60 ns
E)79 ns

Question 18

An airplane flies from point A to point B,a distance of 100 km,and back again with an airspeed of 250 km/h.What is the difference in the time for this round trip on a day when a wind of speed 50.0 km/h blows from A toward B and on a day when a wind of speed 50.0 km/h blows in a direction perpendicular to AB?

A)zero
B)1.0 min
C)5.5 min
D)4.5 min
E)10 min

Question 19

If Michelson and Morley had performed a version of their experiment with sound waves,they would not have "heard a fringe shift" in which of the following cases?

A)The experimental apparatus was on an open flat car that was not moving,and there was no wind.
B)The experimental apparatus was on an open flat car that was not moving,and there was a wind.
C)The experimental apparatus was on an open flat car that was moving,and there was no wind.
D)The experimental apparatus was on an open flat car that was moving,and there was a headwind.
E)All of these are correct.

Question 20

Which of the following statement(s)is (are)a consequence of Einstein's postulates?

A)Every observer in every reference frame measures the same value for the speed of light.
B)Moving clocks appear to run slow.
C)Moving objects appear to be contracted along the direction of motion.
D)Clocks synchronized in one reference frame are not synchronized in any frame moving relative to that reference frame.
E)All of these are consequences of Einstein's postulates.

Question 21

Your strange friend flies past you in a relativistic spacecraft holding a meterstick and a clock.The meterstick appears too _____ to you,and the clock appears _____ to you.

A)short; slow
B)long; slow
C)short; fast
D)long; fast
E)short; normal

Question 22

Spaceship Julio passes spaceship Klara with a relative velocity of 0.8c.An astronaut aboard Julio finds that her heart is beating once every 0.0133 min (75 beats/min).The time between beats according to a sympathetic astronaut aboard Klara is

A)0.00800 min
B)0.0106 min
C)0.0133 min
D)0.0166 min
E)0.0222 min

Question 23

Our galaxy,the Milky Way,has a diameter of about 100 thousand light-years.How many years would it take a spacecraft to cross the galaxy if it could travel at 99% the speed of light?

A)1.4 $\times$ 10³ yrs
B)1.0 $\times$ 10⁵ yrs
C)1.4 $\times$ 10⁴ yrs
D)7.2 $\times$ 10³ yrs
E)None of these is correct.

Question 24

You observed that event A occurred before event B.Which of the following statements is false?

A)Another reference frame must exist in which event A precedes event B.
B)A reference frame must exist in which event B precedes A.
C)A reference frame could exist in which the events are simultaneous.
D)A reference frame could not exist in which event B precedes event A.
E)None of these statements is false.

Question 25

A beam of unstable neutral pions is observed to travel on average 8 m before they decay.If their proper lifetime is 0.8 $\times$ 10^-8 s,then calculate how fast the beam is traveling.

A)0.96c
B)0.92c
C)0.29c
D)0.98c
E)3.5c

Question 26

Because the galaxies are moving away from us,the light they emit

A)is shifted toward the shorter,blue wavelengths.
B)is shifted toward the longer,red wavelengths.
C)is of the same wavelength it would be if they were at rest relative to Earth.
D)arrives with increased intensity.
E)None of these is correct.

Question 27

An astronaut aboard a spacecraft enroute to Mars with a speed of 0.5c relative to Earth observes a meteor approaching head on at a speed of 0.9c.What is the speed of the meteor relative to Earth?

A)1.4c
B)-0.73c
C)0.4c
D)2.55c
E)None of these is correct.

Question 28

What is the difference in age between the mother and son after she returns back to Earth?

A)7.0 years
B)16.8 years
C)23.0 years
D)30.0 years
E)37.0 years

Question 29

Alpha Centauri is not only the closest star system to us (it is actually a triple star system)but it also seems to be an excellent place to look for extra-terrestrial life.It is about 4.3 light-years away from Earth.If an astronaut claims her journey there and back only took 6.3 years,then how fast was she traveling? (Assume she made a fast turnaround once she arrived there!)

A)0.65c
B)0.73c
C)0.86c
D)0.81c
E)0.54c

Question 30

A star system is 100 light-years away.If a spacecraft travels to the star system at 97% the speed of light then what is the ratio of the time for the journey measured by an observer left on Earth divided by the time measured by the astronaut?

A)4.1
B)17
C)1.0
D)1.3
E)2.4

Question 31

Two electrons are ejected in opposite directions from atoms in a sample of radioactive material.Each electron has a speed,as measured by a laboratory observer,of 0.6c.What is the speed of one electron as seen from the other electron?

A)0.361c
B)0.882c
C)1.87c
D)zero
E)1.24c

Question 32

What is the total distance traveled according to the biologist? Give your answer in light-years.

A)1.69
B)4.39
C)6.78
D)7.45
E)9.45

Question 33

Use the following scenario for the next three questions.
A 26-year-old biologist makes a trip to study alien life forms in a distant planet 10 light-years away.The round trip including a stay of 1 year in the distance planet takes 21.5 years according to the clock on earth.The biologist's son is 3-year-old when he left.Assume that the planet is not moving with respect to Earth,and the speed is the same for both outbound and inbound part of the journey.
How fast is the spaceship traveling?

A)0.375c
B)0.5c
C)0.67c
D)0.845c
E)0.976c

Question 34

At rest,pions have a proper lifetime of 26 ns.What is the speed of a beam of pions if their observed lifetime were measured to be 64 ns ? (This is a real experiment that has been performed and found to be consistent with Special Relativity.)

A)0.96c
B)0.84c
C)0.70c
D)0.41c
E)0.91c

Question 35

You measure the length of a passing Imperial Starcruiser spacecraft to be 100 m.If the Starcruiser is moving at 80% the speed of light,what would be its length if it was at rest relative to you?

A)280 m
B)60 m
C)36 m
D)170 m
E)125 m

Question 36

The light emitted by an object traveling at high speed toward Earth would

A)be shifted toward the blue end of the spectrum.
B)be shifted toward the red end of the spectrum.
C)undergo no spectral shifts.
D)arrive with diminished intensity.
E)None of these is correct.

Question 37

You place two clocks that you consider to be synchronized on a road 100 m apart.Your friend drives by at speed V and observes the clocks to be out of sync by an amount T.When you place the clocks 200 m apart and your friend drives by at speed 2V,by what amount will your friend claim the clocks to be out of sync?

A)T
B)2T
C)4T
D)T/2
E)T/4

Question 38

A clock has a period of exactly 1 second when at rest.If you were to measure a period of 1.5 seconds for the same clock,how fast is it moving relative to you as a percentage of the speed of light?

A)44%
B)31%
C)67%
D)75%
E)87%

Question 39

Spaceship Solange passes spaceship Hari with a relative velocity of 0.6c.An astronaut aboard Hari observes the length of Solange to be 30.5 m.The astronauts aboard Solange claim that the length of their spaceship is

A)18.3 m
B)24.4 m
C)30.5 m
D)38.1 m
E)39.6 m

Question 40

An earthbound radar monitors a spaceship moving at 0.9c that is being followed by a second ship moving at 0.8c.The second ship records the velocity of the faster ship as

A)0.080c
B)0.10c
C)0.72c
D)0.36c
E)1.7c

Question 41

The expression relating the bending of the path of a relativistic,charged particle in a magnetic field to the particle's momentum is

A)p² = 2mB
B)p = qBr
C)E² = (pc)² + E₀²
D)p = q²B²r²/2m
E)

Question 42

In the twenty-second century,a hyperfast New York to Los Angeles train roars through St.Louis without stopping at a speed of 0.80c.The front of the train arrives at the St.Louis station at precisely 12:00 noon according to all the clocks on the train (which are all synchronized in the train's frame),and the passengers are called to lunch in the dining car.An observer on the station platform manages to catch a glimpse of a clock at the front of the train that reads exactly 12:00 noon.What is the time at this instant at the rear of the train,according to the observer on the platform,if the train is 500 m long in its rest frame?

A)1.35 $\mu$ s past noon
B)1.35 $\mu$ s before noon
C)noon exactly
D)1.35 ms past noon
E)1.35 ms before noon

Question 43

As an object of mass M approaches the speed of light,its momentum approaches

A)zero
B)infinity
C)Mc
D)Mc²
E)c

Question 44

A proton with a rest energy of 938 MeV has a speed of 0.99c.What is its momentum in units of GeV/c?

A)6.6 GeV/c
B)0.93 GeV/c
C)9.3 GeV/c
D)3.3 GeV/c
E)47 GeV/c

Question 45

What is the speed of an electron whose kinetic energy equals its rest mass?

A)0.5c
B)0.67c
C)
D)
E)

Question 46

Castor and Pollux,identical twins,get into their individual spaceships and blast off simultaneously.Castor's is the faster ship,both return to Earth simultaneously.Which of the following statements is true?

A)Castor is older only if he traveled in the same direction as Pollux.
B)Castor is older only if he traveled in the opposite direction to Pollux.
C)Pollux is older only if he traveled in the same direction as Castor.
D)Pollux is older only if he traveled in the opposite direction to Castor.
E)Pollux is older.

Question 47

How fast does an electron have to travel to have the same mass as a proton at rest?

A)0.9985c
B)0.999985c
C)0.9999985c
D)0.99999985c
E)0.9999999985c

Question 48

At what speed would an electron's mass be measured as 4 times its rest mass?

A)0.88c
B)0.97c
C)0.94c
D)0.25c
E)0.063c

Question 49

The mass of an electron traveling at 0.8c is how many times as great as its rest mass?

A)0.60
B)0.78
C)0.80
D)1.28
E)1.67

Question 50

What is the momentum of an electron whose kinetic energy equals its rest mass,m?

A)0.5 mc kg.m/s
B) kg.m/s
C) kg.m/s
D) kg.m/s
E) kg.m/s

Question 51

Einstein's Second Postulate states that nothing can travel faster than the speed of light.The momentum of a particle of rest mass m

A)has an upper limit of mc.
B)has an upper limit of 2mc.
C)is infinite as the speed approaches c.
D)has an upper limit of 0.5mc.
E)none of the above

Question 52

The momentum of an electron moving at 0.8c is approximately

A)0.511 MeV/c
B)1.02 MeV/c
C)2.18 $\times$ 10^-22 kg · m/s
D)3.60 $\times$ 10^-22 kg · m/s
E)5.82 $\times$ 10^-22 kg · m/s

Question 53

A radioactive atom is traveling through the laboratory at a speed of 0.2c when it undergoes beta decay.The emitted electron moves in the same direction as the atom and has a speed of 0.9c relative to the atom.The speed of the electron,as seen by an observer in the laboratory,is

A)1.10c
B)1.07c
C)c
D)0.93c
E)0.70c

Question 54

While astronauts in a spaceship with a speed of 0.6c relative to Earth move outward from Earth toward Jupiter,they observe a cosmic ray shower that contains particles moving toward them at 0.2c relative to Earth.One of the particles has a rest energy of 3.0 GeV and a momentum,as measured by the astronauts,of 4.0 GeV/c.Its kinetic energy is

A)7.0 GeV
B)4.0 GeV
C)5.0 GeV
D)2.7 GeV
E)2.0 GeV

Question 55

A proton that is being accelerated travels along arcs of a circle through the magnetic fields of a cyclotron.Near the beginning of its path through the cyclotron,the speed of the proton is slow and the radii of the arcs are small.Near the end of its path,the radii are large and the speed is c/3,so the motion of the particle must be treated relativistically.What must the ratio of the average magnetic field at the edge of the cyclotron to that at the center be to compensate for the relativistic momentum of the proton? HINT: The cyclotron frequency f = qB/2 $\pi$ m must remain constant for the proton throughout its path.

A)0.94
B)0.33
C)1.3
D)1.06
E)1.7

Question 56

An electron with a rest mass of 0.511 MeV travels at speed v = 0.500c.What is its kinetic energy?

A)590 keV
B)80 keV
C)510 keV
D)430 keV
E)220 keV

Question 57

The linear momentum (p)times the speed of light (c)of an electron traveling at 0.98c is

A)0.495 MeV
B)0.511 MeV
C)1.12 MeV
D)2.5 MeV
E)938 MeV

Question 58

An electron with a kinetic energy of 2 MeV is produced in a betatron.Its momentum is approximately

A)8.2 $\times$ 10^-3 kg · m/s
B)1.31 $\times$ 10^-27 kg · m/s
C)7.63 $\times$ 10^-22 kg · m/s
D)1.31 $\times$ 10^-21 kg · m/s
E)7.63 $\times$ 10^-25 kg · m/s

Question 59

A man standing on the platform of a railroad station observes two trains approaching him from opposite directions at speeds of 0.5c and 0.75c,respectively.At what speed does one train move with respect to the other?

A)1.25c
B)0.25c
C)0.63c
D)0.91c
E)0.47c

Question 60

If the ratio of the rest mass to the relativistic mass of an electron is 0.8,then the velocity of the electron must be

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

Question 61

An electron is accelerated from rest by a total potential difference of 2.00 $\times$ 10⁸ V.Its mass at this energy is

A)9.1 $\times$ 10^-31 kg
B)2.27 $\times$ 10^-33 kg
C)1.67 $\times$ 10^-27 kg
D)3.64 $\times$ 10^-28 kg
E)1.1 $\times$ 10^-16 kg

Question 62

The kinetic energy of an electron traveling at 0.98c is

A)0.245 MeV
B)0.511 MeV
C)0.756 MeV
D)1.225 MeV
E)2.044 MeV

Question 63

The correct expression relating the energy E of a particle to its rest mass m₀,its momentum p,and the speed of light c,is

A)E² = p²c² + m₀c²
B)E² = p²c² + (m₀c)²
C)E² = p²c + (m₀c²)²
D)E² = pc² + (m₀c²)²
E)E² = p²c² + (m₀c²)²

Question 64

A particle of mass M moving at speed V << c has approximately what total energy?

A)Mc²
B)MV²/2
C)cMV
D)Mc²/2
E)cMV/2

Question 65

If one gram of matter could be completely converted into energy,the yield would be

A)0.51 MeV
B)931 MeV
C)3 F $\times$ 10¹³ J
D)9 $\times$ 10¹³ J
E)9 $\times$ 10¹⁶ J

Question 66

Einstein's Second Postulate states that nothing can travel faster than the speed of light.The kinetic energy of a particle of rest mass m

A)has an upper limit of mc².
B)has an upper limit of mc².
C)has an upper limit of 2mc².
D)is infinite as the speed approaches c.
E)none of the above

Question 67

An electron accelerated from rest through an electrostatic potential difference of 750 kV would have a total energy of approximately

A)1.26 MeV
B)0.750 MeV
C)0.511 MeV
D)0.239 MeV
E)0.038 MeV

Question 68

The energy released by the nuclear bomb that destroyed Hiroshima was equivalent to 12.4 kilotons of TNT.This is equivalent to 9.0 $\times$ 10²⁶ MeV.The mass that was converted into energy in this explosion was

A)1.6 kg
B)1.6 $\times$ 10^-3 kg
C)1.4 $\times$ 10¹⁴ kg
D)1.1 $\times$ 10¹⁰ kg
E)120 kg

Question 69

If an electron,initially at rest,is accelerated through a potential difference of 180 kV,the relativistic mass of the electron is

A)12.3 $\times$ 10^-31 kg
B)9.11 $\times$ 10^-31 kg
C)16.2 $\times$ 10^-31 kg
D)5.90 $\times$ 10^-31 kg
E)infinite

Question 70

When a particle of rest mass m_o undergoes an increase in its velocity,

A)only its mass increases.
B)only its kinetic energy increases.
C)its mass decreases.
D)its mass decreases and its kinetic energy increases.
E)both its mass and its kinetic energy increase.

Question 71

Which of the following statements about an electron that is accelerated from rest through a potential difference of 150 kV is false?

A)The kinetic energy of the electron is 1.5 $\times$ 10⁵ eV.
B)The value of e/m for the accelerated electron is greater than that of a slower electron.
C)The velocity of the electron is less than the velocity of light.
D)The relativistic mass of the electron is greater than its rest mass.
E)In the acceleration the electron will have gone from lower to higher potential.

Question 72

A particle accelerator collides beams of protons and anti-protons with equal and opposite momenta.The aim of an experiment is to create a possible new massive particle with neutral charge and a mass 6 times that of a single proton.Calculate the necessary speed of the protons (and anti-protons)in the collision as a % of the speed of light.

A)85.9% c
B)99.9% c
C)98.7% c
D)94.3% c
E)None of these is correct.

Question 73

A positron traveling at 50% the speed of light collides with an electron traveling at 75% the speed of light.The positron and electron annihilate.How much energy is released in MeV?

A)1.36 MeV
B)0.182 MeV
C)1.022 MeV
D)0.892 MeV
E)1.53 MeV

Question 74

An electron has 1022 keV of kinetic energy.What is its mass?

A)9.11 $\times$ 10^-31 kg
B)1.82 $\times$ 10^-30 kg
C)3.64 $\times$ 10^-30 kg
D)4.56 $\times$ 10^-31 kg
E)2.73 $\times$ 10^-30 kg

Question 75

In a nuclear reaction,(0.0036)(1.67 $\times$ 10^-31 kg)of mass is converted to the kinetic energy of a deuteron that is originally at rest.The kinetic energy of the deuteron is approximately

A)0.34 keV
B)3.6 eV
C)3.9 eV
D)3.2 $\times$ 10¹⁸ eV
E)4.2 $\times$ 10⁸ eV

Question 76

What is the momentum of a photon having the same total energy as an electron with a kinetic energy of 100 keV?

A)zero
B)611 keV/c
C)100 keV/c
D)211 keV/c
E)411 keV/c

Question 77

A proton and an electron are accelerated until their total energy is twice their rest masses.If the rest mass of the proton is M_pc² = 931 MeV and that of the electron is M_ec² = 0.51 MeV,the ratio of the velocity of the electron to that of the proton is

A)0.5
B)1.0
C)1.5
D)2.0
E)not enough data are given

Question 78

An electron traveling at 0.980c has a total energy of

A)0.245 MeV
B)0.511 MeV
C)0.756 MeV
D)1.736 MeV
E)2.55 MeV

Question 79

A particle moves in such a way that its kinetic energy just equals its rest energy.The velocity of this particle is

A)0.866c
B)c/4
C)c
D)0.707c
E)c/2

Question 80

The total yearly world consumption of energy is approximately 4.0 $\times$ 10²⁰ J.How much mass would have to be completely converted into energy to provide this amount of energy?

A)4.4 $\times$ 10³ kg
B)1.3 $\times$ 10¹² kg
C)1.3 $\times$ 10⁴ kg
D)4.4 $\times$ 10⁵ kg
E)2.2 $\times$ 10⁴ kg