Deck 26: Relativity

Question 1

A conclusion from special relativity is that events that are simultaneous in one inertial frame

A) are simultaneous in all inertial reference frames.
B) are simultaneous in all inertial frames moving at the same speed.
C) may not be simultaneous in another inertial reference frame.
D) are simultaneous in inertial reference frames moving in the same direction.
E) are simultaneous in inertial reference frames moving in the opposite direction.

Answer 1

may not be simultaneous in another inertial reference frame.

Question 2

The principle of relativity is

A) momentum is conserved in all reference frames.
B) the Earth is a noninertial reference frame.
C) the speed of light is constant.
D) the laws of physics are the same in all inertial reference frames.
E) Newton's second law does not hold at high speeds.

Answer 2

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

Question 3

What are the limits on the minimum and maximum values for the Lorentz factor, $\gamma$ ?

A) 0,1
B) 1,no maximum limit
C) no minimum limit,1
D) 1,2
E) None of these possibilities are correct.

Answer 3

1,no maximum limit

Question 4

At what speed would an astronaut need to travel so that he would age 4.20 years while traveling a distance of 4.20 ly as measured by a stationary observer?

A) 1.00 c
B) This cannot be done.
C) 1.00 c/2
D) .707 c
E) .750 c

Question 5

Radioactive particles moving at 0.80 c are measured to have a half-life of 4.3 $\times$ 10^-8 s.What is their half-life when at rest?

A) 7.2 $\times$ 10^-8 s
B) 2.6 $\times$ 10^-8 s
C) 3.4 $\times$ 10^-8 s
D) 1.6 $\times$ 10^-8 s
E) 1.7 $\times$ 10^-7 s

Question 6

A spaceship is observed from the Earth to be moving toward a star at a speed of 0.80 c.If the distance from the spaceship to the star is 1.6 ly as measured from earth,how long does an observer on Earth find that it takes for the space ship to reach the star?

A) 2.0 y
B) 2.1 y
C) 1.6 y
D) 1.2 y
E) 0.96 y

Question 7

A pion has a mean lifetime of 25 ns in its own rest frame.A beam of pions traveling through the laboratory at a speed of 0.60 c is measured to have a mean lifetime of

A) 21 $\mu$ s.
B) 21 ns.
C) 31 ns.
D) 31 $\mu$ s.

Question 8

Protons are sent at 0.900 c down a tube of length 27.0 m.How long does it take for the protons to travel this distance as measured in the lab?

A) 100 ns
B) 44.0 ns
C) 230 ns
D) 150 ns
E) 90.0 ns

Question 9

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) Any of these choice could be correct depending on the relative velocity.

Question 10

Which of the following is the best definition of inertial frame?

A) a frame of reference in which Newtonian mechanics holds true,but relativistic mechanics does not
B) a frame of reference in which relativistic mechanics holds true,but Newtonian mechanics does not
C) a frame of reference where there are no accelerations without applied forces
D) a frame of reverence in which Newton's second and third laws hold,but not his first
E) None of these choices are correct.

Question 11

An astronaut in a rocket moving with a speed v = 0.6c relative to Earth performs a collision experiment with two small steel balls and concludes the both momentum and energy are conserved.What would an Earth observer conclude?

A) only momentum is conserved
B) only energy is conserved
C) neither energy or momentum is conserved
D) both energy and momentum are conserved

Question 12

A passenger is on a spaceship traveling at 0.8 c.The passenger observes that her watch

A) is running slow.
B) is running fast.
C) is keeping time as usual.
D) is running slow if the ship is traveling in the positive direction.
E) is running slow if the ship is traveling in the negative direction.

Question 13

A conclusion of the Michelson-Morley experiments was that

A) interference of EM-waves does not happen.
B) the ether doesn't exist.
C) Galilean relativity holds.
D) light has momentum.
E) light has no momentum.

Question 14

What is the Lorentz factor, $\gamma$ ,for a speed of 0.800 c?

A) 0.800
B) 1.67
C) 0.600
D) 0.360
E) 1.25

Question 15

Which best describes the proper time interval between two events?

A) the longest interval measured by any inertial observer
B) the interval measured in the reference frame in which the two events occur a maximum distance from each other
C) the interval measured in a reference frame in which the two events are simultaneous
D) the interval measured in a reference frame in which the two events occur at the same place
E) None of these choices are correct

Question 16

At what speed would a clock be moving so that time dilation would cause it to run slow by 50%?

A) 0.500 c
B) 0.750 c
C) 0.250 c
D) 0.414 c
E) 0.866 c

Question 17

The postulate(s)of special are (is)

A) the speed of light is the same in all inertial reference frames.
B) E₀ = mc².
C) the principle of conservation of momentum is true.
D) the laws of physics are the same in all inertial reference frames.
E) the principle of conservation of energy is true.

Question 18

According to special relativity,what is the speed of light measured in a space ship traveling at 0.40 c?

A) 0.60 c
B) 1.4 c
C) 0.86 c
D) 1.0 c
E) None of these choices are correct.

Question 19

A spaceship is observed from the Earth to be moving toward a star at a speed of 0.80 c.If the distance from the spaceship to the star is 1.6 ly as measured from earth,how much time passes on the space ship while traveling to the star?

A) 2.0 y
B) 2.1 y
C) 1.9 y
D) 1.2 y
E) 0.96 y

Question 20

The mean life of muons is 2.2 $\mu$ s.How fast are they moving if their measured mean life is 1.1 $\mu$ s?

A) 0.50 c
B) 0.87 c
C) 0.56 c
D) 0.94 c
E) This cannot happen.

Question 21

If two protons are heading toward one another at 0.800 c in the laboratory frame,what is the kinetic energy of one proton in the frame of reference of the other proton?

A) 3.13 GeV
B) 5.56 GeV
C) 1.56 GeV
D) 2.50 GeV
E) 3.34 GeV

Question 22

Doubling the total energy of a particle

A) doubles its momentum.
B) more than doubles its momentum.
C) less than doubles its momentum.
D) quadruples its momentum.
E) does not affect its momentum.

Question 23

Two cars are traveling down the highway in the same direction.Car A is traveling at 30.0 m/s and car B is passing car A at a relative speed of 3.0 m/s.What is the speed of car B with respect to the highway?

A) 27.0 m/s
B) 30.0 m/s
C) 33.0 m/s
D) 32.9 m/s
E) 33.1 m/s

Question 24

If a proton has a kinetic energy of 1.000 GeV,what is its momentum? (m_p = 938.0 MeV/c²)

A) 1.938 GeV/c
B) 1.000 GeV/c
C) 938.0 GeV/c
D) 2.872 GeV/c
E) 1.696 GeV/c

Question 25

A spaceship is observed from the Earth to be moving toward a star at a speed of 0.80 c.If the distance from the spaceship to the star is 1.6 ly as measured from earth,how far is the star as measured from the moving space ship?

A) 2.1 ly
B) 1.9 ly
C) 1.6 ly
D) 1.2 ly
E) 0.96 ly

Question 26

If a mass has its speed doubled,what happens to its relativistic momentum?

A) nothing happens
B) the momentum doubles
C) the momentum halves
D) the momentum more than doubles
E) the momentum increases a little less than double

Question 27

A spaceship is observed by a stationary observer to be moving at 0.600 c.A laser beam is shown straight ahead from the front of the spaceship.How fast does the laser beam travel relative to the observer?

A) 1.60 c
B) 1.36 c
C) 1.00 c
D) 0.640 c
E) 0.360 c

Question 28

What is the rest energy of a proton? (m_p = 1.67 $\times$ 10^-27 kg)

A) 1.5 $\times$ 10^-10 J
B) 5.0 $\times$ 10^-13 J
C) 1.6 $\times$ 10^-13 J
D) 1.6 $\times$ 10^-19 J
E) 0.0

Question 29

What is the magnitude of the momentum of a proton moving at 0.95 c? (m_p = 1.67 $\times$ 10^-27 kg)

A) 5.0 $\times$ 10^-18 kg·m/s
B) 4.8 $\times$ 10^-18 kg·m/s
C) 1.5 $\times$ 10^-18 kg·m/s
D) 9.5 $\times$ 10^-18 kg·m/s
E) 4.4 $\times$ 10^-18 kg·m/s

Question 30

The front of a spacecraft forms a point at an angle of 60 $^{\circ}$ .As the spacecraft increases speed,what happens to this angle as observed in the rest frame?

A) It stays the same.
B) It decreases.
C) It increases.
D) It decreases only if the spacecraft is going to the left.
E) It decreases only if the spacecraft is going to the right.

Question 31

In a colliding-beam experiment,protons moving at 0.800 c in opposite directions strike one another.What is the speed of the incoming proton as viewed by the proton about to be hit?

A) 1.60 c
B) 0.00
C) 0.640 c
D) 0.976 c
E) 0.960 c

Question 32

What speed is required for a length to contract to 80% of its proper length?

A) 0.80 c
B) 0.60 c
C) 0.40 c
D) 0.20 c
E) 0.50 c

Question 33

In the lab,charged particles are directed toward one another,each at speed 0.500 c.What is the speed of the particles moving toward the left with respect to the particles moving to the right?

A) 0.500 c
B) 0.00
C) 1.00 c
D) 0.800 c
E) 1.25 c

Question 34

A spaceship is 25 m wide and 100 m long.When traveling at 0.80 c (in a direction along its length),what is its observed width?

A) 42 m
B) 25 m
C) 16 m
D) 15 m
E) 20 m

Question 35

If a spaceship of proper length 40 m is measured to have a length 30 m,how fast is it moving?

A) 0.50 c
B) 0.81 c
C) 0.75 c
D) 0.66 c
E) 0.43 c

Question 36

Two cars are traveling down the highway in the same direction.Car A is traveling at 30.0 m/s and car B is passing car A at a relative speed of 3.0 m/s.Using Galilean relativity to calculate the speed of car B relative to the highway results in an answer incorrect by how many m/s?

A) 3.3 $\times$ 10^-2
B) 3.3 $\times$ 10^-5
C) 3.3 $\times$ 10^-8
D) 3.3 $\times$ 10^-11
E) 3.3 $\times$ 10^-14

Question 37

What error is made calculating the momentum of a particle moving at 0.80 c using classical mechanics rather than relativistic mechanics?

A) less than 1%
B) the classical value is 67% too high
C) the classical value is 67% too low
D) the classical value is 40% too high
E) the classical value is 40% too low

Question 38

A spear is thrown by you at a very high speed.As it passes,you measure its length at 1/2 its normal length.From this you conclude that the moving spear's mass must be

A) one-half its rest mass.
B) twice its rest mass.
C) four times its rest mass.
D) None of these choices are correct.

Question 39

What is the ratio of the relativistic momentum to the classical momentum?

A) $\gamma$
B) $\gamma$ - 1
C) $\gamma$ + 1
D) $\gamma$ ^-1
E) ( $\gamma$ - 1)^-1

Question 40

Event 2 occurs a time $\Delta$ t after event 1.If event 2 was caused by event 1,which of the following must be true?

A) The distance between event 1 and event 2 can be any amount.
B) The distance between event 1 and event 2 is not more than c $\Delta$ t.
C) There are frames of reference in which event 2 is before event 1.
D) There are frames of reference in which event 1 is not related to event 2.
E) All of these choices are false.

Question 41

How much mass must be converted to energy to release one million kilowatt hours?

A) 3.6 $\times$ 10^-6 g
B) 40 $\mu$ g
C) 4.0 g
D) 3.6 $\times$ 10^-12 g
E) 40 pg

Question 42

If the momentum of an electron is 1.53 MeV/c,what is its kinetic energy?

A) 1.53 MeV
B) 1.02 MeV
C) 1.44 MeV
D) 1.10 MeV
E) 2.59 MeV

Question 43

A star like the sun has a luminosity of 3.9 $\times$ 10²⁶ W.How much mass must be turned into energy each second to produce this power?

A) 1.3 $\times$ 10¹⁸ kg
B) 4.3 $\times$ 10⁹ kg
C) 5.7 $\times$ 10⁵ kg
D) 5.9 $\times$ 10⁶ kg
E) 1.5 $\times$ 10¹¹ kg

Question 44

How much energy is released by a nuclear reactor if the total mass of the fuel decreases by 1.0 g?

A) 9.0 $\times$ 10¹³ J
B) 3.0 $\times$ 10¹¹ J
C) 9.0 $\times$ 10¹⁴ J
D) 3.0 $\times$ 10¹⁴ J

Question 45

An electron is accelerated from rest through a potential difference of 1.02 MeV.If the rest energy of the electron is 0.51 MeV,how fast is the electron moving?

A) 0.57 c
B) 0.30 c
C) 0.67 c
D) 0.90 c
E) 0.94 c

Question 46

Tritium (³H) decays to ³He releasing 18.6 keV of energy.How much mass is converted into energy during this process?

A) 2.07 $\times$ 10^-13 kg
B) 2.07 $\times$ 10^-10 kg
C) 2.07 $\times$ 10^-16 kg
D) 3.31 $\times$ 10^-29 kg
E) 3.31 $\times$ 10^-32 kg

Question 47

In a radioactive decay, 2.37 $\times$ 10^-3 u are converted into kinetic energy.How much kinetic energy is this? (1 u = 1.66 $\times$ 10^-27 kg)

A) 2.13 $\times$ 10¹⁴ J
B) 9.31 $\times$ 10⁸ J
C) 3.54 $\times$ 10^-13 J
D) 3.93 $\times$ 10^-30 J
E) 1.60 $\times$ 10^-13 J

Question 48

The sun radiates at a power of 3.9 $\times$ 10²⁶ W.How long does it take for the sun to lose an amount of mass equal to the mass of the Earth (6.0 $\times$ 10²⁴ kg)? Choose the first answer that is correct.

A) less than one year
B) less than 1000 years
C) less than 10⁶ years
D) less than 10⁸ years
E) more than 10⁸ years

Question 49

An astronaut in a rocket with a speed v-0.6c relative to Earth performs a collision experiment and concludes that both momentum and energy are conserved.What would an Earth observer conclude?

A) Neither energy nor momentum is conserved.
B) The collision never happened because the two objects are never in the same place at the same time.
C) Energy is conserved,but momentum is not.
D) Momentum is conserved,but energy is not.
E) Both momentum and energy are conserved.

Question 50

Two observers will always agree on

A) the speed of light.
B) the mass of cosmic ray muons.
C) the charge of cosmic ray muons.
D) the lifetime of cosmic ray muons.

Question 51

What is the kinetic energy of a particle of mass m that has a total energy four times its rest energy?

A) 5 mc²
B) 4 mc²
C) 3 mc²
D) 2 mc²
E) 1 mc²

Question 52

What is the kinetic energy of a proton moving at 0.8000 c? The rest energy of a proton is 938.3 MeV.

A) 1564 MeV
B) 1251 MeV
C) 938.3 MeV
D) 2502 MeV
E) 626.0 MeV

Question 53

How fast is a particle moving if its kinetic energy is equal to its rest energy?

A) 0.00
B) 0.57 c
C) 0.75 c
D) 0.87 c
E) 0.50 c

Question 54

How does the kinetic energy of a proton change when its relativistic mass doubles?

A) It doubles.
B) It more than doubles.
C) It less than doubles.
D) It must increase but it is not possible to say how much.

Question 55

If a proton has a kinetic energy of 1.000 GeV,what is its speed? (m_p = 938 MeV/c²)

A) 0.935 c
B) 0.875 c
C) 0.766 c
D) 0.586 c
E) 0.343 c

Question 56

Which of the following is (are)invariant(s)?

A) mass
B) momentum
C) energy
D) the speed of light
E) mass and the speed of light

Question 57

What is the momentum of an electron moving at a speed of 0.90 c? (m_e = 0.511 MeV/c² = 9.11 $\times$ 10^-31 kg)

A) 3.1 $\times$ 10^-22 kg·m/s
B) 2.5 $\times$ 10^-22 kg·m/s
C) 5.6 $\times$ 10^-22 kg·m/s
D) 4.4 $\times$ 10^-22 kg·m/s
E) 2.5 $\times$ 10^-23 kg·m/s

Question 58

A megaton explosion releases 4.5 $\times$ 10¹⁵ J.How much mass is converted into energy in this process?

A) none,if it a result of a chemical reaction
B) none,since mass is conserved
C) 50 kg
D) 50 g
E) 10⁹ kg

Question 59

At what speed is the relativistic momentum five times the value calculated classically?

A) 0.99 c
B) 0.98 c
C) 0.96 c
D) 0.80 c
E) 0.20 c

Question 60

An electron has a rest energy of 0.511 MeV.At what speed would its kinetic energy equal 1.022 MeV?

A) 0.866 c
B) 0.942 c
C) 0.888 c
D) 0.971 c
E) 0.500 c

Question 61

Time of flight (TOF) is routinely used to distinguish between different particle species.Calculate the difference in time interval required for a proton (rest mass 938 MeV/c²) and a muon (rest mass: 106 MeV/c²) to travel 2.5m,if each have a momentum of 255 MeV/c.

A) 8 ns
B) 15 ns
C) 18 ns
D) 10 ns

Question 62

Calculate the speed of a beam of neutrons produced in a nuclear reactor,having kinetic energies of 1.0 MeV.The rest mass of neutrons is 939 MeV/c².

A) 799 m/s
B) 640 km/s
C) 320 km/s
D) 24.5 km/s

Question 63

If the velocity of a non-relativistic object is doubled,its energy is quadrupled.This is strictly true only for very low velocities.At what velocity is it the case that a doubling of velocity results in a doubling of energy?

A) 0.45c
B) 0.33c
C) 0.11c
D) 0.20c
E) 0.50c

Question 64

In relativistic mechanics,what principle does not apply?

A) The law of non-contradiction
B) The law of conservation of momentum
C) The law of conservation of energy
D) Gauss's Law
E) All of the these choices still apply under relativistic conditions.

Question 65

The expression used for momentum,p = mv,

A) Is a good low-velocity approximation
B) Is a good high-velocity approximation
C) Is correct as long as we properly understand v
D) Always gives too high a value for p

Question 66

A rocket speeding by the Earth is known,when at rest,to be roughly cylindrical with a radius of 15 m and a length of 150 m.When speeding by,its volume is measured to be 4.24 $\times$ 10⁴ m³.What is its speed?

A) 0.917c
B) 0.774c
C) 0.678c
D) Insufficient information is given.

Question 67

A rocket speeding by the Earth at 0.917c is known,when at rest,to be roughly cylindrical with a radius of 15 m and a length of 150 m.When speeding by,what is its volume,as measured by observers on Earth?

A) 6.78 $\times$ 10³ m³
B) 1.70 $\times$ 10⁴ m³
C) 4.24 $\times$ 10⁴ m³
D) 1.35 $\times$ 10⁴ m³
E) 1.06 $\times$ 10⁵ m³

Question 68

A pair of observers moving relative to one another will always agree upon all but which of the following:

A) the length of a space-time interval between two events
B) their respective rest masses
C) whether two events are simultaneous
D) their relative velocity
E) the relativistic factor gamma that links their reference frames

Question 69

A pair of observers moving relative to one another will:

A) always agree on the ordering in time of two events
B) always disagree about whether two events are simultaneous
C) always disagree about the ordering in time of two events
D) sometimes disagree about whether two events are simultaneous

Question 70

How tall is Mount Everest,according to a cosmic ray muon,a subatomic particle traveling straight down toward the Earth at 0.99c? On Earth,the height of Mt.Everest is viewed to be 8846 m.

A) 885 m
B) 6.29 km
C) 1.25 km
D) 176 m