Deck 27: Relativity

Question 1

I am stationary in a reference system but if my reference system is not an inertial reference system, then, relative to me, a system that is an inertial reference system must:

A) be accelerating.
B) move with constant velocity.
C) remain at rest.
D) be none of these choices.

Answer 1

be accelerating.

Question 2

At what speed would a clock have to be moving in order to run at a rate that is one-third the rate of a clock at rest?

A) 0.97c
B) 0.75c
C) 0.87c
D) 0.94c

Answer 2

0.94c

Question 3

From a stationary position, I observe a moving boxcar, which has a mirror along the front wall, but it is open at the back of the boxcar. I send a flash of light from my flashlight and time the flash of light as it goes to the front of the boxcar and returns to the back of the boxcar. A passenger in the boxcar also times the round trip of the flash of light. Previously I had measured the time required for the round trip of a flash of light when the boxcar was stationary, and I call this the stationary time. Which two times are the same?

A) the time recorded on the passenger's watch and the previous stationary time
B) the time recorded on my watch and the time recorded on the passenger's watch
C) the time recorded on my watch and the previous stationary time
D) None of the times are the same.

Answer 3

the time recorded on the passenger's watch and the previous stationary time

Question 4

A ground observer measures the period of a pendulum moving as a part of an inertial frame of reference to be 2.30 s as the inertial frame moves by at a velocity of 0.800c. What would the observed period be of the same pendulum if its inertial frame were at rest with respect to the observer?

A) 3.03 s
B) 1.38 s
C) 1.84 s
D) 4.25 s

Question 5

According to the special theory of relativity, if a 35 year old astronaut sent on a space mission is accelerated to speeds close to that of light, and then returns to Earth after 20 years as measured on earth, what would be his biological age upon returning?

A) less than 55 years
B) more than 55 years
C) exactly 110 years
D) 55 years

Question 6

A boxcar without a front or a back is moving toward the right. Two electrons move through the boxcar, one moving from back to front toward the right, the other moving from front to back toward the left. According to me, each electron is moving with a speed of 0.8c, and the boxcar is moving with a speed of 0.6c. A passenger in the boxcar records how long it takes each electron to pass from one end of the boxcar to the other end. According to the passenger, which took less time?

A) the electron going from front to back
B) the electron going from back to front
C) Since nothing can go faster than light, an electron cannot move toward the left with a speed of 0.8c through a boxcar moving toward the right with a speed of 0.6c.
D) They both took the same time.

Question 7

The astronaut whose heart rate on Earth is 60 beats/min increases his velocity to v = 0.60c. Now what is his heart rate as measured by an Earth observer?

A) 100 beats/min
B) 75 beats/min
C) 36 beats/min
D) 48 beats/min

Question 8

A boxcar without a front or a back is moving toward the right. Two flashes of light move through the boxcar, one moving from back to front toward the right, the other moving from front to back toward the left. A passenger in the boxcar records how long it takes each flash of light to pass from one end of the boxcar to the other end. According to the passenger, which took longer?

A) the flash going from back to front
B) the flash going from front to back
C) They both took the same time.
D) It depends on whether the passenger is sitting at the front or the back of the boxcar.

Question 9

A tuning fork has a frequency of 400 Hz and hence a period of 2.50 *10 ^{- 3} s. If the tuning fork is in an inertial frame of reference moving by the observer at speed of 0.680c, what is the frequency of the fork as measured by the observer? (Assume that measurements are strictly by optical means and that the speed of sound waves in air is not pertinent here.)

A) 454 Hz
B) 293 Hz
C) 605 Hz
D) 265 Hz

Question 10

An astronaut at rest has a heart rate of 65 beats/min. What will her heart rate be as measured by an earth observer when the astronaut's spaceship goes by the earth at a speed of 0.80c?

A) 108 beats/min
B) 39 beats/min
C) 81 beats/min
D) 52 beats/min

Question 11

According to a postulate of Einstein, which of the following describes the nature of the laws of physics as one observes processes taking place in various inertial frames of reference?

A) Laws are the same only in inertial frames moving at near speed of light.
B) Laws are the same in all inertial frames.
C) Laws are the same only in inertial frames with zero velocity.
D) Laws are the same only in inertial frames moving at low velocities.

Question 12

The relativistic effect of time dilation has been verified by which of the following?

A) twin experiments
B) red shift in distant galaxies
C) muon experiments
D) the discovery of black holes

Question 13

The speed of light is equal to:

A) one light-year per year.
B) 5.28 * 10⁷ miles per hour.
C) one meter per nanosecond.
D) none of the above.

Question 14

A muon formed high in the Earth's atmosphere travels at a speed 0.990c for a distance of 6.40 km before it decays. What is the muon's lifetime as measured in its reference frame?

A) 4.65 *10 ^{- 6} s
B) 1.55*10 ^{- 5} s
C) 2.18 *10 ^{- 6} s
D) 3.04 *10 ^{- 6} s

Question 15

According to the special theory of relativity, which of the following happens to the size of the time interval between two events occurring in an inertial frame of reference as the frame's velocity with respect to the observer increases?

A) interval decreases
B) interval vanishes to zero when velocity equals half speed of light
C) interval increases
D) interval remains constant

Question 16

The period of an oscillating weight on a spring in an inertial frame of reference is 0.80 s. What would be its speed if it were to move by an observer who measures its period as 1.2 s? (c = 3.00 * 10⁸ m/s)

A) 2.5 * l0⁸ m/s
B) 1.1* l0⁸ m/s
C) 2.9 * 10⁸ m/s
D) 2.2 *10⁸ m/s

Question 17

Einstein's theory of relativity is based in part on which one of the following postulates?

A) Speed of light in a vacuum is same for all observers regardless of source velocity.
B) Energy is conserved only in elastic collisions.
C) Space and time are absolutes.
D) Mass and energy are equivalent.

Question 18

A mass is bouncing on the end of a spring with a period T when measured by a ground observer. What would the period of oscillation be (as measured by the same observer) if the mass and spring were moving past the ground observer at a speed of 0.600c?

A) 0.440 T
B) 1.25 T
C) 0.600 T
D) 1.67 T

Question 19

From a stationary position, I observe a moving boxcar, which has a mirror along the front wall, but it is open at the back of the boxcar. I send a flash of light from my flashlight and time the flash of light as it goes to the front of the boxcar and returns to the back of the boxcar. A passenger in the boxcar also times the round trip of the flash of light. Compare the times recorded on our watches.

A) The time recorded on the two watches is the same.
B) The time recorded on his watch is shorter.
C) The time recorded on his watch is longer.
D) The answer depends on the reference system you are in.

Question 20

The period of a pendulum is 2.0 s in a stationary inertial frame of reference. What is its period when measured by an observer moving at a speed of 0.80c with respect to the inertial frame of reference?

A) 1.6 s
B) 1.2 s
C) 2.5 s
D) 3.3 s

Question 21

According to the special theory of relativity, which of the following happens to the length of an object, measured in the dimension parallel to the motion of its inertial frame of reference, as the velocity of this frame increases with respect to a stationary observer?

A) the length remains constant
B) the length vanishes to zero when velocity equals half the speed of light
C) the length increases
D) the length decreases

Question 22

If astronauts could travel at v = 0.90c, we on Earth would say it takes (4.2/0.90) = 4.7 years to reach Alpha Centauri, 4.2 lightyears away. The astronauts disagree. How much time passes on the astronaut's clocks?

A) 2.0 years
B) 2.4 years
C) 1.4 years
D) 3.0 years

Question 23

An astronaut is traveling at a high rate of speed from the Earth to a distant star system. Observers here on Earth note the relativistic effect that the astronaut's clocks run slow. What relativistic effect, if any, does the astronaut observe?

A) Her pulse rate slows.
B) The distance from the Earth to the star system has decreased.
C) Her clocks run faster.
D) There is no relativistic effect to be observed by the astronaut since she is the one doing the moving.

Question 24

A meterstick moving in a direction parallel to its length appears to be only 60.0 cm long to an observer. What is the meterstick's speed relative to the observer? (c = 3.00 *10⁸ m/s)

A) 1.19 *10⁸ m/s
B) 2.40 * 10⁸ m/s
C) 2.93 * 10⁸ m/s
D) 2.75* 10⁸ m/s

Question 25

How fast would a rocket have to move past a ground observer if the latter were to observe a 3.0% length shrinkage in the rocket length? (c = 3.00 * 10⁸ m/s)

A) 1.2 * 10⁸ m/s
B) 0.60 * 10⁸ m/s
C) 0.73 * 10⁸ m/s
D) 0.12 * 10⁸ m/s

Question 26

What is proper time?

A) Proper time is the time measured by a clock at rest with respect to the observer.
B) Proper time is time based on your actual longitude, not your time zone.
C) Proper time is the time given on your GPS.
D) Proper time means standard time as opposed to daylight savings time.

Question 27

As measured from the Earth, a spacecraft is moving at speed 0.80c toward another spacecraft moving at speed 0.60c in the same direction, i.e., the first spacecraft is catching up with the second spacecraft. What is the speed of the first spacecraft as viewed from the second spacecraft?

A) 0.38c
B) -0.20c
C) -0.38c
D) not given

Question 28

Muons at speed 0.9994c are sent round and round a circular storage ring of radius 1500 m. If a muon at rest decays into other particles after an average T = 2.2*10 sup>- ⁶ s, how many trips around the storage ring do we expect the 0.9994c muons to make before they decay?

A) 2
B) 4
C) 0.2
D) 6

Question 29

Our best measurements from Earth indicate that the star system Alpha Centauri is 4.2 light-years away. Suppose some of our astronauts traveled there at a speed v = 0.90c. What would the astronauts measure as the distance to Alpha Centauri?

A) 1.3 lightyears
B) 4.0 lightyears
C) 1.8 lightyears
D) 2.7 lightyears

Question 30

A spaceship is moving away from an observer at relativistic speed. Its length at rest is 100 m, but the observer measures its length as 67 m. A time interval of 100 s on the spaceship would be measured by the observer to be which of the following?

A) 200 s
B) 150 s
C) 50 s
D) 100 s

Question 31

A knight on horseback holds a 10-m lance. The horse can run at 0.78c. (It wins most of its races!) How long will the lance appear to a person that is standing still on the ground as the horse runs past?

A) 7.1 m
B) 15 m
C) 10 m
D) 6.3 m

Question 32

The observed relativistic length of a super rocket moving by the observer at 0.57c will be what factor times that of the measured rocket length if it were at rest?

A) 0.82
B) 0.45
C) 1.4
D) 0.71

Question 33

A muon formed high in Earth's atmosphere travels at a speed 0.9900c for a distance (as we see it) of 9200 m before it decays. How far does the muon travel as measured in its frame?

A) 2596 m
B) 1298 m
C) 4554 m
D) 649 m

Question 34

A space probe has an 24.7-m length when measured at rest. What length does an observer at rest measure when the probe is going by at a speed of 0.860c?

A) 25.2 m
B) 6.43 m
C) 9.19 m
D) 12.6 m

Question 35

A rocket ship is 74.0 m in length when measured before leaving the launching pad. What would its velocity be if a ground observer measured its length as 60.0 m while it is in flight? (c = 3.00 * 10⁸ m/s)

A) 1.76 * 10⁸ m/s
B) 0.980 * 10⁸ m/s
C) 1.98 *10⁸ m/s
D) 1.15 * 10⁸ m/s

Question 36

A laboratory in space has a window so an experiment can be observed from outside. The apparatus has two light sources, red at one end and blue at the other, that can be switched on at the same time. When the light from either source reaches a detector at the midpoint between the sources, a detector light comes on that is red if the red light reaches it first, that is blue if the blue light reaches first, and is white if both the red and reach the detector at the same time. The experimenter triggers both the blue and the red light sources at the same time, and as a result the white light signals their simultaneous arrival. An observer traveling in a spacecraft at high speed in a direction parallel to the length of the apparatus so as to pass the detector as it turns on during the experiment. What color light does the observer see coming through the window from the detector?

A) red
B) white
C) blue
D) This requires the length of the apparatus and observer's speed to answer.

Question 37

As measured from the Earth, a spacecraft is moving at speed 0.80c toward a second spacecraft moving at speed 0.60c back toward the first spacecraft. What is the speed of the first spacecraft as viewed from the second spacecraft?

A) 0.81c
B) 0.95c
C) 0.38c
D) 0.20c

Question 38

A particle is moving the +x direction at speed c/2. Another particle is moving in the -x direction at speed c/2 toward the first particle. Which of the following best describes the speed of one particle as seen by an observer moving with the other particle?

A) c
B) some value less than 3c/4
C) some value more than 3c/4
D) 3c/4

Question 39

The short lifetime of muons created in the upper atmosphere of the Earth would not allow them to reach the surface of the Earth unless their lifetime increased by time dilation. From the reference system of the muons, the muons can reach the surface of the Earth because:

A) time dilation increases their energy.
B) time dilation increases their velocity.
C) the relativistic speed of the Earth toward them is added to their velocity.
D) length contraction decreases the distance to the Earth.

Question 40

An Earth observer sees a spaceship at an altitude of 980 m moving downward toward the Earth at a speed of 0.600c. What is the spaceship's altitude as measured by an observer in the spaceship?

A) 588 m
B) 784 m
C) 1630 m
D) 1270 m

Question 41

A proton with mass 1.67*10^-27 kg moves in an accelerator with a speed of 0.600c. What is its total energy? (c = 3.00 * 10⁸ m/s)

A) 3.26 * 10^-10 J
B) 1.88 *10^-10 J
C) 0.540 * 10^-10 J
D) 2.51 *10^-10 J

Question 42

What is the total energy of a proton moving at a speed of 2.10 * 10⁸ m/s? (proton mass is 1.67 * 10 ^{- 27} kg and c = 3.00 * 10⁸ m/s)

A) 1.11 *10 ^{- 27} J
B) 2.10 *10 ^{- 10} J
C) 2.02 *10 ^{- 10} J
D) 2.24 * 10 ^{- 27} J

Question 43

As measured from the Earth, a spacecraft is moving at speed c/2 toward a second spacecraft that is not moving. The first spacecraft emits a laser pulse toward the second spacecraft. What is the speed of the laser pulse measured by the second spacecraft as it passes by?

A)
B)
C)
D)

Question 44

What is the relativistic kinetic energy of an electron moving at a speed of 2.00 * 10⁸ m/s? (electron mass is 9.11 *10^-31 kg and c = 3.00 * 10⁸ m/s)

A) 2.80 *10^-14 J
B) 1.27 * 10^-14 J
C) 11.6 *10^-14 J
D) 9.47 *10^-14 J

Question 45

The total energy of a particle:

A) increases with increasing relativistic momentum.
B) is not related to its relativistic momentum.
C) is a constant.
D) decreases with increasing relativistic momentum.

Question 46

A particle of mass m is moving at speed . What is its momentum?

A)
B)
C)
D)

Question 47

An object moves by an observer at 0.600c. The total energy of the object will be what factor times that of the rest energy?

A) 1.25
B) 0.970
C) 1.15
D) 0.600

Question 48

An electron of mass 9.11 *10^-31 kg moves with a speed of 0.800c. What is its momentum? (c = 3.00 * 10⁸ m/s)

A) 3.64 * 10^-22 kg.m/s
B) 2.05 * 10^-22 kg.m/s
C) 6.03 * 10^-22 kg.m/s
D) 1.34 *10^-22 kg.m/s

Question 49

A proton with mass 1.67 *10^-27 kg moves with a speed of 0.800c in an accelerator. What is its kinetic energy? (c = 3.00*10⁸ m/s)

A) 7.52*10^-11 J
B) 1.00 *10^-10 J
C) 9.02 *10^-11 J
D) 3.76 *10^-11 J

Question 50

Two spaceships are approaching one another, one with speed and the other with speed . Neither speed is 0. Their speed of approach, according to Newtonian mechanics, is . Special relativity tells us that the speed of approach

A) is more than the Newtonian value if each speed is more than half the speed of light.
B) is always greater than the Newtonian value.
C) is the same as the Newtonian value if each speed is less than half the speed of light.
D) is always less than the Newtonian value.

Question 51

When one compares the relativistic kinetic energy to the classically calculated kinetic energy for a moving object, at which of the speeds listed below does the classical calculation give a greater value than the relativistic calculation?

A) 0.707c
B) 0.5c
C) 0.2c
D) None of the above values will give such a result.

Question 52

Including relativistic effects, doubling the speed of a object:

A) has no effect on its momentum.
B) more than doubles its momentum.
C) less than doubles its momentum.
D) doubles its momentum.

Question 53

At what speed is the momentum of an object triple that found classically?

A) c/3
B) 0.942 c
C) 0.866c
D) 2c/3

Question 54

A proton with mass 1.67 * 10^-27 kg moves with a speed of 0.800c in an accelerator. What is its relativistic momentum? (c = 3.00*10⁸ m/s)

A) 2.40 *10^-19 kg.m/s
B) 6.68 *10^-19 kg.m/s
C) 0.530 *10^-19 kg.m/s
D) 3.76 *10^-19 kg.m/s

Question 55

A nuclear reaction, which gives off a total of 2.0 * 10¹⁶ J of energy, expends how much mass in the process? (c = 3.00 * 10⁸ m/s)

A) 2.2 kg
B) 180 kg
C) 22 kg
D) 0.22 kg

Question 56

Doubling the momentum of a particle:

A) does not change its relativistic total energy.
B) quadruples its relativistic total energy.
C) doubles its relativistic total energy.
D) requires less of a speed increase as the speed increases.

Question 57

If a proton with mass 1.67 *10^-27 kg moves in an accelerator such that its total energy is two times its rest energy, what is its speed? (c = 3.00 * 10⁸ m/s)

A) 1.00 * 10⁸ m/s
B) 2.83 * 10⁸ m/s
C) 1.41 * 10⁸ m/s
D) 2.60 * 10⁸ m/s

Question 58

As the speed of an object increases, its relativistic momentum:

A) stays the same as its classical momentum.
B) does not change since momentum is a conserved quantity.
C) increases less than it classical momentum.
D) increases more than its classical momentum.

Question 59

As measured from the Earth, a spacecraft is moving at speed 0.80c when it releases a probe at speed 0.60c relative to the spacecraft in a forward direction. What would be the speed of the probe as measured from the Earth?

A) 0.70c
B) 0.81c
C) c
D) 0.95c

Question 60

An unknown particle in an accelerator moving at a speed of 2.00 * 10⁸ m/s has a measured total energy of 1.22*10^-9 J. What is its mass? (c = 3.00 * 10⁸ m/s)

A) 1.49 *10^-26 kg
B) 0.650 *10^-26 kg
C) 0.810 *10^-26 kg
D) 1.01 *10^-26 kg

Question 61

At what speed must an object be moving in order that it has a kinetic energy 2.50 times its rest energy? (c = 3.00 * 10⁸ m/s)

A) 2.52 *10⁸ m/s
B) 1.91 * 10⁸ m/s
C) 2.75 *10⁸ m/s
D) 2.87 *10⁸ m/s

Question 62

When a four-megaton nuclear bomb is exploded, approximately 18 *10¹⁵ J of energy is released. How much mass would this represent in a mass-to-energy conversion? (c = 3.00 *10⁸ m/s)

A) 0.20 kg
B) 18 kg
C) 1.8* 10³ kg
D) 0.050 kg

Question 63

Which form of relativity applies for observers who are accelerating?

A) General relativity applies.
B) Special relativity applies.
C) Both special relativity and general relativity apply.
D) Neither applies since the observer must be in an inertial frame to use either one.

Question 64

Relativity dealing with gravitation is known as:

A) gravitational relativity.
B) Galilean relativity.
C) general relativity.
D) inertial relativity.

Question 65

If the mass of a proton is 1.67 *10 ^{- 27} kg, what is the rest energy of the proton? (c = 3.00 *10⁸ m/s and 1 eV = 1.6 *10 ^{- 19} J)

A) 9.4*10⁸ eV
B) 4.1 * 10⁸ eV
C) 3.7* 10⁸ eV
D) 1.2 * 10⁸ eV

Question 66

The gravitational field is equivalent to:

A) the inertial mass.
B) an event horizon.
C) a clock running slowly.
D) an accelerated frame of reference.

Question 67

In an X-ray tube, high-speed electrons are slammed into a lead target, giving off X-rays. If the electrons are accelerated from rest through a potential difference of 100,000 volts, what speed do they have when they strike the target? (q_e = 1.6 *10 ^{- 19} C, m_e = 9.11 *10 ^{- 31} kg, and c = 3.00 10⁸ m/s)

A) 0.17c
B) 0.41c
C) 0.91c
D) 0.55c

Question 68

Through what potential difference would an electron initially at rest need to be accelerated to have its total energy be triple its rest energy? (m_e = 9.11 *10^-31 kg, c = 3.00 *10⁸ m/s, and q_e = 1.6 *10 ^{- 19} C)

A) 5.1* 10⁵ V
B) 1.6 *10^-19 V
C) 1.0 *10⁶ V
D) 2.6 *10⁵ V

Question 69

A lump of uranium has a mass of 2.0 kg, and begins at rest. One half of the lump's mass is going to be totally converted into kinetic energy of the other half. After this is done, how fast is the remaining half going?

A) 1.0c
B) 0.60c
C) 0.94c
D) 0.87c

Question 70

A proton with mass 1.67 *10^-27 kg moves in an accelerator with speed of 0.900c. What is its kinetic energy? (c = 3.00 * 10⁸ m/s)

A) 1.95 * 10^-10 J
B) 1.00 * 10^-10 J
C) 3.70 * 10^-10 J
D) 1.35 *10^-10 J

Question 71

An electron of mass 9.11 *10 ^{- 31} kg moves with a speed of 0.800c. What is its total energy? (c = 3.00 *10⁸ m/s)

A) 13.7 * 10 ^{- 14} J
B) 10.2*10 ^{- 14} J
C) 4.80 *10 ^{- 14} J
D) 7.30 *10 ^{- 14} J

Question 72

If the total energy of an electron in an accelerator is five times its rest energy, what is its speed? (c = 3.00 *10⁸ m/s)

A) 1.98 * 10⁸ m/s
B) 2.94 * 10⁸ m/s
C) 2.32 * 10⁸ m/s
D) 2.90 * 10⁸ m/s

Question 73

An electron of mass 9.11 *10 ^{- 31} kg moves with a speed of 0.800c. What is its kinetic energy? (c = 3.00 * 10⁸ m/s)

A) 5.47 *10 ^{- 14} J
B) 2.05 *10 ^{- 14} J
C) 3.90 *10 ^{- 14} J
D) 6.22 *10 ^{- 14} J

Question 74

A satellite is powered by a small nuclear generator that puts out 20 W. How much matter is converted into energy over the 10 year life span of the generator?

A) 70 µg
B) 53 g
C) 53 kg
D) 53 µg

Question 75

The mass of a proton at rest is m. If the proton is moving so fast that its total energy is four times its rest energy, then what is the kinetic energy of the proton?

A) 3mc²
B) mc²
C) 2mc²
D) 4mc²

Question 76

What is the speed of a particle having a kinetic energy equal to its rest energy?

A) The mass of the particle must be given since the answer can only be given in terms of the mass.
B)
C)
D)

Question 77

A spaceship of mass 10⁶ kg is to be accelerated to 0.60c. How much energy does this require?

A) 2.3 * 10²² J
B) 6.0 *10²² J
C) 2.5 *10²³ J
D) 1.5 *10²³ J