Deck 29: Relativity

Question 1

The special theory of relativity predicts that there is an upper limit to the speed of an object.It therefore follows that there is also an upper limit on which of the following properties of the object? (There could be more than one correct choice. )

A)The kinetic energy of the object.
B)The total energy of the object.
C)The linear momentum of the object.
D)None of the above.

Answer 1

None of the above.

Question 2

The relativistic kinetic energy formula is valid

A)only for speeds near the speed of light.
B)at all speeds.
C)only for subatomic particles,such as electrons and protons.

Answer 2

at all speeds.

Question 3

Observer A sees a pendulum oscillating back and forth in a relativistic rocket and measures its period to be T_A.Observer B moves along with the rocket and measures the period of the pendulum to be T_B.What is true about these two time measurements?

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.

Answer 3

T_A > T_B

Question 4

Observer A sees a ruler moving by in a relativistic rocket and measures its length to be L_A.Observer B moves along with the rocket and measures the length of the ruler to be L_B.What is true about these two length measurements?

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 5

If you were in a spaceship traveling close to the speed of light with respect to Earth,you would notice that

A)some of your physical dimensions were smaller than normal.
B)your mass was less than normal.
C)your mass was greater than normal.
D)your pulse rate was greater than normal.
E)none of the above effects occur.

Question 6

According to the equation E = mc²,an object turns into energy when it reaches the speed of light.

Question 7

Which of the following are basic postulates of special relativity? (There could be more than one correct choice. )

A)Nothing can travel faster than the speed of light.
B)No material object can be accelerated to the speed of light.
C)The speed of light is the same for all observers.
D)The laws of physics are the same in all reference frames.
E)The laws of physics are the same in all inertial reference frames.

Question 8

You are riding in a spaceship that has no windows,radios,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.How can you do this?

A)You can determine if the ship is moving by determining the apparent velocity of light in the spaceship.
B)You can determine if the ship is moving by checking your precision time piece.If it's running slow,the ship is moving.
C)You can determine if the ship is moving by lying down and measuring your height.If you are shorter than usual,the ship is moving.
D)You should give up because you have taken on an impossible task!

Question 9

An astronaut is resting on a bed inclined at an angle above the floor of a spaceship,as shown in the figure.From the point of view of an observer who sees the spaceship moving near the speed of light parallel to the floor,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 whether the rocket is moving to the right or to the left.

Question 10

You are moving at a speed 2/3 c toward Randy when shines a light toward you.At what speed do you see the light approaching you?

A)1/3 c
B)2/3 c
C)4/3 c
D)c

Question 11

Suppose one twin takes a ride in a spaceship traveling at a very high speed to a distant star and then back again,while the other twin remains on Earth.Compared to the twin who remained on Earth,the astronaut twin is

A)younger than the Earth-twin.
B)the same age as the Earth-twin.
C)older than the Earth-twin.
D)The ages cannot be determined from the information provided.

Question 12

A spaceship is moving in a straight line away from Earth at 0.80c,measured relative to Earth.It launches a missile that moves away from the spaceship in the forward direction at 0.60c,relative to the ship.Relative to Earth,what is the speed of this missile?

A)greater than 0.80c but less than c
B)1.4 c
C)c
D)greater than c but less than 1.4c

Question 13

A spaceship traveling at constant velocity 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 14

One of Einstein's postulates in formulating the special theory of relativity was that the laws of physics are the same in reference frames that

A)accelerate.
B)move at constant velocity with respect to an inertial frame.
C)oscillate.
D)are stationary,but not in moving frames.

Question 15

You are a passenger on a spaceship.As the speed of the spaceship increases,you will 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 the behavior of your watch.

Question 16

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

A)the length of your spaceship getting shorter.
B)the length of your spaceship getting longer.
C)the length of your spaceship is zero.
D)no change in the length of your spaceship.

Question 17

When an object moves close to the speed of light relative to Earth,what happens to its dimensions compared to what they were before it began moving,as measured by an Earth-based observer?

A)Only lengths parallel to the direction of travel are decreased.
B)Only lengths perpendicular to the direction of travel are decreased.
C)All lengths are decreased.
D)No lengths are affected.

Question 18

A really high-speed train moves in a direction parallel to its length with a speed that approaches the speed of light.The length of the train,as measured by a stationary observer on the ground,

A)approaches infinity.
B)increases due to the motion.
C)decreases due to the motion.
D)is not affected by the motion.

Question 19

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,at the end of the mission,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 20

A really high-speed train moves in a direction parallel to its length with a speed that approaches the speed of light.The height of the train,as measured by a stationary observer on the ground,

A)approaches infinity.
B)approaches zero.
C)increases slightly.
D)decreases slightly.
E)does not change due to the motion.

Question 21

Someone in Earth's rest frame says that a spaceship's trip between two planets took 10.0 y,while an astronaut on the space ship says that the trip took
What is the speed of the spaceship,assuming the planets are at essentially at rest?

A)0.816 c
B)0.735 c
C)0.975 c
D)0.384 c

Question 22

Two stars are at rest relative to each other.A spaceship is moving between these two stars at 0.932c relative to each star.To someone in the ship,the distance between the two stars appears to be
What is the distance between the stars in their own rest frame?

A)72.8 light-years
B)9.57 light-years
C)21.1 light-years
D)55.4 light-years

Question 23

As measured in Earth's rest frame,a spaceship traveling at 0.9640c takes
To travel between two planets that are not moving relative to each other.How long does the trip take as measured by someone on the spaceship?

A)2.79 y
B)6.83 y
C)39.5 y
D)28.8 y

Question 24

A spaceship with a constant speed of 0.800c relative to Earth travels to a star that is 4.30 light-years from Earth.How much time for this trip would elapse on a clock on board the spaceship?

A)3.23 y
B)4.40 y
C)5.15 y
D)5.38 y

Question 25

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 26

Two stars are at rest relative to each other.In their common rest frame,these stars are 90.0 light-years apart.If they are measured to be
Apart by the navigator of a spaceship traveling between them,how fast is the spaceship moving relative to these stars?

A)0.646c
B)0.604c
C)0.558c
D)0.505c

Question 27

A pion is an unstable particle that has a mean 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 28

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

Question 29

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 30

A spaceship carrying a light clock moves at a speed of 0.960c relative to an observer on Earth.If the clock on the ship advances by 1.00 s as measured by the space travelers aboard the ship,how long did that advance take as measured by the observer on Earth?

A)0.96 s
B)1.2 s
C)2.6 s
D)3.6 s
E)5.8 s

Question 31

At age 21,you set out for a star that is 50 light-years from Earth.How fast would your spaceship have to travel in order to reach that star when you are 61 years old? 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 32

A particle in a 799=m-long linear particle accelerator is moving at
How long does the particle accelerator appear to the particle?

A)387 m
B)1,039 m
C)184 m
D)1,651 m

Question 33

A set of twins,Andrea and Courtney,are initially 10 years old.While Courtney remains on Earth,Andrea rides on a spaceship that travels away from Earth at a speed of 0.60c for 10 years (as measured by Courtney).At the end of the trip,Courtney is 20 years old.How old is Andrea?

A)10 years
B)12 years
C)18 years
D)20 years

Question 34

One 20-year-old twin brother takes a space trip with a speed of 0.80c for 30 years according to a clock on his spaceship.At the end of this trip,what are (a)his own age and (b)the age of his Earth-based twin brother?

A)(a)20 y (b)30 y
B)(a)30 y (b)50 y
C)(a)50 y (b)70 y
D)(a)70 y (b)90 y

Question 35

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 36

A particle physicist observes cosmic rays creating a new particle high in the atmosphere,and the speed of this particle is measured at 99.7% the speed of light.It is unstable,and is observed to decay in an average 37.0 μs.If this particle were at rest in the laboratory,what would be its average lifetime?

A)2.9 µs
B)18 µs
C)5.3 µs
D)12 µs
E)4.3 µs

Question 37

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 years
B)15 years
C)11 years
D)4.2 years
E)23 years

Question 38

An astronaut on a spaceship moving at 0.927c says that the trip between two stationary stars took
How long does this journey appear to take to someone in the rest frame of the two stars?

A)11.4 y
B)1.60 y
C)2.30 y
D)12.6 y

Question 39

A certain unstable particle has a mean 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 particle.An average such particle is observed by a scientist on Earth to travel 342 m in its lifetime.What is the speed of the particle relative to Earth? (c = 3.00 × 10⁸ m/s)

A)0.821c
B)0.681c
C)0.600c
D)0.551c
E)0.335c

Question 40

A spaceship with a constant speed of 0.800c relative to Earth travels to a star that is 4.30 light-years from Earth.How much time for this trip would elapse on a clock on Earth?

A)3.23 y
B)4.40 y
C)5.15 y
D)5.38 y

Question 41

A spaceship,traveling at 0.100c away from a stationary space platform,launches a secondary rocket towards the station,with a speed of 0.560c relative to the spaceship.What is the speed of the secondary rocket relative to the space platform?

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

Question 42

The figure shows a right-angled construction frame ABC.When measured at rest,it has dimensions as follows: AB = 26.0 m,AC = 10.0 m,and BC = 24.0 m.This frame is now given a new velocity of 0.760c,relative to Earth,in a direction parallel to AC.How long is part AC of this frame with the new velocity as measured by Earth-based engineers?

A)6.50 m
B)25.4 m
C)24.3 m
D)23.7 m
E)24.9 m

Question 43

A spaceship is moving away from an asteroid with a speed of 0.80c relative to the asteroid.The spaceship then fires a missile with a speed of 0.50c relative to the spaceship.What is the speed of the missile measured by astronauts on the asteroid if the missile is fired toward the asteroid?

A)0.30c
B)0.50c
C)0.93c
D)1.3c
E)0.65c

Question 44

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 45

A spaceship,traveling at 0.560c towards a stationary space platform,launches a secondary towards the station with a speed of 0.100c relative to the spaceship.What is the speed of the secondary rocket relative to the space platform?

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

Question 46

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 47

A spaceship approaching an asteroid at a speed of 0.60c launches a scout rocket with speed 0.40c relative to the spaceship.At what speed is the scout rocket approaching the asteroid?

A)0.81c
B)1.0c
C)0.76c
D)0.64c
E)0.96c

Question 48

The figure shows a right-angled construction frame ABC.When measured at rest,it has dimensions as follows: AB = 18.9 m,AC = 10.0 m,and BC = 16.0 m.This frame is now given a new velocity of 0.420c,relative to Earth,in a direction parallel to AC.How long is part BC of this frame with the new velocity as measured by Earth-based engineers?

A)16.0 m
B)14.0 m
C)12.0 m
D)10.0 m
E)18.0 m

Question 49

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 50

A spaceship with a constant velocity of 0.800c relative to Earth travels to the star that is 4.30 light-years from Earth.What distance does the space ship travel as measured by a passenger on the ship?

A)2.58 light-years
B)3.52 light-years
C)4.12 light-years
D)4.30 light-years

Question 51

A spaceship traveling at 0.50c away from Earth launches a secondary rocket in the forward direction at 0.50c relative to the spaceship.As measured by Earthlings,how fast is the secondary rocket moving away from Earth?

A)0.90c
B)0.50c
C)0.80c
D)0.70c
E)c

Question 52

In an "atom smasher," two particles collide head on at relativistic speeds.If the velocity of the first particle is 0.741c to the left,and the velocity of the second particle is
To the right (both as measured in the lab rest frame),how fast are the particles moving with respect to each other?

A)0.916c
B)1.284c
C)0.934c
D)0.834c

Question 53

How fast must a meter stick move,relative to the frame of the observer making the measurement,so its length will be measured to be 0.60 m?

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

Question 54

A star is moving toward Earth at 90% the speed of light.The star emits light,which moves away from the star at the speed of light.What do Earth-based astronomers measure for the speed of this light?

A)c
B)1.9c
C)1.2c
D)0.98c
E)0.95c

Question 55

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 56

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 relative to Earth?

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

Question 57

Astronaut Hans leaves Earth in a spaceship traveling at a speed of 0.280c relative to the observer Brian at rest on Earth.Hans is holding a pencil at an angle of 30° with the direction of travel,as seen by Hans.What angle does the pencil make with the direction of travel,as seen by Brian on Earth?

A)29°
B)30°
C)31°
D)33°
E)90°

Question 58

A spaceship leaves Earth at a steady forward speed of 70% the speed of light.How fast relative to the ship must the spaceship launch a shuttlecraft in the forward direction so that it will be moving away from Earth at 98.7% the speed of light?

A)0.91c
B)0.97c
C)0.93c
D)0.99c
E)0.84c

Question 59

A spaceship is moving away from an asteroid with a speed of 0.80c relative to the asteroid.The spaceship then fires a missile with a speed of 0.50c relative to the spaceship.What is the speed of the missile measured by astronauts on the asteroid if the missile is fired away from the asteroid?

A)0.30c
B)0.50c
C)0.93c
D)1.3c
E)0.65c

Question 60

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 61

Consider three galaxies,Alpha,Beta and Gamma.An astronomer in Beta sees each of the other two galaxies moving away from him in opposite directions at 0.70c.At what speed would an observer in Alpha see the galaxy Gamma moving?

A)0.70c
B)1.4c
C)0.82c
D)0.94c
E)0.98c

Question 62

As shown in the figure,the captain of spaceship A observes spaceship E escaping with a relative velocity of 0.35c.A missile M is fired from ship A directly toward ship E,with a velocity of 0.76c relative to ship A.What does the captain of ship E measure for the velocity of the missile M?

A)0.56c
B)0.41c
C)0.52c
D)0.48c
E)0.45c

Question 63

Two satellites with equal rest masses of 100 kg are traveling toward each other in deep space.They have identical speeds of 0.600c.The satellites collide and somehow manage to stick together.What is the rest mass of the combined object after the collision?

A)200 kg
B)225 kg
C)250 kg
D)275 kg
E)300 kg

Question 64

An object with a rest mass of 0.456-kg is moving at 1.20 × 10⁸ m/s.What is the magnitude of its momentum? (c = 3.00 × 10⁸ m/s)

A)5.47 × 10⁷ kg ∙ m/s
B)5.57 × 10⁷ kg ∙ m/s
C)5.67 × 10⁷ kg ∙ m/s
D)5.87 × 10⁷ kg ∙ m/s
E)5.97 × 10⁷ kg ∙ m/s

Question 65

A satellite with a rest mass of 200 kg and a speed of 0.800c and a second satellite with a rest mass of 100 kg and a speed of 0.600c are traveling toward each other in deep space.The satellites collide and somehow manage to stick together.What is the speed of the combined object after the collision?

A)0.333c
B)0.374c
C)0.397c
D)0.418c
E)0.432c

Question 66

What is the momentum of a proton when it is moving with a speed of 0.60c? (m_proton = 1.67 × 10^-27 kg)

A)1.2 × 10^-19 kg∙ m/s
B)1.5 × 10^-19 kg ∙ m/s
C)3.0 × 10^-19 kg ∙ m/s
D)3.8 × 10^-19 kg ∙ m/s

Question 67

A satellite with a rest mass of 200 kg and a speed of 0.800c and a second satellite with a rest mass of 100 kg and a speed of 0.600c are traveling toward each other in deep space.The satellites collide and somehow manage to stick together.What is the rest mass of the combined object after the collision?

A)300 kg
B)389 kg
C)416 kg
D)457 kg
E)587 kg

Question 68

A particle is moving at 0.86c.By what magnitude percentage is the Newtonian expression for momentum in error? (The percentage error is the difference between the erroneous and correct expressions,relative the correct one).

A)49%
B)40%
C)55%
D)62%

Question 69

Two satellites with equal rest masses of 100 kg are traveling toward each other in deep space.One is traveling at 0.650c and the other at 0.850c.The satellites collide and somehow manage to stick together.What is the rest mass of the combined object after the collision?

A)100 kg
B)200 kg
C)277 kg
D)378 kg
E)312 kg

Question 70

Three spaceships A,B,and C are in motion as shown in the figure.The commander on ship B observes ship C approaching with a relative velocity of 0.82c.The commander also observes ship A,advancing in the rear,with a relative velocity of 0.50c.What is the speed of ship C as measured by the captain of ship A?

A)0.94c
B)0.23c
C)2.2c
D)0.54c
E)1.3c

Question 71

If the kinetic energy of a proton is 80% of its total energy,what is the speed of the proton?

A)0.02c
B)0.87c
C)0.98c
D)1.0c

Question 72

Consider three galaxies,Alpha,Beta and Gamma.An astronomer in Beta sees each of the other two galaxies moving away from her in opposite directions at 0.70c.At what speed would an observer in Alpha see the galaxy Beta moving?

A)0.82c
B)0.70c
C)0.94c
D)0.35c
E)0.57c

Question 73

A proton,which has a mass of 1.67 × 10^-27, is moving at 0.80c relative to the laboratory.What does a physicist in that lab measure for its momentum? (c = 3.0 × 10⁸ m/s)

A)4.0 × 10^-19 kg ∙ m/s
B)4.4 × 10^-19 kg ∙ m/s
C)5.0 × 10^-19 kg ∙ m/s
D)5.8 × 10^-19 kg ∙ m/s
E)6.7 × 10^-19 kg ∙ m/s

Question 74

Two satellites with equal rest masses are traveling toward each other in deep space.One is traveling at 0.550c and the other at 0.750c.The satellites collide and somehow manage to stick together.What is the speed of the combined object after the collision?

A)0.100c
B)0.113c
C)0.150c
D)0.175c
E)0.311c

Question 75

If an electron in the lab has a kinetic energy equal to twice its rest energy,what is its speed in the lab?

A)0.84c
B)0.87c
C)0.89c
D)0.91c
E)0.94c

Question 76

When a proton is traveling at 0.80c,what is the ratio of its kinetic energy to its rest energy?

A)0.60
B)0.67
C)0.80
D)1.2
E)1.7

Question 77

Calculate the amount of energy needed to accelerate an electron from
To
Express your answer in
The rest mass energy of an electron is 0.511 MeV.

A)2.71 MeV
B)1.90 MeV
C)4.61 MeV
D)5.69 MeV

Question 78

A satellite,initially at rest in deep space,separates into two pieces,which move away from each other.One piece has a rest mass of 190 kg and moves away with a speed 0.280c,and the second piece moves in the opposite direction with a speed 0.600c.What is the rest mass of the second piece?

A)88.7 kg
B)79.6 kg
C)73.9 kg
D)68.8 kg
E)52.7 kg

Question 79

A satellite,initially at rest in deep space,separates into two pieces,which move away from each other.One piece has a rest mass of 190 kg and moves away with a speed 0.500c,and the second piece has a rest mass of 250 kg and moves in the opposite direction.What is the speed of the second piece?

A)0.212c
B)0.380c
C)0.402c
D)0.473c
E)0.500c

Question 80

Calculate the speed at which a 0.723-kg object has the same momentum as a 1.30-kg object that is moving 0.515c.

A)0.734c
B)0.712c
C)0.981c
D)0.592c