Deck 27: Relativity

Question 1

Someone in Earth's rest frame says that a spaceship's trip between two planets took 10.0 y,while an astronaut on the spaceship says that the trip took 6.27 y.Find the velocity of the spaceship in terms of the speed of light.

A)0.779 c
B)0.687 c
C)0.975 c
D)0.384 c

Answer 1

0.779 c

Question 2

Two fixed navigation beacons mark the approach lane to a star.The beacons are in line with the star and are 40 Mm apart.A spaceship approaches the star with a relative velocity of 0.30 c and passes the beacons.The passage of the ship between the beacons is timed by observers on the beacons.The time interval of the passage is closest to:

A)440 ms
B)470 ms
C)420 ms
D)250 ms
E)170 ms

Answer 2

440 ms

Question 3

An astronaut on a spaceship moving at 0.927 c says that the trip between the two stars took 4.26 y.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

Answer 3

11.4 y

Question 4

As measured in Earth's rest frame,a spaceship traveling at 0.964 c takes 11.2 y to travel between planets.How long does the trip appear to take for someone on the spaceship?

A)2.98 y
B)7.28 y
C)42.1 y
D)30.7 y

Question 5

Astronaut Mark Uri is space-travelling from planet X to planet Y at a speed of 0.65 c.When he is precisely halfway between the planets,a distance of 1 light-hour from each,nuclear devices are detonated.The explosions are simultaneous in Mark's frame.What is the difference in time of arrival of the flashes from the explosions as observed by Mark?

A)0 min
B)180 min
C)90 min
D)360 min

Question 6

A right-angled construction frame ABC,when measured at rest,has dimensions as follows: AB = 19.00 m,AC = 10.00 m,and BC = 16.16 m.The frame is given a velocity of 0.56 c,relative to the space platform,in a direction parallel to AC.The dimensions of the moving frame are measured simultaneously by observers on the platform.In the figure,the length BC measured by these observers is closest to:

A)16 m
B)14 m
C)12 m
D)10 m
E)18 m

Question 7

Assume that a typical city consumes electrical energy at a rate of 2.0 × 10^-9 W.How many kilograms of matter would have to be converted entirely into energy in order to keep this city running for 21 weeks?

A)0.28 kg
B)0.32 kg
C)0.40 kg
D)0.48 kg

Question 8

One spaceship leaves planet X and heads toward planet Y,which is 70 ly away,as measured in the rest frame of the two planets.100 ly later (again,in the two planets' rest frame),a second spaceship leaves planet Y and heads for planet X.Calculate the space time interval between these two events.

A)71 ly
B)57 ly
C)80 ly
D)89 ly

Question 9

In their common rest frame,two stars are 90.0 ly apart.If they appear to be 68.7 ly apart to a spaceship,how fast is the spaceship moving? Express your answer in terms of c.

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

Question 10

Calculate the speed at which a 0.272 kg object has the same momentum as a 1.30 kg object moving 0.515 c.

A)0.944 c
B)0.922 c
C)0.981 c
D)0.592 c

Question 11

Situation 27.1
A proton (rest energy = 938 MeV)has a speed of 0.80 c.
In Situation 27.1,the ratio of the kinetic energy of the proton to its rest energy is closest to:

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

Question 12

A right-angled construction frame ABC,when measured at rest,has dimensions as follows: AB = 28.00 m,AC = 10.00 m,and BC = 26.15 m.The frame is given a velocity of 0.80 c,relative to the space platform,in a direction parallel to AC.The dimensions of the moving frame are measured simultaneously by observers on the platform.In the figure,the length AB measured by these observers is closest to:

A)26.8 m
B)27.4 m
C)26.2 m
D)25.7 m
E)28.0 m

Question 13

Calculate the kinetic energy of an electron moving at 0.737 c.Express your answer in keV.

A)250 keV
B)210 keV
C)280 keV
D)320 keV

Question 14

In a common rest frame,event A happens on planet A and event B occurs on planet B 100 y later.If the space time interval between these two events is 90 ly,how far apart are the 2 planets in their common rest frame?

A)44 ly
B)35 ly
C)49 ly
D)54 ly

Question 15

A spaceship is moving between two distant stars at 0.932 c.To someone in the ship,the distance between the two stars appears to be 26.4 ly.What is the distance between the stars in the stars' rest frame?

A)72.8 ly
B)9.57 ly
C)21.1 ly
D)55.4 ly

Question 16

A hydrogen atom and a neutron fuse to form deuterium.If the energy released is 3.6 × 10^-13 J,what is the mass of the deuterium? Take the H atom nucleus as a single proton.

A)3.3 × 10^-27 kg
B)3.4 × 10^-27 kg
C)2.0 × 10^-30 kg
D)1.3 × 10^-27 kg

Question 17

Situation 27.1
A proton (rest energy = 938 MeV)has a speed of 0.80 c.
In Situation 27.1,the momentum of the proton in kg ∙ m/s is closest to:

A)4.0 × 10^-19
B)4.4 × 10^-19
C)5.0 × 10^-19
D)5.8 × 10^-19
E)6.7 × 10^-19

Question 18

An electron has a speed of 0.643 c.Through what potential difference would the electron need to be accelerated in order to reach this speed? Assume that the electron was initially at rest.

A)160 kV
B)130 kV
C)180 kV
D)200 kV

Question 19

A particle in a 453 m-long particle accelerator is moving at 0.875 c.How long does the particle accelerator appear to the particle?

A)219 m
B)589 m
C)104 m
D)936 m

Question 20

Astronaut Spud Nick is space-travelling from planet X to planet Y at a speed of 0.60 c.When he is precisely halfway between the planets,a distance of 1 light-hour from each,nuclear devices are detonated.The explosions are simultaneous in the frame of the planets.What is the difference in time of arrival of the flashes from the explosions as observed by Spud?

A)300 min
B)150 min
C)75 min
D)0 min

Question 21

Assume that it takes you one week to read a book in your own rest frame.Would it appear to you to take longer to read this book if you were in a spaceship moving at a constant speed of 0.98 c than it would if you read the same book while sitting in a chair at home?

Question 22

The kinetic energy of a particle of mass M traveling at 1/2 the speed of light is Mc²/8.

Question 23

An astronomer on Earth sees a meteor hit the Moon at exactly the same time as he sees a solar flare erupt on the sun.The solar flare and the meteor impact are simultaneous events in this astronomer's reference frame.

Question 24

If,in a certain reference frame,an object with no unbalanced forces on it keeps moving with constant velocity,then that frame must be an inertial reference frame.

Question 25

A particle has speed 0.95 c and total energy 4.8 × 10^-10 J.What is its momentum?

A)1.5 × 10^-18 kg ∙ m/s
B)2.5 × 10^-15 kg ∙ m/s
C)5.6 × 10^-13 kg ∙ m/s
D)1.0 × 10^-9 kg ∙ m/s

Question 26

The total energy of a moving electron is 0.758 MeV.What is the speed of the electron in terms of c?

A)0.739 c
B)0.794 c
C)0.306 c
D)0.933 c

Question 27

Calculate the amount of energy needed to accelerate an electron from 0.888 c to 0.991 c.Express your answer in MeV.

A)2.71 MeV
B)1.89 MeV
C)4.60 MeV
D)5.68 MeV

Question 28

In an "atom smasher," two particles collide head on at relativistic speeds.If the velocity of the first particle is 0.741 c to the left,and the velocity of the second particle is 0.543 c to the right (both of these speeds are measured in Earth's rest frame),how fast are the particles moving with respect to each other?

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

Question 29

Consider two synchronized,extremely accurate clocks.One clock is on the ground,the other is placed in a jet and flown once around the world,then taken out of the plane and compared with the ground clock.Will the clock on the jet read a time earlier than,the same as,or later than the stationary clock? Support your answer?

Question 30

In a spaceship that is approaching Earth at 80% the speed of light,the captain shines a laser beam directly toward Earth.The captain measures the laser light's speed to be 3.00 × 10⁸ m/s and the receiving station on Earth will measure exactly the same speed for this light.

Question 31

The star Alpha Centauri is 4.25 light years from us,so it takes its light 4.25 years to reach Earth.It is impossible,in principle,for any rocket from Earth ever to reach this star in less than 4.25 light years.

Question 32

Adding heat to an object will increase its mass because the added heat energy is equivalent to mass.

Question 33

The special theory of relativity predicts that there is an upper limit to the speed of a particle.It thus follows that there is also an upper limit on the following property of a particle:

A)the kinetic energy
B)the total energy
C)the linear momentum
D)More than one of these
E)None of these

Question 34

The United States is approximately 3000 mi wide as measured by people on Earth.If astronauts in a spaceship traveling at 45% the speed of light measure this distance,they will measure it to be more than 3000 mi.

Question 35

A rocket is moving at 1/4 the speed of light relative to Earth.At the center of this rocket,a light suddenly flashes.To an observer at rest on Earth,the light will reach the front of the rocket at the same instant that it reaches the back of the rocket.

Question 36

Free neutrons (unlike those in the nucleus of an atom)decay spontaneously into a proton,an electron,and an antineutrino.The masses of these particles are (approx. ):
mn = 1.67492 × 10^-27 kg
Mp = 1.67262 × 10^-27 kg
Me = 9.10939 × 10^-31 kg
The mass of the neutrino is zero (or nearly so).How much energy is released in this decay?

A)1.01 × 10^-14 J
B)1.25 × 10^-13 J
C)4.66 × 10^-12 J
D)7.08 × 10^-13 J
E)5.61 × 10^-12 J

Question 37

An astronaut is traveling in a rocket at 90% the speed of light.If she measures 1.0 s between her heart beats,observers in all other intertial reference frames will measure more than 1.0 s between her heart beats.

Question 38

The rest mass of a particle depends upon how fast it is moving.

Question 39

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

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

Question 40

If you were in a spaceship traveling at a speed 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 is different than normal.
C)your pulse rate is different than normal.
D)None of these effects occur.
E)More than one of these effects occur.

Question 41

Explain why it is impossible for an object to travel at the speed of light.

Question 42

Astronauts travel to a star 2000 light-years from Earth in a spaceship capable of speeds approaching,but not exceeding,the speed of light.Is it possible that the original astronauts will still be alive when the spaceship reaches the star? Why or why not?

Question 43

An object of mass M is initially moving at a speed of 0.999 c and collides inelastically (they stick)with another identical object that was initially at rest.After the collision,the two objects are moving with a speed

A)considerably greater than c/2.
B)roughly equal to c/2.
C)considerably less than c/2.

Question 44

A star is moving toward Earth with a speed of 0.9 c (90% the speed of light).It emits light,which moves away from the star at the speed of light.Relative to us on Earth,the speed of the light moving toward us (emitted by the star)is

A)c.
B)1.9 c.
C)1.2 c.
D)0.98 c.

Question 45

The kinetic energy of an object moving at 10% the speed of light is

A)slightly higher than that given by (1/2)m v².
B)slightly less than that given by (1/2)m v².
C)exactly equal to (1/2)m v².

Question 46

A person buys a SUV and discovers that it is too long to fit in the garage (the length of the SUV is 1.3 times the length of the garage).He decides to drive the SUV into the garage at a speed of 0.99 c.Which statement is true?

A)A person standing near the garage sees the SUV fit inside the garage prior to it colliding into the back wall of the garage,but the driver will claim that it never was entirely inside.
B)The driver of the SUV sees that the entire SUV is inside the garage prior to it colliding into the back wall,but the person standing near the garage will claim it never was entirely inside.
C)Both the driver and the person standing near the garage will claim that the SUV was entirely inside the garage prior to the front smashing into the back wall of the garage.
D)Neither the driver nor the person standing near the garage will claim that the SUV was entirely inside the garage.

Question 47

A light source is flashing on and off with a frequency of 1 Hz.If you were to run really fast (say 80% the speed of light),with your direction of motion perpendicular to the direction of the light,you would observe the frequency of the flashing to

A)decrease.
B)increase.
C)remain the same.

Question 48

A spaceship is moving in a straight line at a speed of 0.8 c (relative to Earth).It launches a missile that moves away from the spaceship (traveling in the same direction as the spaceship)at a speed of 0.6 c.Relative to Earth,the speed of the missile is

A)greater than 0.8 c and less than c.
B)1.4 c.
C)c.
D)greater than c and less than 1.4 c.