Deck 35: Relativity

Question 1

A 101-meter long relativistic train approaches a 100-m long platform at high speed.How fast must the train be going to fit entirely inside the length of the platform?

A)3.0 * 10⁸ m/s
B)4.2 * 10⁷ m/s
C)9.5 * 10⁶ m/s
D)4.7 * 10⁶ m/s
E)6.2 * 10⁵ m/s

Answer 1

4.2 * 10⁷ m/s

Question 2

Right before takeoff,a passenger on a plane flying from town A to town B synchronizes his clock with the clock of his friend waiting for him in town B. The plane flies without interruption for 5.00 hours at a constant velocity.The moment the plane touches the ground the two friends check simultaneously the indication of their clocks.The difference between the readings of the clocks B and A is 7.56 ns.Ignoring any effects of acceleration,the constant velocity of the plane was

A)178 m/s.
B)354 m/s.
C)243 m/s.
D)328 m/s.
E) 275 m/s.

Answer 2

275 m/s.

Question 3

A spacecraft travels along a straight line from the Earth to the Moon a distance of 3.84 * 10⁸ m.Its speed measured on Earth is 0.70 c.How long does the trip take according to a clock on the spacecraft?

A)1.2 s
B)1.3 s
C)1.5 s
D)1.8 s

Answer 3

1.3 s

Question 4

An observer on the Earth sees the U.S.S.Enterprise approaching from one direction at 0.600 c and a Klingon Battle Cruiser approaching from the opposite direction at 0.800 c.According to Mr.Spock,who is aboard the Enterprise,what is the speed of the Klingon Battle Cruiser?

A)0.200 c
B)0.800 c
C)0.95 c
D)1.40 c
E)None are correct.

Question 5

A spacecraft travels along a straight line from the Earth to the Moon a distance of 3.84 * 10⁸ m.Its speed measured on Earth is 0.70 c.How long does the trip take according to a clock on Earth?

A)1.2 s
B)1.3 s
C)1.5 s
D)1.8 s

Question 6

Two observers standing upright on their feet,move horizontally past each other and look at each other.The acceleration of both is zero and their relative speed is 0.500 c.Observer one looks at observer two and sees that she looks thinner than she is when she isn't moving.What does observer two see?

A)Observer one looks wider than she is when she isn't moving.
B)Observer one looks thinner than she is when she isn't moving.
C)Observer one looks the same as when she isn't moving.
D)Observer one looks like a vertical line with no width.

Question 7

An astronaut on the space shuttle traveling at a speed of 0.70 c is holding a meter stick parallel to the direction of motion.If an observer on Earth could observe the meter stick,what length of the meter stick would he measure?

A)0.71 m
B)1.0 m
C)1.2 m
D)1.8 m
E)2.1 m

Question 8

How much energy is released when a neutron (rest mass 939.6 MeV/c²)decays into a proton (rest mass 938.3 MeV/c²),an electron (rest mass 0.511 MeV/c²)and an anti-electron neutrino (rest mass approximately zero)?

A)789 keV
B)1.81 MeV
C)1.88 GeV
D)None are correct.

Question 9

An observer on the Earth sees the U.S.S.Enterprise approaching from one direction at 0.60 c and a Klingon Battle Cruiser approaching from the opposite direction.According to Mr.Spock,who is aboard the Enterprise,the Klingon Battle Cruiser is approaching the Enterprise,that 0.80 c.What is the speed of the Klingon Battle Cruiser as observed from Earth?

A)0.20 c
B)0.45 c
C)0.32 c
D)0.38 c
E)None are correct.

Question 10

Sam sees two events as simultaneous: (i)event A occurs at the point (0,0,0)at the instant 0:00:00 Universal time;
(ii.event B occurs at the point (569 m,0,0)at the same moment.
Tim,moving past Sam with a velocity of (0.998 c)",also observes the two events.Relative to the time Tim measures for event A,when does Tim see event B occur?

A)3.74 µs before event A
B)3.74 µs after event A
C)29.9 µs before event A
D)29.9 µs after event A
E)at the same time as event A

Question 11

A new particle is discovered at Stanford Linear Accelerator.If the total energy of the particle is 17.0 GeV and its momentum is 5.00 GeV/c,what is the rest mass of the particle?

A)15.5 GeV/c²
B)16.2 GeV/c²
C)12.0 GeV/c²
D)17.0 GeV/c²

Question 12

A spacecraft travels along a straight line from the Earth to the Moon a distance of 3.84 * 10⁸ m.Its speed measured on Earth is 0.70 c.Determine the distance between the Earth and Moon if it were measured by a person on the spacecraft.

A)1.0 * 10⁸ m
B)2.4 * 10⁸ m
C)2.7 * 10⁸ m
D)3.1 * 10⁸ m

Question 13

A new particle is discovered at Stanford Linear Accelerator whose rest mass is 12.0 GeV/c².If the total energy of the particle is 17.0 GeV,what is the momentum of this new particle?

A)12.0 GeV/c
B)7.03 GeV/c
C)5.00 GeV/c
D)9.85 GeV/c

Question 14

Two observers move past each other and look at each other's clock.The acceleration of both is zero and their relative speed is 0.750 c.Observer one looks at observer two's clock and sees that it's running more slowly than hers.What does observer two see?

A)Observer one's clock is running more quickly than her clock.
B)Observer one's clock is running more slowly than her clock.
C)Observer one's clock is running at the same rate as her clock.
D)Observer one's clock has stopped running.

Question 15

Sam sees two events as simultaneous:
i.event A occurs at the point (0,0,0)at the instant 0:00:00 Universal time;
ii.event B occurs at the point (x_B,0,0)at the same moment.
Tim,moving past Sam with a velocity of (0.998 c)",also observes the two events and sees that event B happened 3.74 µs after event A. Then x_B is

A)+71.1 m.
B)-71.1 m.
C)+569 m.
D)-569 m.

Question 16

Right before takeoff,a passenger on a plane flying from town A to town B synchronizes his clock with the clock of his friend waiting for him in town B. The plane flies without interruption at a constant velocity of 280 m/s. The moment the plane touches the ground the two friends check simultaneously the indication of their clocks.The clock of the passenger on the plane shows that it takes exactly 7.50 h to travel from A to B. Ignoring any effects of acceleration,the difference between the readings of the clocks B and A is

A)11.8 ns.
B)-11.8 ns.
C)23.5 ns.

Question 17

Right before takeoff,a passenger on a plane flying from town A to town B synchronizes his clock with the clock of his friend waiting for him in town B. The plane flies without interruption at a constant velocity of 285 m/s.The moment the plane touches the ground the two friends check simultaneously the indication of their clocks.The difference between the readings of the clocks B and A is 4.88 ns.Ignoring any effects of acceleration,the clock A of the passenger on the plane indicated that the flight took

A)1.00 h.
B)2.00 h.
C)3.00 h.
D)4.00 h.
E) 5.00 h.

Question 18

A new particle is discovered at Stanford Linear Accelerator whose rest mass is 12.0 GeV/c².If the momentum of this new particle was 5.00 GeV/c,then what would be its total energy?

A)7.00 GeV
B)12.0 GeV
C)13.0 GeV
D)17.0 GeV

Question 19

An observer on the Earth sees the U.S.S.Enterprise approaching from one direction at 0.600 c and a Klingon Battle Cruiser approaching from the opposite direction at 0.800 c.According to Mr.Spock,who is aboard the Enterprise,what is the speed of the Klingon Battle Cruiser?

A)0.200 c
B)0.800 c
C)1.40 c
D)None are correct.

Question 20

An astronaut on the space shuttle traveling at a speed of 0.70 c is holding a meter stick parallel to the direction of motion.What is the length of the meter stick as measured by another astronaut on the shuttle?

A)0.74 m
B)1.0 m
C)1.2 m
D).8 m
E)2.1 m

Question 21

A laser with wavelength of 632.8 nm is used to excite a gas of atoms which are moving atom that is moving away from the laser at 1.2 * 10⁶ m/s.What is the wavelength of the radiation that these atoms strongly absorb?

A)632.8 nm
B)635.3 nm
C)630.3 nm
D)629.1 nm
E)634.4 nm

Question 22

By what percentage must the speed of an electron travelling at 2.968 *10⁸ m/s be increased to increase its energy by 150%? The speed of light is 2.9979 * 10⁸ m/s.

A)1.4 %
B)0.56 %
C)0.87 %
D)0.29 %
E)1.0 %

Question 23

What is the Schwarzschild radius of an electron (m = 9.11 * 10^-31 kg)?

A)1.35 * 10^-57 m
B)1.98 * 10^-46 m
C)3.04 * 10^-39 m
D)2.98 * 10^-38 m
E)2.43 * 10^-12 m

Question 24

A 50-meter spaceship (as measured in the rest frame)is travelling at 0.6c relative to a stationary observer.How long does the spaceship appear to the stationary observer?

A)35 m
B)40 m
C)45 m
D)55 m
E)60 m

Question 25

An electron travelling is at 2.968 * 10⁸ m/s,what is the new speed of the electron if its energy is increased by150%? The speed of light is 2.9979 * 10⁸ m/s.

A)2.992 * 10⁸ m/s
B)2.985 * 10⁸ m/s
C)2.977 * 10⁸ m/s
D)2.968 * 10⁸ m/s
E)3.64 * 10⁸ m/s

Question 26

Albert is sitting in his office when you go by in a high-speed train at the speed of 80% of the speed of light.Both you and Albert have a meter stick,held parallel to the direction of travel.How long does Albert see you meter stick and how long does his stick appear to you?

A)Option A
B)Option B
C)Option C
D)Option D
E)Option E

Question 27

How fast would a 50-meter spaceship (as measured in the rest frame)have to travel to appear 35 meter to a stationary observer?

A)0.25 c
B)0.60 c
C)0.71 c
D)1.0 c
E)1.23 c

Question 28

A laser with wavelength of 633 nm is used to excite a gas of atoms which strongly absorb radiation at 638 nm.Which gas atoms will absorb the laser radiation best?

A)An atom that is moving toward the laser at 2.4 * 10⁶ m/s.
B)An atom that is moving away from the laser at 2.4 * 10⁶ m/s.
C)An atom that is moving away from the laser at 1.2 * 10⁶ m/s.
D)An atom that is moving toward the laser at 1.2 * 10⁶ m/s.
E)An atom that is that is at rest with respect to the laser.

Question 29

The Schwarzschild radius of muon is 2.79 * 10^-55 m.What is the mass of a muon?

A)1.88 * 10^-28 kg
B)9.11 * 10^-31 kg
C)4.36 * 10^-26 kg
D)1.67 * 10^-27 kg
E)2.06 * 10^-29 kg

Question 30

If our Sun were to suddenly explode,how long after the explosion would it take observers on Earth to notice?

A)0 s
B)10 s
C)3 minutes
D)5 minutes
E)8 minutes

Question 31

A set of twins,Bobby and Betty,are born on the Earth.Bobby sets off to a distant planet at high speed,arrives,and heads back to Earth.Betty remains on Earth.In Bobby's frame he is at rest and Betty is moving so,according to Einstein,he has aged 20 years while Betty has aged only 2.In Betty's frame she is at rest,so she has aged 20 years and Bobby has only aged 2.Who will be older when Bobby and Betty meet again?

A)Bobby
B)Betty
C)They both seem to be older to the other person.
D)They both seem to be younger than the other person.
E)They are the same age.

Question 32

In Jules Verne's classic Around the World in Eighty Days,Phileas Fogg travels around the world in,according to his calculation,81 days.Due to crossing the International Date Line he actually made it only 80 days.How fast would his descendent have to travel in his space ship in order for time dilation to make 7.0 days in his frame be measured as 8.0 days to observers on the Earth?

A)0.23 c
B)0.35 c
C)0.48 c
D)0.88 c
E)0.94 c

Question 33

A space ship travelling at 55% the speed of light relative to a stationary observer shoots a probe to a receiving ship moving at 65% the speed of light relative to the observer in the same direction.The speed of the probe relative to the first ship is 80% the speed of light.How fast does the receiving ship perceive the speed of the probe to be?

A)0.11 c
B)0.23 c
C)0.54 c
D)0.74 c
E)0.89 c

Question 34

Which quantity is invariant,i.e.,has the same value,in all reference frames?

A)Time, $\Delta$ t
B)Space, $\Delta$ x
C)Velocity,v
D)Spacetime interval,[( $\Delta$ r)² - c²( $\Delta$ t)²]^1/2

Question 35

If spaceship A is travelling at 70% the speed of light relative to an observer at rest,and spaceship B is travelling at 90% the speed of light relative to an observer at rest,which of the following have the greatest velocity as measured by an observer in spaceship B?

A)A cannon shot from A to B at 50% the speed of light as measured in A's reference frame.
B)A ball thrown from B to A at 50% the speed of light as measured in B's reference frame.
C)A particle beam shot from a stationary observer to B at 70% the speed of light as measured in stationary reference frame.
D)A beam of light shot from A to B travelling at the speed of light in A's reference frame.
E)All of the choices have the same velocity as measured in B's reference frame.

Question 36

By what percentage must the energy of an electron travelling at 2.968 * 10⁸ m/s be increased to increase its speed by 1%? The speed of light is 2.9979 * 10⁸ m/s.

A)1%
B)2%
C)150%
D)370 %
E)450%

Question 37

"Fat Man," the atomic bomb dropped on Nagasaki at the end of World War II released approximately 88 * 10¹² J of explosive energy.How much mass was converted into energy in this bomb?

A)0.88 g
B)0.98 g
C)1.1 g
D)2.1 g
E)2.9 * 10⁵ kg

Question 38

A spaceship is travelling at 0.6c relative to a stationary observer and appears to be 30 m long to the stationary observer.How long is the spaceship in the spaceship's rest frame?

A)25 m
B)42 m
C)35 m
D)38 m
E)47 m

Question 39

A wedge-shaped space ship has a width of 20 m and a length of 50 m and is shaped like and isosceles triangle.What is the angle between the base of the ship and the side of the ship as measured by a stationary observer if the ship is travelling by at a speed of 40% the speed of light?

A)22.3 ^$\circ$
B)34.5 ^$\circ$
C)43.6 ^$\circ$
D)77.7 ^$\circ$
E)88.6 ^$\circ$

Question 40

The International Space Station orbits 350 km above the Earth's surface at a speed of 27700 km/hr.It takes approximately 1.5 hours to complete each orbit.At the same moment in 2008,two clocks mark the ten year anniversary of the Station orbiting the Earth.Both clocks are accurate to 1 ms,but one is on the Earth and the other is on the Station itself.How does the reading on the Station's clock compare with that of the Earth-based clock,which reads exactly 10 years?

A)They are the same,exactly 10 years.
B)The Station's clock reads 0.10 s less than 10 years.
C)The Station's clock reads 0.10 s more than 10 years.
D)The Station's clock reads 0.20 s less than 10 years.
E)The Station's clock reads 0.20 s more than 10 years.

Question 41

A cosmic ray muon travels down through the atmosphere,travelling from the top of a 5.0-km tall mountain to sea level in 17 $\mu$ s as measured by astronomers on Earth.What height would one travelling with the muon observe the mountain to be? Use 3.0 * 10⁸ for the speed of light.

A)0.098 km
B)0.19 km
C)0.70 km
D)0.99 km

Question 42

An electron at the Stanford Linear Accelerator has a kinetic energy of 20 GeV.The magnitude of the momentum of the electron is

A)5.5 * 10^-15 kg.m/s.
B)4.9 * 10^-16 kg.m/s.
C)1.1 * 10^-17 kg.m/s.
D)7.5 * 10^-18 kg.m/s.

Question 43

What is the difference in time-of-flight (the elapsed time)required for pions (rest mass 139.5 MeV/c²)and kaons (rest mass 497 MeV/c²)each with momentum 150 MeV/c to travel 55 cm? Use 3.0 x 10⁸ for the speed of light.

A)1.8 ns
B)3.8 ns
C)4.0 ns
D)4.1 ns

Question 44

The starship Enterprise has a length of 305 m in its rest frame.What will be its length,as observed by a stationary observer,when motoring along at Warp 0.952,that is to say 95.2% of the speed of light?

A)93.3 m
B)95.2 m
C)297 m
D)305 m
E)997 m

Question 45

A rectangular box in a rocket travelling past the Earth at 0.50 c appears to people on the Earth to be a perfect cube,0.50 m on a side.What is the proper volume of the box?

A)0.11 m³
B)0.12 m³
C)0.14 m³
D)0.18 m³
E)0.19 m³

Question 46

What is the relative speed between two objects approaching each other if each is travelling at speed of 0.6 c as measured by an observer on Earth?

A)0.72 c
B)0.66 c
C)0.88 c
D)1.2 c

Question 47

The length of a moving meter stick is 75 cm.What is its speed parallel to its length?

A)0.25 c
B)0.50 c
C)0.66 c
D)0.78 c

Question 48

What is the energy of a particle with speed of 0.8 cand momentum of 10^-20 Ns?

A)0.8 * 10^-20 J
B)3.8 * 10^-12 J
C)2.4 * 10^-13 J
D)1.6 * 10^-28 J

Question 49

The rest energy of an electron is 0.511 MeV,and its rest mass is 0.511 MeV/c². If an electron has a speed of 99% that of light,what fraction of its total energy is in the form of kinetic energy?

A)76%
B)50%
C)68%
D)86%

Question 50

A rocket ship travels to the Sun (1.51 * 10¹¹ m)in exactly 13 hours.The distance appears to be shortened,from the rocket pilot's point of view,by how much?

A)8730 km
B)17,600 km
C)8.2 * 10⁵ km
D)1.65 * 10⁶ km

Question 51

If an electron (rest mass = 0.511 MeV/c²)has a speed of 99% of that of light,what is its total energy?

A)0.511 MeV
B)0.750 MeV
C)3.62 MeV
D)7.33 MeV
E)19.2 MeV

Question 52

How fast must you be traveling relative to a source of blue light (480 nm)for the light to appear shifted towards the red by 10 nm?

A)0.02 c
B)0.10 c
C)0.12 c
D)0.96 c
E)0.98 c

Question 53

Suppose a clock at rest measures 20 s for a task.The speed of the clock that would measure 10 s for the same task is

A)0.22 c.
B)0.59 c.
C)0.69 c.
D)0.87 c.

Question 54

A spaceship is traveling directly towards a stationary asteroid with a speed equal to one-half of the speed of light as measured by someone on the asteroid.The spaceship turns on its headlights and the light is observed by the crew of the spaceship and by the person on the asteroid.Compare the speed of the light as observed by someone on the spaceship to the speed of the light as observed by someone on the asteroid.

A)The crew of the spaceship observes the light traveling faster.
B)The person on the asteroid observes the light traveling faster.
C)Everyone measures the speed of the light to be the same.

Question 55

A 1-g particle has momentum of magnitude 4 * 10⁵ kg m/s.The speed of the particle is

A)40 * 10⁸ m/s.
B)2.4 * 10⁸ m/s.
C)1.8 * 10⁸ m/s.
D)1.1 * 10⁸ m/s.

Question 56

Two stationary space stations are separated by a distance of 20 light-years as measured by someone on one of the space stations.A spaceship traveling at 0.90 c relative to the space stations passes by one of the space stations heading directly towards the other one.How long will it take to reach the other space station as measured by someone on the spaceship?

A)7.0 years
B)8.7 years
C)9.7 years
D)22.2 years
E)24.7 years

Question 57

A spacecraft travels a distance of 10^-3 light-years in 20 hours as measured by an observer stationed on Earth.How long does the journey take as measured by the captain of the spacecraft?

A)18 hours
B)20 hours
C)24 hours
D)14 hours

Question 58

A beam of pions (a pion with rest mass 139.5 MeV/c²)travels down a beam pipe in a laboratory such that the pions have kinetic energy equal to half their rest energy.The pion lifetime is 26 ns.Given this information,how far,on average,will the pions travel in the lab before decaying? Use 3.0 x 10⁸ for the speed of light.

A)5.8 m
B)8.7 m
C)6.8 m
D)4.5 m
E)5.2 m

Question 59

Two rockets approach each other;each rocket has a speed of 0.65 c in Earth's frame of reference.The speed of one rocket in the other's frame of reference is

A)0.91c.
B)0.72 c.
C)0.66 c.
D)0.54 c.

Question 60

A proton observed to have a momentum of 2.0 GeV/c is moving with what velocity relative to the observer?

A)0.22 c
B)0.47 c
C)0.68 c
D)0.91 c
E)2.13 c

Question 61

In the context of special relativity,which of these statements are true?
a) The laws of physics are the same in each reference frame, independent of the motion of the reference frame.
b) The speed of light, c, is the same in every reference frame.
c) Light can travel faster than 3.0 108 m/s
d) Time is the same in all reference frames.
e) The length of an object is the same in all frames.

A) None of the statements are true.
B) d only is true.
C) a and b are true.
D) c and e are true.
E) All statements are true.