# Quiz 36: Relativity

Physics & Astronomy

Q 1Q 1

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
A) the light will reach the front of the rocket at the same instant that it reaches the back of the rocket.
B) the light will reach the front of the rocket before it reaches the back of the rocket.
C) the light will reach the front of the rocket after it reaches the back of the rocket.

Free

Multiple Choice

C

Q 2Q 2

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 in the rocket
A) the light will reach the front of the rocket at the same instant that it reaches the back of the rocket.
B) the light will reach the front of the rocket before it reaches the back of the rocket.
C) the light will reach the front of the rocket after it reaches the back of the rocket.

Free

Multiple Choice

A

Q 3Q 3

An astronaut in an inertial reference frame measures a time interval Δt between her heartbeats. What will observers in all other inertial reference frames measure for the time interval between her heartbeats?
A) Δt
B) more thanΔt
C) less than Δt
D) The answer depends on whether they are moving toward her or away from her.

Free

Multiple Choice

B

Q 4Q 4

You are a passenger on a spaceship. As the speed of the spaceship increases, you would observe that
A) the length of your spaceship is getting shorter.
B) the length of your spaceship is getting longer.
C) the length of your spaceship is not changing.

Free

Multiple Choice

Q 5Q 5

A star is moving towards the earth with a speed at 90% the speed of light. It emits light, which moves away from the star at the speed of light. Relative to us on earth, what is the speed of the light moving toward us from the star?
A) 0.90c
B) c
C) 1.1c
D) 1.20c
E) 1.9c

Free

Multiple Choice

Q 6Q 6

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

Free

Multiple Choice

Q 7Q 7

Astronaut Spud Nick is space-traveling from planet X to planet Y at a speed of 0.60c relative to the planets, which are at rest relative to each other. When he is precisely halfway between the planets, a distance of 1.0 light-hour from each one as measured in the planet frame, nuclear devices are detonated on each planet. The explosions are simultaneous in the frame of the planets. What is the difference in the 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
E) 113 min

Free

Multiple Choice

Q 8Q 8

Astronaut Mark Uri is space-traveling from planet X to planet Y at a speed of 0.65c relative to the planets, which are at rest relative to each other. When he is precisely halfway between the planets, a distance of 1.0 light-hour from each one as measured in the planet frame, nuclear devices are detonated on both planets. The explosions are simultaneous in Mark's frame. What is the difference in the 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
E) 113 min

Free

Multiple Choice

Q 9Q 9

As measured in Earth's rest frame, a spaceship traveling at 0.964c takes 11.2 y to travel between planets. How long does the trip take as measured by someone on the spaceship?
A) 2.98 y
B) 7.28 y
C) 42.1 y
D) 30.7 y

Free

Multiple Choice

Q 10Q 10

An astronaut on a spaceship moving at 0.927c says that the trip between two stationary stars took
7.49 y. How long does this journey take as measured by someone at rest relative to the two stars?
A) 20.0 y
B) 2.81 y
C) 4.05 y
D) 22.1 y

Free

Multiple Choice

Q 11Q 11

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 6.27 y. Find the speed of the spaceship in terms of the speed of light.
A) 0.779c
B) 0.687c
C) 0.975c
D) 0.384c

Free

Multiple Choice

Q 12Q 12

An unstable particle is moving at a speed of 2.6 × 10

^{8}m/s relative to a laboratory. Its lifetime is measured by a stationary observer in the laboratory to be 4.7 × 10^{-6}seconds. What is the lifetime of the particle, measured in the rest frame of the particle? (c = 3.00 × 10^{8}m/s)Free

Short Answer

Q 13Q 13

The closest known star to our solar system is Alpha Centauri, which is approximately 4.30 light years away. A spaceship with a constant speed of 0.800c relative to the earth travels from Earth to this star.
(a) How much time would elapse during the trip on a clock on board the spaceship?
(b) How much time would elapse during the trip on a clock on Earth?

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Essay

Q 14Q 14

A spaceship approaches the 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 the earth?
A) 69 beats per minute
B) 73 beats per minute
C) 65 beats per minute
D) 61 beats per minute
E) 80 beats per minute

Free

Multiple Choice

Q 15Q 15

A set of twins, Andrea and Courtney, are initially 10 years old. While Courtney remains on Earth, Andrea rides on a spaceship which travels away from Earth at a speed of 0.60c for five years (as measured by Courtney), then immediately turns around and comes back at 0.60c. When Andrea returns, Courtney is 20 years old. How old is Andrea upon her return?
A) 10 y
B) 12 y
C) 15 y
D) 18 y
E) 20 y

Free

Multiple Choice

Q 16Q 16

Relative to the frame of the observer making the measurement, at what speed parallel to its length is the length of a meterstick 60 cm?
A) 0.80c
B) 0.60c
C) 0.50c
D) 0.70c
E) 0.90c

Free

Multiple Choice

Q 17Q 17

An astronaut leaves Earth in a spaceship at a speed of 0.960c relative to an observer on Earth. The astronaut's destination is a star system 14.4 light-years away (one light-year is the distance light travels in one year.) According to the astronaut, how long does the trip take?
A) 14.4 y
B) 22.7 y
C) 9.34 y
D) 15.0 y
E) 4.20 y

Free

Multiple Choice

Q 18Q 18

In their common rest frame, two stars are 90.0 light-years (ly) apart. If they are 12.0 ly apart as measured by the navigator in a spaceship traveling between them, how fast is the spaceship moving? Express your answer in terms of c.
A) 0.991c
B) 0.986c
C) 0.980c
D) 0.972c

Free

Multiple Choice

Q 19Q 19

A particle in a 453 m-long linear particle accelerator is moving at 0.875c. How long does the particle accelerator appear to the particle?
A) 219 m
B) 589 m
C) 104 m
D) 936 m

Free

Multiple Choice

Q 20Q 20

A spaceship is moving between two distant stars at 0.932c. To someone in the ship, the distance between the two stars appears to be 26.9 light-years (ly). What is the distance between the stars in the rest frame of the stars?
A) 74.2 ly
B) 9.75 ly
C) 21.5 ly
D) 56.5 ly

Free

Multiple Choice

Q 21Q 21

Two space stations are at rest relative to each other and are 6.0 × 10

^{7}m apart, as measured by observers on the stations. A spaceship traveling from one station to the other at 0.90c relative to the stations passes both of them, one after the other. As measured by an observer in the spaceship, how long does it take to travel from one station to the other? (c = 3.00 × 10^{8}m/s) A) 97 ms B) 220 ms C) 510 ms D) 58 ms E) 39 msFree

Multiple Choice

Q 22Q 22

A spacecraft is measured by an observer on the ground to have a length of 53 m as it flies toward the earth with a speed 1.7 × 10

^{8}m/s. The spacecraft then lands and its length is again measured by the observer on the ground, this time while the spacecraft is at rest on the launchpad. What result does he now get for the length? (c = 3.00 × 10^{8}m/s)Free

Short Answer

Q 23Q 23

System S' has a velocity u = +0.45c relative to system S, as shown in the figure. The clocks of S and S'are synchronized at t = = 0 when the origins O and O' coincide. An event is observed in both systems. The event takes place at x = 600 m and at time t = 1.9 μs, as measured by an observer in S. What is the x'-coordinate of the event, measured by an observer in S' ?
A) 380 m
B) 340 m
C) 360 m
D) 350 m
E) 310 m

Free

Multiple Choice

Q 24Q 24

System S' has a velocity u = +0.56c relative to system S, as shown in the figure. The clocks of S and S'are synchronized at t = t' = 0 when the origins O and O' coincide. An event is observed in both systems. The event takes place at x = 800 m and at time t = 3.0 μs as measured by an observer in S. What is the time t' of the event, measured by an observer in S'?
A) 1.8 μs
B) -4.9 μs
C) 1.7 μs
D) 1.3 μs
E) 1.5 μs

Free

Multiple Choice

Q 25Q 25

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 0.350c 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) 0.866c
B) 1.091c
C) 0.883c
D) 0.788c

Free

Multiple Choice

Q 26Q 26

A spaceship approaching an asteroid at a speed of 0.60c launches a rocket forward with a speed of 0.40c relative to the spaceship. At what speed is the rocket approaching the asteroid as measured by an astronaut on the asteroid?
A) 0.81c
B) 1.0c
C) 0.76c
D) 0.64c
E) 0.96c

Free

Multiple Choice

Q 27Q 27

The captain of spaceship A observes enemy spaceship E escaping with a relative velocity of 0.48c, as shown in the figure. A missile M is fired from ship A, with a velocity of 0.72c relative to ship A. What is the relative velocity of approach of missile M, observed by the crew on ship E?
A) 0.37c
B) 0.24c
C) 0.34c
D) 0.30c
E) 0.27c

Free

Multiple Choice

Q 28Q 28

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 0.78c. The commander also observes ship A, advancing in the rear, with a relative velocity of 0.31c. What is the velocity of ship C, relative to an observer on ship A?
A) 0.88c
B) 0.38c
C) 1.4c
D) 0.62c
E) 1.1c

Free

Multiple Choice

Q 29Q 29

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 0.83c. The commander also observes ship A, advancing in the rear, with a relative velocity of 0.48c. As measured by commander on ship B, at what speed is ship A approaching ship C?
A) 1.3c
B) 0.94c
C) 0.25c
D) 0.58c
E) 2.2c

Free

Multiple Choice

Q 30Q 30

Consider three galaxies, Alpha, Beta and Gamma. An observer in Beta sees the other two galaxies each moving away from him in opposite directions at speed 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

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Multiple Choice

Q 31Q 31

Two spaceships are approaching one another, each at a speed of 0.28c relative to a stationary observer on Earth. What speed does an observer on one spaceship record for the other approaching spaceship?

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Short Answer

Q 32Q 32

A spaceship is moving away from the earth with a constant speed of 0.80c. The spaceship fires a 28-kg missile with a speed of 0.50c relative to the spaceship. What is the speed of the missile measured by observers on the earth if the missile is fired
(a) away from the earth?
(b) toward the earth?

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Essay

Q 33Q 33

At what speed relative to the lab will a 0.272-kg object have the same momentum as a 1.30-kg object that is moving at 0.515c relative to the lab?
A) 0.944c
B) 0.922c
C) 0.981c
D) 0.592c

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Multiple Choice

Q 34Q 34

A particle is moving at 0.75c relative to a lab on Earth. By what percentage is the Newtonian expression for its momentum in error? (The percentage error is the difference between the erroneous and correct values, divided by the correct one).
A) 34%
B) 28%
C) 38%
D) 43%

Free

Multiple Choice

Q 35Q 35

In the lab, a relativistic proton has a momentum of 1.00 × 10

^{-19}kg ∙ m/s and a rest energy of 0.150 nJ. What is the speed of the proton in the lab? (c = 3.00 × 10^{8}m/s, m_{proton}= 1.67 × 10^{-27}kg) A) 0.170c B) 0.196c C) 0.911c D) 0.930c E) 0.951cFree

Multiple Choice

Q 36Q 36

An electron has a speed of 0.643c. Through what potential difference would the electron need to be accelerated (starting from rest) in order to reach this speed? (c = 3.00 × 10

^{8}m/s, e = 1.60 × 10^{-19}C, M_{el}= 9.11 × 10^{-31}kg) A) 160 kV B) 130 kV C) 180 kV D) 200 kVFree

Multiple Choice

Q 37Q 37

An electron is accelerated from rest through a potential difference of 50.0 kV. What is the speed of the electron? (c = 3.00 × 10

^{8}m/s, e = 1.60 × 10^{-1}^{9}C, m_{el}= 9.11 × 10^{-31}kg) A) 1.24 × 10^{8}m/s B) 1.33 × 10^{8}m/s C) 3.24 × 10^{8}m/s D) 3.33 × 10^{8}m/s E) 4.12 × 10^{8}m/sFree

Multiple Choice

Q 38Q 38

In a certain particle accelerator, a proton has a kinetic energy that is equal to its rest energy. What is the speed of the proton relative to the accelerator?
A) 0.25c
B) 0.50c
C) 0.71c
D) 0.75c
E) 0.87c

Free

Multiple Choice

Q 39Q 39

How many joules of energy are required to accelerate a 1.0-kg mass from rest to a speed of 86.6% the speed of light? (c = 3.00 × 10

^{8}m/s) A) 1.8 × 10^{17}J B) 9.0 × 10^{16}J C) 2.7 × 10^{12}J D) 4.5 × 10^{9}J E) 3.0 × 10^{3}JFree

Multiple Choice

Q 40Q 40

How much work must be done to accelerate a particle of mass 2.1 × 10

^{-14}kg from a speed of 1.5 × 10^{8}to a speed of 2.5 × 10^{8}m/s? (c = 3.00 × 10^{8}m/s)Free

Short Answer

Q 41Q 41

Assume that a certain city consumes electrical energy at an average rate of 2.0 × 10

^{9}W. What would be the mass change in producing enough energy to keep this city running for 21 weeks? (c = 3.00 × 10^{8}m/s) A) 0.28 kg B) 0.32 kg C) 0.40 kg D) 0.48 kgFree

Multiple Choice

Q 42Q 42

During a nuclear reaction, the particles involved lose 4.8 × 10

^{-28 }kg of mass. How many joules of energy are released by this reaction? (c = 3.00 × 10^{8}m/s) A) 4.3 × 10^{-11}J B) 1.4 × 10^{-19}J C) 1.6 × 10^{-36}J D) 2.1 × 10^{-40}J E) 5.3 × 10^{-45}JFree

Multiple Choice

Q 43Q 43

During a nuclear reaction, 1.7 × 10

^{-4}J of energy is released. What is the resulting change in mass of the particles involved? (c = 3.00 × 10^{8}m/s) A) 5.1 × 10^{-4}kg B) 4.3 × 10^{-11}kg C) 1.5 × 10^{-13}kg D) 4.8 × 10^{-18}kg E) 1.9 × 10^{-21}kgFree

Multiple Choice

Q 44Q 44

An electron is accelerated from rest through a potential difference of 50.0 kV. What is the TOTAL energy of the electron? (c = 3.00 × 10

^{8}m/s, e = 1.60 × 10^{-19}C, m_{el}= 9.11 × 10^{-31}kg) A) 8.00 × 10^{-}^{15}J B) 16.2 × 10^{-15}J C) 8.20 × 10^{-14}J D) 9.00 × 10^{-14}J E) 16.2 × 10^{-14}JFree

Multiple Choice

Q 45Q 45

A relativistic proton has a momentum of 1.0 × 10

^{-17 }kg ∙ m/s and a rest energy of 0.15 nJ. What is the kinetic energy of this proton? (c = 3.00 × 10^{8}m/s, m_{proton}= 1.67 × 10^{-27}kg) A) 1.3 pJ B) 1.6 pJ C) 3.0 pJ D) 2.2 pJ E) 2.5 pJFree

Multiple Choice

Q 46Q 46

A proton in a certain particle accelerator has a kinetic energy that is equal to its rest energy. What is the TOTAL energy of the proton as measured by a physicist working with the accelerator? (c = 3.00 × 10

^{8}m/s, m_{proton}= 1.67 × 10^{-27}kg) A) 5.69 × 10^{-11}J B) 1.50 × 10^{-10}J C) 2.07 × 10^{-10}J D) 3.01 × 10^{-10}J E) 8.77 × 10^{-10}JFree

Multiple Choice

Q 47Q 47

A proton in a certain particle accelerator has a kinetic energy that is equal to its rest energy. What is the momentum of the proton as measured by a physicist working with the accelerator? (c = 3.00 × 10

^{8}m/s, m_{proton}= 1.67 × 10^{-27}kg) A) 2.51 × 10^{-19}kg ∙ m/s B) 2.89 × 10^{-19}kg ∙ m/s C) 4.34 × 10^{-19}kg ∙ m/s D) 5.01 × 10^{-19}kg ∙ m/s E) 8.68 × 10^{-19}kg ∙ m/sFree

Multiple Choice

Q 48Q 48

How fast must a proton move so that its kinetic energy is 80% of its total energy?
A) 0.020c
B) 0.87c
C) 0.92c
D) 0.98c
E) 0.80c

Free

Multiple Choice

Q 49Q 49

As a spaceship is moving toward Earth, an Earthling measures its length to be 325 m, while the captain on board radios that her spaceship's length is 1150 m. (c = 3.00 × 10

^{8}m/s) (a) How fast is the rocket moving relative to Earth? (b) What is the TOTAL energy of a 75.0-kg crewman as measured by (i) the captain in the rocket and (ii) the Earthling?Free

Essay