Deck 29: Electromagnetic Induction

Question 1

Time dilation: 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 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

Answer 1

0.779c

Question 2

Total energy: 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

Answer 2

none of these

Question 3

Length contraction: In their common rest frame, two stars are 90.0 light-years (ly) apart. If they are 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

Answer 3

0.991c

Question 4

Velocity addition: 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

Question 5

Simultaneity: 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

Question 6

Time dilation: 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?

Question 7

Length contraction: 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 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

Question 8

Length contraction: 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.

Question 9

Time dilation: An astronaut on a spaceship moving at 0.927c says that the trip between two stationary stars took 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

Question 10

Time dilation: As measured in Earth's rest frame, a spaceship traveling at takes 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

Question 11

Length contraction: 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

Question 12

Time dilation: 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

Question 13

Time dilation: 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

Question 14

Length contraction: A particle in a 453 m-long linear particle accelerator is moving at How long does the particle accelerator appear to the particle?

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

Question 15

Length contraction: 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

Question 16

Simultaneity: 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.

Question 17

Simultaneity: Astronaut Mark Uri is space-traveling from planet X to planet Y at a speed of 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

Question 18

Time dilation: 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.

Question 19

Time dilation: An unstable particle is moving at a speed of 2.6 × 10⁸ 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 × 10⁸ m/s)

Question 20

Simultaneity: 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.

Question 21

Lorentz transformation: 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 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

Question 22

Kinetic energy: 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

Question 23

Velocity addition: 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

Question 24

Velocity addition: 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?

Question 25

Momentum: 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%

Question 26

Velocity addition: 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

Question 27

Doppler effect: A navigational beacon in deep space broadcasts at a radio frequency of 50 MHz. A spaceship approaches the beacon with a relative velocity of 0.40c. The spaceship passes the beacon and departs from it with a DIFFERENT relative velocity. The beacon signal is now detected at a frequency of 40 MHz. What is the new velocity of the spaceship relative to the beacon?

A) 0.20c
B) 0.22c
C) 0.24c
D) 0.26c
E) 0.28c

Question 28

Momentum: 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 × 10⁸ m/s, m_proton = 1.67 × 10^-27 kg)

A) 0.170c
B) 0.196c
C) 0.911c
D) 0.930c
E) 0.951c

Question 29

Kinetic energy: An electron is accelerated from rest through a potential difference of 50.0 kV. What is the speed of the electron? (c = 3.00 × 10⁸ m/s, e = 1.60 × 10^-19 C, m_el = 9.11 × 10^-31 kg)

A) 1.24 × 10⁸ m/s
B) 1.33 × 10⁸ m/s
C) 3.24 × 10⁸ m/s
D) 3.33 × 10⁸ m/s
E) 4.12 × 10⁸ m/s

Question 30

Velocity addition: 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 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

Question 31

Velocity addition: 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

Question 32

Length contraction: Two space stations are at rest relative to each other and are 6.0 × 10⁷ 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 × 10⁸ m/s)

A) 97 ms
B) 220 ms
C) 510 ms
D) 58 ms
E) 39 ms

Question 33

Velocity addition: 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?

Question 34

Momentum: 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

Question 35

Lorentz transformation: 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 = 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

Question 36

Length contraction: 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 × 10⁸ 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 × 10⁸ m/s)

Question 37

Velocity addition: 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

Question 38

Kinetic energy: 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 × 10⁸ 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 kV

Question 39

Doppler effect: A navigational beacon in deep space broadcasts at a radio frequency of 50 MHz. A spaceship approaches the beacon with a relative velocity of 0.40c. What is the frequency of the beacon radio signal that is detected on the ship?

A) 55 MHz
B) 60 MHz
C) 66 MHz
D) 71 MHz
E) 76 MHz

Question 40

Velocity addition: 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

Question 41

Total energy: 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 × 10⁸ 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 pJ

Question 42

Total energy: 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 × 10⁸ 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?

Question 43

Total energy: 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 × 10⁸ 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 J

Question 44

Total energy: 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 × 10⁸ 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 kg

Question 45

Total energy: Assume that a certain city consumes electrical energy at an average rate of 2.0 × 10⁹ W. What would be the mass change in producing enough energy to keep this city running for 21 weeks? (c = 3.00 × 10⁸ m/s)

A) 0.28 kg
B) 0.32 kg
C) 0.39 kg
D) 0.48 kg

Question 46

Total energy: 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 × 10⁸ 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 J

Question 47

Total energy: 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 × 10⁸ 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/s

Question 48

Total energy: 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

Question 49

Kinetic energy: 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 × 10⁸ m/s)

A) 1.8 × 10¹⁷ J
B) 9.0 × 10¹⁶ J
C) 2.7 × 10¹² J
D) 4.5 × 10⁹ J
E) 3.0 × 10³ J

Question 50

Total energy: 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 × 10⁸ 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 J

Question 51

Kinetic energy: How much work must be done to accelerate a particle of mass from a speed of to a speed of