Question 1

How fast must a proton move so that its kinetic energy is 80% of its total energy?

Accepted Answer

A) 0.020c 
B) 0.87c 
C) 0.92c 
D) 0.98c 
E) 0.80c 
A) 0.020c 
B) 0.87c 
C) 0.92c 
D) 0.98c 
E) 0.80c

Question 2

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?

Accepted Answer

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

Question 3

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?

Accepted Answer

A) 74.2 ly 
B) 9.75 ly 
C) 21.5 ly 
D) 56.5 ly 
A) 74.2 ly 
B) 9.75 ly 
C) 21.5 ly 
D) 56.5 ly

Question 4

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?

Accepted Answer

A) 300 min 
B) 150 min 
C) 75 min 
D) 0 min 
E) 113 min 
A) 300 min 
B) 150 min 
C) 75 min 
D) 0 min 
E) 113 min

Question 5

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?

Accepted Answer

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

Question 6

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?

Accepted Answer

A) 0 min 
B) 180 min 
C) 90 min 
D) 360 min 
E) 113 min 
A) 0 min 
B) 180 min 
C) 90 min 
D) 360 min 
E) 113 min

Question 7

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?

Accepted Answer

A) Δt 
B) more than Δt 
C) less than Δt 
D) The answer depends on whether they are moving toward her or away from her. 
A) Δt 
B) more than Δt 
C) less than Δt 
D) The answer depends on whether they are moving toward her or away from her.

Question 8

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?

Accepted Answer

(a)0.959c = 2.88 × 1

Question 9

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?

Accepted Answer

A) 0.80c 
B) 0.60c 
C) 0.50c 
D) 0.70c 
E) 0.90c 
A) 0.80c 
B) 0.60c 
C) 0.50c 
D) 0.70c 
E) 0.90c

Question 10

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,mproton = 1.67 × 10-27 kg)

Accepted Answer

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 
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 11

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)

Accepted Answer

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 
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 12

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?

Accepted Answer

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

Question 13

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,

Accepted Answer

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. 
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 14

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,mel = 9.11 × 10-31 kg)

Accepted Answer

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 
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 15

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,mel = 9.11 × 10-31 kg)

Accepted Answer

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

Question 16

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?

Accepted Answer

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 
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 17

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,mproton = 1.67 × 10-27 kg)

Accepted Answer

A) 1.3 pJ 
B) 1.6 pJ 
C) 3.0 pJ 
D) 2.2 pJ 
E) 2.5 pJ 
A) 1.3 pJ 
B) 1.6 pJ 
C) 3.0 pJ 
D) 2.2 pJ 
E) 2.5 pJ

Question 18

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?

Accepted Answer

A) 0.25c 
B) 0.50c 
C) 0.71c 
D) 0.75c 
E) 0.87c 
A) 0.25c 
B) 0.50c 
C) 0.71c 
D) 0.75c 
E) 0.87c

Question 19

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

Accepted Answer

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. 
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 20

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)

Accepted Answer

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 
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

Exam 36: Relativity

How fast must a proton move so that its kinetic energy is 80% of its total energy?

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 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 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?

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?

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 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,mproton = 1.67 × 10-27 kg)

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)

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 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,

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,mel = 9.11 × 10-31 kg)

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,mel = 9.11 × 10-31 kg)

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 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,mproton = 1.67 × 10-27 kg)

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?

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

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)

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Kinematics in One Dimension

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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)

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)

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)

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 relativistic proton has a momentum of 1.0 × 10^-17kg ∙ 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)

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)