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 D

Question 2

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 E

Question 3

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 D

Question 4

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?

Accepted Answer

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

Question 5

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)

Accepted Answer

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 
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 6

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?

Accepted Answer

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

Question 7

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'?

Accepted Answer

A)  1.8 μs 
B)  -4.9 μs 
C)  1.7 μs 
D)  1.3 μs 
E)  1.5 μs 
A)  1.8 μs 
B)  -4.9 μs 
C)  1.7 μs 
D)  1.3 μs 
E)  1.5 μs

Question 8

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 9

How much work must be done to accelerate a particle of mass 2.1 × 10-14 kg from a speed of
1.5 × 108 m/s to a speed of 2.5 × 108 m/s? (c = 3.00 × 108 m/s)

Accepted Answer

Question 10

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 11

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?

Accepted Answer

A)  0.37c 
B)  0.24c 
C)  0.34c 
D)  0.30c 
E)  0.27c 
A)  0.37c 
B)  0.24c 
C)  0.34c 
D)  0.30c 
E)  0.27c

Question 12

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 13

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,mproton = 1.67 × 10-27 kg)

Accepted Answer

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 
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 14

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?

Accepted Answer

A)  0.90c 
B)  c 
C)  1.1c 
D)  1.20c 
E)  1.9c 
A)  0.90c 
B)  c 
C)  1.1c 
D)  1.20c 
E)  1.9c

Question 15

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,mproton = 1.67 × 10-27 kg)

Accepted Answer

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

Question 16

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 17

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)

Accepted Answer

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

Question 18

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

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 20

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

Exam 14: Special Relativity

How fast must a proton move so that its kinetic energy is 80% of its 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,mproton = 1.67 × 10-27 kg)

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?

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 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 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)

How much work must be done to accelerate a particle of mass 2.1 × 10-14 kg from a speed of 1.5 × 108 m/s to a speed of 2.5 × 108 m/s? (c = 3.00 × 108 m/s)

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)

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?

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)

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,mproton = 1.67 × 10-27 kg)

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?

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,mproton = 1.67 × 10-27 kg)

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?

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?

Foundations

A: Foundations

Motion in One Dimension

Acceleration

Momentum

Energy

Principle of Relativity

Interactions

Force

Work

Motion in a Plane

Motion in a Circle

Torque

Gravity

Periodic Motion

Waves in One Dimension

Waves in Two and Three Dimensions

Fluids

Entropy

Energy Transferred Thermally

Degradation of Energy

Electric Interactions

The Electric Field

Gausss Law

Work and Energy in Electrostatics

Charge Separation and Storage

Magnetic Interactions

Magnetic Fields of Charged Particles in Motion

Changing Magnetic Fields

Changing Electric Fields

Electric Circuits

Electronics

Ray Optics

Wave and Particle Optics

Filters

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)

During a nuclear reaction,the particles involved lose 4.8 × 10^-28kg of mass. How many joules of energy are released by this reaction? (c = 3.00 × 10⁸ m/s)

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)

How much work must be done to accelerate a particle of mass 2.1 × 10^-14kg from a speed of 1.5 × 10⁸m/s to a speed of 2.5 × 10⁸m/s? (c = 3.00 × 10⁸ m/s)

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)

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)

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_p_roton = 1.67 × 10^-27 kg)