Question 1

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?

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 A

Question 2

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

Accepted Answer

1200 J

Question 3

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 C

Question 4

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 5

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?

Accepted Answer

A)  20.0 y 
B)  2.81 y 
C)  4.05 y 
D)  22.1 y 
A)  20.0 y 
B)  2.81 y 
C)  4.05 y 
D)  22.1 y

Question 6

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 7

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 8

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?

Accepted Answer

A)  1.3c 
B)  0.94c 
C)  0.25c 
D)  0.58c 
E)  2.2c 
A)  1.3c 
B)  0.94c 
C)  0.25c 
D)  0.58c 
E)  2.2c

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

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 11

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 12

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' ?

Accepted Answer

A)  380 m 
B)  340 m 
C)  360 m 
D)  350 m 
E)  310 m 
A)  380 m 
B)  340 m 
C)  360 m 
D)  350 m 
E)  310 m

Question 13

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 14

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 15

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 16

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 17

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

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 18

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 19

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, mel = 9.11 × 10-31 kg)

Accepted Answer

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 
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 20

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

Exam 36: Relativity

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?

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

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?

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?

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 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?

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?

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?

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

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)

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 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

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?

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, mel = 9.11 × 10-31 kg)

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?

Concepts of Motion

Kinematics in One Dimension

Vectors and Coordinate Systems

Kinematics in Two Dimensions

Force and Motion

Dynamics I: Motion Along a Line

Newtons Third Law

Dynamics Ii: Motion in a Plane

Impulse and Momentum

Energy

Work

Rotation of a Rigid Body

Newtons Theory of Gravity

Oscillations

Fluids and Elasticity

A Macroscopic Description of Matter

Work, Heat, and the First Law of Thermodynamics

The Micromacro Connection

Heat Engines and Refrigerators

Traveling Waves

Superpositions

Wave Optics

Ray Optics

Optical Instruments

Electric Charges and Forces

The Electric Field

Gausss Law

The Electric Potential

Potential and Field

Current and Resistance

Fundamentals of Circuits

The Magnetic Field

Electromagnetic Induction

Electromagnetic Fields and Waves

Ac Circuits

The Foundations of Modern Physics

Quantization

Wave Functions and Uncertainty

One-Dimensional Quantum Mechanics

Atomic Physics

Nuclear Physics

Filters

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

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 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 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)

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)