Question 1

If a spaceship of proper length 40 m is measured to have a length 30 m, how fast is it moving?

Accepted Answer

A)  0.50 c 
B)  0.81 c 
C)  0.75 c 
D)  0.66 c 
E)  0.43 c 
A)  0.50 c 
B)  0.81 c 
C)  0.75 c 
D)  0.66 c 
E)  0.43 c

Question 2

In the lab, charged particles are directed toward one another, each at speed 0.500 c. What is the speed of the particles moving one way with respect to the particles moving the other way?

Accepted Answer

A)  1.25 c 
B)  1.00 c 
C)  0.800 c 
D)  0.500 c 
E)  0 
A)  1.25 c 
B)  1.00 c 
C)  0.800 c 
D)  0.500 c 
E)  0

Question 3

A pion has a mean lifetime of 25 ns in its own rest frame. A beam of pions traveling through the laboratory at a speed of 0.60 c is measured to have a mean lifetime of

Accepted Answer

A)  21 µs. 
B)  20 ns. 
C)  31 ns. 
D)  31 µs. 
A)  21 µs. 
B)  20 ns. 
C)  31 ns. 
D)  31 µs.

Question 4

Spaceships A and B are moving in the same direction. Spaceship A is moving at 0.80 c relative to a stationary observer, and spaceship B is moving at 0.80 c relative to spaceship A. What does the stationary observer find for the speed of spaceship B?

Accepted Answer

A)  1.6 c 
B)  1.3 c 
C)  1.0 c 
D)  0.78 c 
E)  0.98 c 
A)  1.6 c 
B)  1.3 c 
C)  1.0 c 
D)  0.78 c 
E)  0.98 c

Question 5

A star like the Sun has a luminosity (energy emitted per unit time) of 3.8 × 1026 W. How much mass must be turned into energy each second to produce this power?

Accepted Answer

A)  1.3 × 1018 kg 
B)  4.2 × 109 kg 
C)  5.6 × 105 kg 
D)  5.8 × 106 kg 
E)  1.5 × 1011 kg 
A)  1.3 × 1018 kg 
B)  4.2 × 109 kg 
C)  5.6 × 105 kg 
D)  5.8 × 106 kg 
E)  1.5 × 1011 kg

Question 6

The mean lifetime of muons is 2.2 μs. How fast are they moving if their measured mean lifetime is 1.1 μs?

Accepted Answer

A)  0.50 c 
B)  0.87 c 
C)  0.56 c 
D)  0.94 c 
E)  This cannot happen. 
A)  0.50 c 
B)  0.87 c 
C)  0.56 c 
D)  0.94 c 
E)  This cannot happen.

Question 7

Radioactive particles moving at 0.80 c are measured to have a half-life of 4.3 × 10-8 s. What is their half-life when at rest?

Accepted Answer

A)  7.2 × 10-8 s 
B)  2.6 × 10-8 s 
C)  3.4 × 10-8 s 
D)  1.6 × 10-8 s 
E)  1.7 × 10-7 s 
A)  7.2 × 10-8 s 
B)  2.6 × 10-8 s 
C)  3.4 × 10-8 s 
D)  1.6 × 10-8 s 
E)  1.7 × 10-7 s

Question 8

According to special relativity, what is the speed of light measured in a spaceship traveling at 0.40 c?

Accepted Answer

A)  0.60 c 
B)  1.4 c 
C)  0.86 c 
D)  1.0 c 
E)  None of these choices are correct. 
A)  0.60 c 
B)  1.4 c 
C)  0.86 c 
D)  1.0 c 
E)  None of these choices are correct.

Question 9

In a colliding-beam experiment, protons moving at 0.800 c in opposite directions strike one another. What is the speed of the incoming proton as viewed by the proton about to be hit?

Accepted Answer

A)  1.60 c 
B)  0.00 
C)  0.640 c 
D)  0.976 c 
E)  0.960 c 
A)  1.60 c 
B)  0.00 
C)  0.640 c 
D)  0.976 c 
E)  0.960 c

Question 10

What is the kinetic energy of a particle of mass m that has a total energy four times its rest energy?

Accepted Answer

A)  5 mc2 
B)  4 mc2 
C)  3 mc2 
D)  2 mc2 
E)  1 mc2 
A)  5 mc2 
B)  4 mc2 
C)  3 mc2 
D)  2 mc2 
E)  1 mc2

Question 11

A spaceship is observed from the Earth to be moving toward a star at a speed of 0.80 c. If the distance from the spaceship to the star is 1.6 ly as measured from Earth, how much time passes on the spaceship while traveling to the star?

Accepted Answer

A)  3.3 y 
B)  2.0 y 
C)  1.3 y 
D)  1.2 y 
E)  0.96 y 
A)  3.3 y 
B)  2.0 y 
C)  1.3 y 
D)  1.2 y 
E)  0.96 y

Question 12

A rocket speeding by the Earth is roughly cylindrical in shape and oriented such that its axis is parallel to its velocity. At rest, it is measured to have a radius of 15 m and a length of 150 m. When speeding by, its volume is measured to be 4.24 × 104 m3. What is its speed?

Accepted Answer

A)  0.917 c 
B)  0.774 c 
C)  0.678 c 
D)  Insufficient information is given. 
A)  0.917 c 
B)  0.774 c 
C)  0.678 c 
D)  Insufficient information is given.

Question 13

In relativistic mechanics, what law or principle does not apply?

Accepted Answer

A)  principle of relativity 
B)  conservation of momentum 
C)  conservation of energy 
D)  Gauss's Law 
E)  All these choices still apply under relativistic conditions. 
A)  principle of relativity 
B)  conservation of momentum 
C)  conservation of energy 
D)  Gauss's Law 
E)  All these choices still apply under relativistic conditions.

Question 14

Event 2 occurs a time Δt after event 1. If event 2 is caused by event 1, which of the following is true?

Accepted Answer

A)  The distance between event 1 and event 2 can be anything. 
B)  The distance between event 1 and event 2 is not more than c Δt. 
C)  There are frames of reference in which event 2 occurs before event 1. 
D)  There are frames of reference in which event 1 and event 2 are simultaneous. 
E)  None of these choices are correct. 
A)  The distance between event 1 and event 2 can be anything. 
B)  The distance between event 1 and event 2 is not more than c Δt. 
C)  There are frames of reference in which event 2 occurs before event 1. 
D)  There are frames of reference in which event 1 and event 2 are simultaneous. 
E)  None of these choices are correct.

Question 15

Two cars are traveling down the highway in the same direction. Car A is traveling at 30.0 m/s and car B is passing car A at a relative speed of 3.0 m/s. What is the speed of car B with respect to the highway?

Accepted Answer

A)  27.0 m/s 
B)  30.0 m/s 
C)  33.0 m/s 
D)  32.9 m/s 
E)  33.1 m/s 
A)  27.0 m/s 
B)  30.0 m/s 
C)  33.0 m/s 
D)  32.9 m/s 
E)  33.1 m/s

Question 16

A spear is thrown at a very high speed. As it passes, you measure its length to be half its normal length. From this you conclude that the spear must be moving at

Accepted Answer

A)  1.00 c 
B)  0.866 c 
C)  0.707 c 
D)  0.500 c 
E)  Not enough information 
A)  1.00 c 
B)  0.866 c 
C)  0.707 c 
D)  0.500 c 
E)  Not enough information

Question 17

Calculate the speed of a beam of neutrons with kinetic energies of 1.0 MeV. The mass of a neutron is 940 MeV/c2.

Accepted Answer

A)  799 m/s 
B)  640 km/s 
C)  9.8 × 106 m/s 
D)  1.4 × 107 m/s 
A)  799 m/s 
B)  640 km/s 
C)  9.8 × 106 m/s 
D)  1.4 × 107 m/s

Question 18

At what speed would a clock be moving if time dilation caused it to run slow by 50%?

Accepted Answer

A)  0.500 c 
B)  0.750 c 
C)  0.250 c 
D)  0.414 c 
E)  0.866 c 
A)  0.500 c 
B)  0.750 c 
C)  0.250 c 
D)  0.414 c 
E)  0.866 c

Question 19

What is the ratio of the relativistic momentum to the classical momentum?

Accepted Answer

A)  γ 
B)  γ − 1 
C)  γ + 1 
D)  γ−1 
E)  (γ − 1)−1 
A)  γ 
B)  γ − 1 
C)  γ + 1 
D)  γ−1 
E)  (γ − 1)−1

Question 20

What is the magnitude of the momentum of a proton moving at 0.95 c? (mp = 1.67 × 10-27 kg)

Accepted Answer

A)  5.0 × 10-18 kg·m/s 
B)  4.8 × 10-18 kg·m/s 
C)  1.5 × 10-18 kg·m/s 
D)  9.5 × 10-18 kg·m/s 
E)  4.4 × 10-18 kg·m/s 
A)  5.0 × 10-18 kg·m/s 
B)  4.8 × 10-18 kg·m/s 
C)  1.5 × 10-18 kg·m/s 
D)  9.5 × 10-18 kg·m/s 
E)  4.4 × 10-18 kg·m/s

Exam 26: Relativity

If a spaceship of proper length 40 m is measured to have a length 30 m, how fast is it moving?

In the lab, charged particles are directed toward one another, each at speed 0.500 c. What is the speed of the particles moving one way with respect to the particles moving the other way?

A pion has a mean lifetime of 25 ns in its own rest frame. A beam of pions traveling through the laboratory at a speed of 0.60 c is measured to have a mean lifetime of

Spaceships A and B are moving in the same direction. Spaceship A is moving at 0.80 c relative to a stationary observer, and spaceship B is moving at 0.80 c relative to spaceship A. What does the stationary observer find for the speed of spaceship B?

A star like the Sun has a luminosity (energy emitted per unit time) of 3.8 × 1026 W. How much mass must be turned into energy each second to produce this power?

The mean lifetime of muons is 2.2 μs. How fast are they moving if their measured mean lifetime is 1.1 μs?

Radioactive particles moving at 0.80 c are measured to have a half-life of 4.3 × 10-8 s. What is their half-life when at rest?

According to special relativity, what is the speed of light measured in a spaceship traveling at 0.40 c?

In a colliding-beam experiment, protons moving at 0.800 c in opposite directions strike one another. What is the speed of the incoming proton as viewed by the proton about to be hit?

What is the kinetic energy of a particle of mass m that has a total energy four times its rest energy?

A spaceship is observed from the Earth to be moving toward a star at a speed of 0.80 c. If the distance from the spaceship to the star is 1.6 ly as measured from Earth, how much time passes on the spaceship while traveling to the star?

A rocket speeding by the Earth is roughly cylindrical in shape and oriented such that its axis is parallel to its velocity. At rest, it is measured to have a radius of 15 m and a length of 150 m. When speeding by, its volume is measured to be 4.24 × 104 m3. What is its speed?

In relativistic mechanics, what law or principle does not apply?

Event 2 occurs a time Δt after event 1. If event 2 is caused by event 1, which of the following is true?

Two cars are traveling down the highway in the same direction. Car A is traveling at 30.0 m/s and car B is passing car A at a relative speed of 3.0 m/s. What is the speed of car B with respect to the highway?

A spear is thrown at a very high speed. As it passes, you measure its length to be half its normal length. From this you conclude that the spear must be moving at

Calculate the speed of a beam of neutrons with kinetic energies of 1.0 MeV. The mass of a neutron is 940 MeV/c2.

At what speed would a clock be moving if time dilation caused it to run slow by 50%?

What is the ratio of the relativistic momentum to the classical momentum?

What is the magnitude of the momentum of a proton moving at 0.95 c? (mp = 1.67 × 10-27 kg)

Introduction

Motion Along a Line

Motion in a Plane

Force and Newtons Laws of Motion

Circular Motion

Conservation of Energy

Linear Momentum

Torque and Angular Momentum

Fluids

Elasticity and Oscillations

Waves

Sound

Temperature and the Ideal Gas

Heat

Thermodynamics

Electric Forces and Fields

Electric Potential

Electric Current and Circuits

Magnetic Forces and Fields

Electromagnetic Induction

Alternating Current

Electromagnetic Waves

Reflection and Refraction of Light

Optical Instruments

Interference and Diffraction

Early Quantum Physics and the Photon

Quantum Physics

Nuclear Physics

Particle Physics

Filters

A star like the Sun has a luminosity (energy emitted per unit time) of 3.8 × 10²⁶ W. How much mass must be turned into energy each second to produce this power?

Radioactive particles moving at 0.80 c are measured to have a half-life of 4.3 × 10^-8 s. What is their half-life when at rest?

A rocket speeding by the Earth is roughly cylindrical in shape and oriented such that its axis is parallel to its velocity. At rest, it is measured to have a radius of 15 m and a length of 150 m. When speeding by, its volume is measured to be 4.24 × 10⁴ m³. What is its speed?

Calculate the speed of a beam of neutrons with kinetic energies of 1.0 MeV. The mass of a neutron is 940 MeV/c².

What is the magnitude of the momentum of a proton moving at 0.95 c? (m_p = 1.67 × 10^-27 kg)