Question 1

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 E

Question 2

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 A

Question 3

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 A

Question 4

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 5

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)

Accepted Answer

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

Question 6

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 7

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 8

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.

Accepted Answer

A)  the kinetic energy 
B)  the total energy 
C)  the linear momentum 
D)  more than one of these 
E)  none of these 
A)  the kinetic energy 
B)  the total energy 
C)  the linear momentum 
D)  more than one of these 
E)  none of these

Question 9

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?

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 10

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 11

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 12

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 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 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 14

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).

Accepted Answer

A)  34% 
B)  28% 
C)  38% 
D)  43% 
A)  34% 
B)  28% 
C)  38% 
D)  43%

Question 15

A particle in a 453 m-long linear particle accelerator is moving at   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 16

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 17

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 18

In their common rest frame, two stars are 90.0 light-years (ly) apart. If they are 12.0 ly 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.

Accepted Answer

A)  0.991c 
B)  0.986c 
C)  0.980c 
D)  0.972c 
A)  0.991c 
B)  0.986c 
C)  0.980c 
D)  0.972c

Question 19

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

Accepted Answer

The answer of How much work must be done to...

Question 20

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

Exam 36: Relativity

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)

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 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?

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 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?

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)

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.

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

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 their common rest frame, two stars are 90.0 light-years (ly) apart. If they are 12.0 ly 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.

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

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)

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

Work and Kinetic Energy

Interactions and Potential Energy

Impulse and Momentum

Rotation of a Rigid Body

Newtons Theory of Gravity

Fluids and Elasticity

Oscillations

Traveling Waves

Superposition

A Macroscopic Description of Matter

Work, Heat, and the First Law of Thermodynamics

The Micromacro Connection

Heat Engines and Refrigerators

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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

Wave Optics

Ray Optics

Optical Instruments

The Foundations of Modern Physics

Quantization

Wave Functions and Uncertainty

One-Dimensional Quantum Mechanics

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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)

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)

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)

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)

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)