Question 1

A 1.00-kg gold ingot is carried from the bottom of the Eiffel tower to the top,300 m above ground level.By what amount does its mass change? (c = 3.00 × 108 m/s)

Accepted Answer

A) Its mass does not change. 
B) Its mass increases by 3.27 × 10-14 kg 
C) Its mass decreases by 3.27 × 10-14 kg 
D) Its mass increases by 1.64 × 10-14 kg 
E) Its mass decreases by 1.64 × 10-14 kg 
A) Its mass does not change. 
B) Its mass increases by 3.27 × 10-14 kg 
C) Its mass decreases by 3.27 × 10-14 kg 
D) Its mass increases by 1.64 × 10-14 kg 
E) Its mass decreases by 1.64 × 10-14 kg B

Question 2

An alpha particle has a mass of 6.64 × 10-27 kg and a charge of 3.20 × 10-19 C,and it is traveling at 0.9650c.(c = 3.00 × 108 m/s),1 eV = 1.60 × 10-19 J)
(a)What is its rest energy (in GeV)?
(b)What is its total energy (in GeV)?
(c)What is its kinetic energy (in GeV)?

Accepted Answer

(a)3.74 GeV 
(b)14.2 GeV 
(c)10.5 GeV

Question 3

At age 21,you set out for a star that is 50 light-years from Earth.How fast would your spaceship have to travel in order to reach that star when you are 61 years old? One light-year is the distance light travels in one year.

Accepted Answer

A) 0.58c 
B) 0.68c 
C) 0.78c 
D) 0.88c 
E) 0.96c 
A) 0.58c 
B) 0.68c 
C) 0.78c 
D) 0.88c 
E) 0.96c C

Question 4

A spaceship is moving away from an asteroid with a speed of 0.80c relative to the asteroid.The spaceship then fires a missile with a speed of 0.50c relative to the spaceship.What is the speed of the missile measured by astronauts on the asteroid if the missile is fired away from the asteroid?

Accepted Answer

A) 0.30c 
B) 0.50c 
C) 0.93c 
D) 1.3c 
E) 0.65c 
A) 0.30c 
B) 0.50c 
C) 0.93c 
D) 1.3c 
E) 0.65c

Question 5

Two spaceships approach Earth from the same direction.One has a speed of 0.21c and the other a speed of 0.34c,both relative to Earth.What is the speed of one spaceship relative to the other?

Accepted Answer

A) 0.13c 
B) 0.14c 
C) 0.15c 
D) 0.16c 
E) 0.18c 
A) 0.13c 
B) 0.14c 
C) 0.15c 
D) 0.16c 
E) 0.18c

Question 6

During a reaction,170 µJ of energy is released.What change of mass would accompany this release? (c = 3.0 × 108 m/s)

Accepted Answer

A) 5.1 × 10-4 kg 
B) 1.5 × 10-13 kg 
C) 4.8 × 10-18 kg 
D) 1.9 × 10-21 kg 
A) 5.1 × 10-4 kg 
B) 1.5 × 10-13 kg 
C) 4.8 × 10-18 kg 
D) 1.9 × 10-21 kg

Question 7

How many joules of energy are required to accelerate a 1.0-kg rock from rest to a speed of 0.866c? (c = 3.0 × 108 m/s)

Accepted Answer

A) 1.8 × 1017 J 
B) 9.0 × 1016 J 
C) 3.0 × 103 J 
D) 3.3 × 1016 J 
A) 1.8 × 1017 J 
B) 9.0 × 1016 J 
C) 3.0 × 103 J 
D) 3.3 × 1016 J

Question 8

A star is moving toward Earth at 90% the speed of light.The star emits light,which moves away from the star at the speed of light.What do Earth-based astronomers measure for the speed of this light?

Accepted Answer

A) c 
B) 1.9c 
C) 1.2c 
D) 0.98c 
E) 0.95c 
A) c 
B) 1.9c 
C) 1.2c 
D) 0.98c 
E) 0.95c

Question 9

If an electron in the lab has a kinetic energy equal to twice its rest energy,what is its speed in the lab?

Accepted Answer

A) 0.84c 
B) 0.87c 
C) 0.89c 
D) 0.91c 
E) 0.94c 
A) 0.84c 
B) 0.87c 
C) 0.89c 
D) 0.91c 
E) 0.94c

Question 10

A pion is an unstable particle that has a mean lifetime of 2.55 × 10-8 s.This is the time interval between its creation in a nuclear process and its extinction into decay products,as measured in a frame of reference at rest with respect to the pion.An average pion is traveling at 0.230c relative to Earth.How far does it travel in its lifetime,relative to Earth?

Accepted Answer

A) 2.07 m 
B) 1.81 m 
C) 2.23 m 
D) 3.22 m 
E) 3.50 m 
A) 2.07 m 
B) 1.81 m 
C) 2.23 m 
D) 3.22 m 
E) 3.50 m

Question 11

A spaceship approaches 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 Earth?

Accepted Answer

A) 61 beats per minute 
B) 65 beats per minute 
C) 69 beats per minute 
D) 73 beats per minute 
E) 75 beats per minute 
A) 61 beats per minute 
B) 65 beats per minute 
C) 69 beats per minute 
D) 73 beats per minute 
E) 75 beats per minute

Question 12

An object with a rest mass of 0.456-kg is moving at 1.20 × 108 m/s.What is the magnitude of its momentum? (c = 3.00 × 108 m/s)

Accepted Answer

A) 5.47 × 107 kg ∙ m/s 
B) 5.57 × 107 kg ∙ m/s 
C) 5.67 × 107 kg ∙ m/s 
D) 5.87 × 107 kg ∙ m/s 
E) 5.97 × 107 kg ∙ m/s 
A) 5.47 × 107 kg ∙ m/s 
B) 5.57 × 107 kg ∙ m/s 
C) 5.67 × 107 kg ∙ m/s 
D) 5.87 × 107 kg ∙ m/s 
E) 5.97 × 107 kg ∙ m/s

Question 13

Someone in Earth's rest frame says that a spaceship's trip between two planets took 10.0 y,while an astronaut on the space ship says that the trip took $5.78 y$ What is the speed of the spaceship,assuming the planets are at essentially at rest?

Accepted Answer

A) 0.816 c 
B) 0.735 c 
C) 0.975 c 
D) 0.384 c 
A) 0.816 c 
B) 0.735 c 
C) 0.975 c 
D) 0.384 c

Question 14

A muon at rest decays in 2.2 μs.Moving at 99.00% the speed of light,it would be seen to "live" for how long?

Accepted Answer

The answer of A muon at rest decays in 2.2...

Question 15

What is the total energy of an electron moving with a speed of 0.950c? (c = 3.0 × 108 m/s,mel = 9.11 × 10-31 kg)

Accepted Answer

A) 2.6 × 10-13 J 
B) 8.2 × 10-14 J 
C) 1.1 × 10-13 J 
D) 1.2 × 10-14 J 
A) 2.6 × 10-13 J 
B) 8.2 × 10-14 J 
C) 1.1 × 10-13 J 
D) 1.2 × 10-14 J

Question 16

An astronaut on a spaceship moving at 0.927c says that the trip between two stationary stars took $4.26 \mathrm { y }$ How long does this journey appear to take to someone in the rest frame of the two stars?

Accepted Answer

A) 11.4 y 
B) 1.60 y 
C) 2.30 y 
D) 12.6 y 
A) 11.4 y 
B) 1.60 y 
C) 2.30 y 
D) 12.6 y

Question 17

The figure shows a right-angled construction frame ABC.When measured at rest,it has dimensions as follows: AB = 18.9 m,AC = 10.0 m,and BC = 16.0 m.This frame is now given a new velocity of 0.420c,relative to Earth,in a direction parallel to AC.How long is part BC of this frame with the new velocity as measured by Earth-based engineers?

Accepted Answer

A) 16.0 m 
B) 14.0 m 
C) 12.0 m 
D) 10.0 m 
E) 18.0 m 
A) 16.0 m 
B) 14.0 m 
C) 12.0 m 
D) 10.0 m 
E) 18.0 m

Question 18

Two stars are at rest relative to each other.In their common rest frame,these stars are 90.0 light-years apart.If they are measured to be $68.7 \text { light-years }$ apart by the navigator of a spaceship traveling between them,how fast is the spaceship moving relative to these stars?

Accepted Answer

A) 0.646c 
B) 0.604c 
C) 0.558c 
D) 0.505c 
A) 0.646c 
B) 0.604c 
C) 0.558c 
D) 0.505c

Question 19

How many MeV of energy is released during a reaction in which 1.67 × 10-25 kg of material is converted to energy? (c = 3.0 × 108 m/s,1 eV = 1.67 × 10-19 J)

Accepted Answer

A) 5.0 × 10-14 MeV 
B) 4.1 × 10-7 MeV 
C) 3.1 × 10-4 MeV 
D) 9.4 × 104 MeV 
A) 5.0 × 10-14 MeV 
B) 4.1 × 10-7 MeV 
C) 3.1 × 10-4 MeV 
D) 9.4 × 104 MeV

Question 20

Which of the following are basic postulates of special relativity? (There could be more than one correct choice.)

Accepted Answer

A) Nothing can travel faster than the speed of light. 
B) No material object can be accelerated to the speed of light. 
C) The speed of light is the same for all observers. 
D) The laws of physics are the same in all reference frames. 
E) The laws of physics are the same in all inertial reference frames. 
A) Nothing can travel faster than the speed of light. 
B) No material object can be accelerated to the speed of light. 
C) The speed of light is the same for all observers. 
D) The laws of physics are the same in all reference frames. 
E) The laws of physics are the same in all inertial reference frames.

Exam 26: Special Relativity

A 1.00-kg gold ingot is carried from the bottom of the Eiffel tower to the top,300 m above ground level.By what amount does its mass change? (c = 3.00 × 108 m/s)

An alpha particle has a mass of 6.64 × 10-27 kg and a charge of 3.20 × 10-19 C,and it is traveling at 0.9650c.(c = 3.00 × 108 m/s),1 eV = 1.60 × 10-19 J) (a)What is its rest energy (in GeV)? (b)What is its total energy (in GeV)? (c)What is its kinetic energy (in GeV)?

At age 21,you set out for a star that is 50 light-years from Earth.How fast would your spaceship have to travel in order to reach that star when you are 61 years old? One light-year is the distance light travels in one year.

A spaceship is moving away from an asteroid with a speed of 0.80c relative to the asteroid.The spaceship then fires a missile with a speed of 0.50c relative to the spaceship.What is the speed of the missile measured by astronauts on the asteroid if the missile is fired away from the asteroid?

Two spaceships approach Earth from the same direction.One has a speed of 0.21c and the other a speed of 0.34c,both relative to Earth.What is the speed of one spaceship relative to the other?

During a reaction,170 µJ of energy is released.What change of mass would accompany this release? (c = 3.0 × 108 m/s)

How many joules of energy are required to accelerate a 1.0-kg rock from rest to a speed of 0.866c? (c = 3.0 × 108 m/s)

A star is moving toward Earth at 90% the speed of light.The star emits light,which moves away from the star at the speed of light.What do Earth-based astronomers measure for the speed of this light?

If an electron in the lab has a kinetic energy equal to twice its rest energy,what is its speed in the lab?

A spaceship approaches 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 Earth?

An object with a rest mass of 0.456-kg is moving at 1.20 × 108 m/s.What is the magnitude of its momentum? (c = 3.00 × 108 m/s)

Someone in Earth's rest frame says that a spaceship's trip between two planets took 10.0 y,while an astronaut on the space ship says that the trip took 5.78y5.78 y5.78y What is the speed of the spaceship,assuming the planets are at essentially at rest?

A muon at rest decays in 2.2 μs.Moving at 99.00% the speed of light,it would be seen to "live" for how long?

What is the total energy of an electron moving with a speed of 0.950c? (c = 3.0 × 108 m/s,mel = 9.11 × 10-31 kg)

An astronaut on a spaceship moving at 0.927c says that the trip between two stationary stars took 4.26y4.26 \mathrm { y }4.26y How long does this journey appear to take to someone in the rest frame of the two stars?

How many MeV of energy is released during a reaction in which 1.67 × 10-25 kg of material is converted to energy? (c = 3.0 × 108 m/s,1 eV = 1.67 × 10-19 J)

Which of the following are basic postulates of special relativity? (There could be more than one correct choice.)

Introduction

Kinematics: Motion in One Dimension

Newtonian Mechanics

Applying Newtons Laws

Circular Motion

Impulse and Linear Momentum

Work and Energy

Extended Bodies at Rest

Rotational Motion

Gases

Static Fluids

Fluids in Motion

First Law of Thermodynamics

Second Law of Thermodynamics

Electric Charge force and Energy

The Electric Field

Dc Circuits

Magnetism

Electromagnetic Induction

Vibrational Motion

Mechanical Waves

Reflection and Refraction

Mirrors and Lenses

Wave Optics

Electromagnetic Waves

Quantum Optics

Atomic Physics

Nuclear Physics

Particle Physics

Filters

A 1.00-kg gold ingot is carried from the bottom of the Eiffel tower to the top,300 m above ground level.By what amount does its mass change? (c = 3.00 × 10⁸ m/s)

An alpha particle has a mass of 6.64 × 10^-27 kg and a charge of 3.20 × 10^-19 C,and it is traveling at 0.9650c.(c = 3.00 × 10⁸ m/s),1 eV = 1.60 × 10^-19 J) (a)What is its rest energy (in GeV)? (b)What is its total energy (in GeV)? (c)What is its kinetic energy (in GeV)?

During a reaction,170 µJ of energy is released.What change of mass would accompany this release? (c = 3.0 × 10⁸ m/s)

How many joules of energy are required to accelerate a 1.0-kg rock from rest to a speed of 0.866c? (c = 3.0 × 10⁸ m/s)

An object with a rest mass of 0.456-kg is moving at 1.20 × 10⁸ m/s.What is the magnitude of its momentum? (c = 3.00 × 10⁸ m/s)

Someone in Earth's rest frame says that a spaceship's trip between two planets took 10.0 y,while an astronaut on the space ship says that the trip took $5.78 y$ What is the speed of the spaceship,assuming the planets are at essentially at rest?

What is the total energy of an electron moving with a speed of 0.950c? (c = 3.0 × 10⁸ m/s,m_el = 9.11 × 10^-31 kg)

An astronaut on a spaceship moving at 0.927c says that the trip between two stationary stars took $4.26 \mathrm { y }$ How long does this journey appear to take to someone in the rest frame of the two stars?

How many MeV of energy is released during a reaction in which 1.67 × 10^-25 kg of material is converted to energy? (c = 3.0 × 10⁸ m/s,1 eV = 1.67 × 10^-19 J)