Question 1

A muon formed high in the Earth's atmosphere travels at a speed 0.870c for a distance of 4.00 km before it decays.What is the muon's lifetime as measured in its reference frame?

Accepted Answer

A) 3.1E-5 s 
B) 7.6E-6 s 
C) 1.5E-5 s 
D) 5.1E-5 s 
E) ​4.3E-5 s 
A) 3.1E-5 s 
B) 7.6E-6 s 
C) 1.5E-5 s 
D) 5.1E-5 s 
E) ​4.3E-5 s

Question 2

A spaceship of mass 106 kg is to be accelerated to 0.75c.How much energy does this require?

Accepted Answer

A) 13.61 × 1023 J 
B) 5.95 × 1023 J 
C) 5.06 × 1022 J 
D) ​4.61 × 1022 J 
E) ​27.00 × 1023 J 
A) 13.61 × 1023 J 
B) 5.95 × 1023 J 
C) 5.06 × 1022 J 
D) ​4.61 × 1022 J 
E) ​27.00 × 1023 J

Question 3

A particle of mass m is moving at speed v = c/2.At what speed does the particle have double the momentum that it has at ​v​ = ​c​/2?

Accepted Answer

A) There is no speed at which the particle can have double the momentum since it would require the particle to move at speed 
B)    
C)   
D)    
A) There is no speed at which the particle can have double the momentum since it would require the particle to move at speed 
B)    
C)   
D)

Question 4

If astronauts could travel at v = 0.90c,we on Earth would say it takes (4.2/0.90)= 4.7 years to reach Alpha Centauri,4.2 lightyears away.The astronauts disagree.How much time passes on the astronaut's clocks?

Accepted Answer

A) 2.0 years 
B) 2.4 years 
C) 1.4 years 
D) 3.0 years 
A) 2.0 years 
B) 2.4 years 
C) 1.4 years 
D) 3.0 years

Question 5

An object moves by an observer at 0.400c.The total energy of the object will be what factor times that of the rest energy?

Accepted Answer

A) 1.19 
B) 1.44 
C) 1.09 
D) 1.20 
E) ​1.38 
A) 1.19 
B) 1.44 
C) 1.09 
D) 1.20 
E) ​1.38

Question 6

A mass is bouncing on the end of a spring with a period T when measured by a ground observer.What would the period of oscillation be (as measured by the same observer)if the mass and spring were moving past the ground observer at a speed of 0.600c?

Accepted Answer

A) 0.440 T 
B) 1.25 T 
C) 0.600 T 
D) 1.67 T 
A) 0.440 T 
B) 1.25 T 
C) 0.600 T 
D) 1.67 T

Question 7

In a test of equipment the following procedure is carried out.Spacecraft №1 is traveling at 0.75c and fires a laser pulse in the forward direction at Spacecraft №2,which is testing its device that measures the speed of laser pulses as they pass by the spacecraft.Spacecraft №2 is traveling at 0.95c in a direction away from Spacecraft №1.The device is working properly,and the speed of the pulse as it passes is successfully measured.What is the speed of the laser pulse measured in this case?

Accepted Answer

A) 0.80c 
B) 0.70c 
C) c 
D) This is a question that cannot be answered without knowing in which reference frames the speeds given in the problem.If you agree,then this is the answer that you should choose. 
A) 0.80c 
B) 0.70c 
C) c 
D) This is a question that cannot be answered without knowing in which reference frames the speeds given in the problem.If you agree,then this is the answer that you should choose.

Question 8

Which statement regarding Einstein's theories is correct?​

Accepted Answer

A) ​According to special relativity,moving clocks run more slowly than those at rest,and according to general relativity,clocks higher in a gravity field run more quickly.. 
B) ​According to special relativity,moving clocks run more quickly than those at rest,and according to general relativity,clocks higher in a gravity field also run more quickly.. 
C) ​According to special relativity,moving clocks run more quickly than those at rest,and according to general relativity,clocks higher in a gravity field run more slowly.. 
D) ​According to special relativity,moving clocks run more quickly than those at rest,and according to general relativity,clocks higher in a gravity field also run more quickly. 
A) ​According to special relativity,moving clocks run more slowly than those at rest,and according to general relativity,clocks higher in a gravity field run more quickly.. 
B) ​According to special relativity,moving clocks run more quickly than those at rest,and according to general relativity,clocks higher in a gravity field also run more quickly.. 
C) ​According to special relativity,moving clocks run more quickly than those at rest,and according to general relativity,clocks higher in a gravity field run more slowly.. 
D) ​According to special relativity,moving clocks run more quickly than those at rest,and according to general relativity,clocks higher in a gravity field also run more quickly.

Question 9

The relativistic effect of time dilation has been verified by which of the following?

Accepted Answer

A) the discovery of black holes 
B) muon experiments 
C) twin experiments 
D) red shift in distant galaxies 
A) the discovery of black holes 
B) muon experiments 
C) twin experiments 
D) red shift in distant galaxies

Question 10

Einstein's theory of relativity is based in part on which one of the following postulates?

Accepted Answer

A) Mass and energy are equivalent. 
B) Space and time are absolutes. 
C) Energy is conserved only in elastic collisions. 
D) Speed of light in a vacuum is same for all observers regardless of source velocity. 
A) Mass and energy are equivalent. 
B) Space and time are absolutes. 
C) Energy is conserved only in elastic collisions. 
D) Speed of light in a vacuum is same for all observers regardless of source velocity.

Question 11

A boxcar without a front or a back is moving toward the right.Two electrons move through the boxcar,one moving from back to front toward the right,the other moving from front to back toward the left.According to me,each electron is moving with a speed of 0.8c,and the boxcar is moving with a speed of 0.6c.A passenger in the boxcar records how long it takes each electron to pass from one end of the boxcar to the other end.According to the passenger,which took longer?

Accepted Answer

A) the electron going from back to front 
B) the electron going from front to back 
C) They both took the same time. 
D) Since nothing can go faster than light,an electron cannot move toward the left with a speed of 0.8c through a boxcar moving toward the right with a speed of 0.6c. 
A) the electron going from back to front 
B) the electron going from front to back 
C) They both took the same time. 
D) Since nothing can go faster than light,an electron cannot move toward the left with a speed of 0.8c through a boxcar moving toward the right with a speed of 0.6c.

Question 12

The total energy of a particle

Accepted Answer

A) is not related to its relativistic momentum. 
B) increases with increasing relativistic momentum. 
C) decreases with increasing relativistic momentum. 
D) is a constant. 
A) is not related to its relativistic momentum. 
B) increases with increasing relativistic momentum. 
C) decreases with increasing relativistic momentum. 
D) is a constant.

Question 13

From a stationary position,I observe a moving boxcar,which has a mirror along the front wall,but it is open at the back of the boxcar.I send a flash of light from my flashlight and time the flash of light as it goes to the front of the boxcar and returns to the back of the boxcar.A passenger in the boxcar also times the round trip of the flash of light.Previously I had measured the time required for the round trip of a flash of light when the boxcar was stationary,and I call this the stationary time.Which two times are the same?

Accepted Answer

A) the time recorded on my watch and the previous stationary time 
B) the time recorded on the passenger's watch and the previous stationary time 
C) the time recorded on my watch and the time recorded on the passenger's watch 
D) None of the times are the same. 
A) the time recorded on my watch and the previous stationary time 
B) the time recorded on the passenger's watch and the previous stationary time 
C) the time recorded on my watch and the time recorded on the passenger's watch 
D) None of the times are the same.

Question 14

According to the special theory of relativity,if a 30-year old astronaut sent on a space mission is accelerated to speeds close to that of light,and then returns to Earth after 20 years as measured on Earth,what would be his biological age upon returning?

Accepted Answer

A) less than 50 years 
B) 50 years 
C) more than 50 years 
D) exactly 100 years 
A) less than 50 years 
B) 50 years 
C) more than 50 years 
D) exactly 100 years

Question 15

The significant result of the Michelson-Morley experiment was that it found

Accepted Answer

A) the ether moved with the Sun. 
B) the ether moved with the Earth. 
C) the speed of the ether wind was greater than expected. 
D) no effect. 
A) the ether moved with the Sun. 
B) the ether moved with the Earth. 
C) the speed of the ether wind was greater than expected. 
D) no effect.

Question 16

​What is the relativistic momentum of a proton traveling at 0.97c?

Accepted Answer

A) ​2.00E-18 kg·m/s 
B) ​2.81E-18 kg·m/s 
C) ​2.06E-18 kg·m/s 
D) ​2.89E-18 kg·m/s 
A) ​2.00E-18 kg·m/s 
B) ​2.81E-18 kg·m/s 
C) ​2.06E-18 kg·m/s 
D) ​2.89E-18 kg·m/s

Question 17

In an x-ray tube,high-speed electrons are slammed into a lead target,giving off x-rays.If the electrons are accelerated from rest through a potential difference of 160 000 volts,what speed do they have when they strike the target? (qe = 1.6 × 10−19 C,me = 9.11 × 10−31 kg,and c = 3.00 × 108 m/s)

Accepted Answer

A) 0.79c 
B) 0.65c 
C) 0.83c 
D) 0.49c 
E) ​0.48c 
A) 0.79c 
B) 0.65c 
C) 0.83c 
D) 0.49c 
E) ​0.48c

Question 18

The period of an oscillating weight on a spring in an inertial frame of reference is 2.5 s.What would be its speed if it were to move by an observer who measures its period as 3.4 s? (c = 3.00 × 108 m/s)

Accepted Answer

A) 1.5 × l08 m/s 
B) 2.0 × 108 m/s 
C) 2.8 × l08 m/s 
D) 6.8 × 107 m/s 
E) ​1.3 × 108 m/s 
A) 1.5 × l08 m/s 
B) 2.0 × 108 m/s 
C) 2.8 × l08 m/s 
D) 6.8 × 107 m/s 
E) ​1.3 × 108 m/s

Question 19

In 2015,gravity waves were observed using which device?​

Accepted Answer

A) ​The Large Hadron Collider 
B) ​The Sudbury Graviton Observatory 
C) ​The Laser Interferometer Gravitational-Wave Observatory 
D) ​The Superconducting Super Collider 
A) ​The Large Hadron Collider 
B) ​The Sudbury Graviton Observatory 
C) ​The Laser Interferometer Gravitational-Wave Observatory 
D) ​The Superconducting Super Collider

Question 20

The observed relativistic length of a super rocket moving by the observer at 0.70c will be what factor times that of the measured rocket length if it were at rest?

Accepted Answer

A) 0.55 
B) 0.71 
C) 0.51 
D) 1.4 
E) ​1.8 
A) 0.55 
B) 0.71 
C) 0.51 
D) 1.4 
E) ​1.8

Exam 26: Relativity

A muon formed high in the Earth's atmosphere travels at a speed 0.870c for a distance of 4.00 km before it decays.What is the muon's lifetime as measured in its reference frame?

A spaceship of mass 106 kg is to be accelerated to 0.75c.How much energy does this require?

A particle of mass m is moving at speed v = c/2.At what speed does the particle have double the momentum that it has at ​v​ = ​c​/2?

If astronauts could travel at v = 0.90c,we on Earth would say it takes (4.2/0.90)= 4.7 years to reach Alpha Centauri,4.2 lightyears away.The astronauts disagree.How much time passes on the astronaut's clocks?

An object moves by an observer at 0.400c.The total energy of the object will be what factor times that of the rest energy?

A mass is bouncing on the end of a spring with a period T when measured by a ground observer.What would the period of oscillation be (as measured by the same observer)if the mass and spring were moving past the ground observer at a speed of 0.600c?

Which statement regarding Einstein's theories is correct?​

The relativistic effect of time dilation has been verified by which of the following?

Einstein's theory of relativity is based in part on which one of the following postulates?

The total energy of a particle

According to the special theory of relativity,if a 30-year old astronaut sent on a space mission is accelerated to speeds close to that of light,and then returns to Earth after 20 years as measured on Earth,what would be his biological age upon returning?

The significant result of the Michelson-Morley experiment was that it found

​What is the relativistic momentum of a proton traveling at 0.97c?

The period of an oscillating weight on a spring in an inertial frame of reference is 2.5 s.What would be its speed if it were to move by an observer who measures its period as 3.4 s? (c = 3.00 × 108 m/s)

In 2015,gravity waves were observed using which device?​

The observed relativistic length of a super rocket moving by the observer at 0.70c will be what factor times that of the measured rocket length if it were at rest?

Units, Trigonometry, and Vectors

Motion in One Dimension

Motion in Two Dimensions

Newtons Laws of Motion

Energy

Momentum, Impulse, and Collisions

Rotational Motion and Gravitation

Rotational Equilibrium and Dynamics

Fluids and Solids

Thermal Physics

Energy in Thermal Processes

The Laws of Thermodynamics

Vibrations and Waves

Sound

Electric Forces and Fields

Electrical Energy and Capacitance

Current and Resistance

Direct-Current Circuits

Magnetism

Induced Voltages and Inductance

Alternating-Current Circuits and Electromagnetic Waves

Reflection and Refraction of Light

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Wave Optics

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Quantum Physics

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Filters

A spaceship of mass 10⁶ kg is to be accelerated to 0.75c.How much energy does this require?

A particle of mass m is moving at speed v = c/2.At what speed does the particle have double the momentum that it has at v = c/2?

Which statement regarding Einstein's theories is correct?

What is the relativistic momentum of a proton traveling at 0.97c?

The period of an oscillating weight on a spring in an inertial frame of reference is 2.5 s.What would be its speed if it were to move by an observer who measures its period as 3.4 s? (c = 3.00 × 10⁸ m/s)

In 2015,gravity waves were observed using which device?