Question 1

The astronaut whose heart rate on Earth is 63 beats/min increases his velocity to v = 0.70c.Now what is his heart rate as measured by an Earth observer?

Accepted Answer

A) 45 beats/min 
B) 88 beats/min 
C) 19 beats/min 
D) 90 beats/min 
E) ​210 beats/min 
A) 45 beats/min 
B) 88 beats/min 
C) 19 beats/min 
D) 90 beats/min 
E) ​210 beats/min A

Question 2

The mass of a proton at rest is m. If the proton is moving so fast that its total energy is three times its rest energy,then what is the kinetic energy of the proton?

Accepted Answer

A) mc2 
B) 2mc2 
C) 3mc2 
D) 4mc2 
A) mc2 
B) 2mc2 
C) 3mc2 
D) 4mc2 B

Question 3

A satellite is powered by a small nuclear generator that puts out 10 W.How much matter is converted into energy over the 20-year life span of the generator?

Accepted Answer

A) 70 µg 
B) 70 g 
C) 7 g 
D) 7 kg 
E) ​4 mg 
A) 70 µg 
B) 70 g 
C) 7 g 
D) 7 kg 
E) ​4 mg A

Question 4

As measured from the Earth,a spacecraft is moving at speed 0.80c toward a second spacecraft moving at speed 0.60c back toward the first spacecraft.What is the speed of the first spacecraft as viewed from the second spacecraft?

Accepted Answer

A) 0.81c 
B) 0.95c 
C) 0.38c 
D) 0.20c 
A) 0.81c 
B) 0.95c 
C) 0.38c 
D) 0.20c

Question 5

At what speed must an object be moving in order that it has a kinetic energy 2.6 times its rest energy? (c = 3.00 × 108 m/s)

Accepted Answer

A) 2.77 × 108 m/s 
B) 2.17 × 108 m/s 
C) 2.88 × 108 m/s 
D) 1.15 × 108 m/s 
E) ​2.55 × 108 m/s 
A) 2.77 × 108 m/s 
B) 2.17 × 108 m/s 
C) 2.88 × 108 m/s 
D) 1.15 × 108 m/s 
E) ​2.55 × 108 m/s

Question 6

A boxcar without a front or a back is moving toward the right.Two flashes of light move through the boxcar,one moving from back to front toward the right,the other moving from front to back toward the left.A passenger in the boxcar records how long it takes each flash of light to pass from one end of the boxcar to the other end.According to the passenger,which took longer?

Accepted Answer

A) the flash going from back to front 
B) the flash going from front to back 
C) They both took the same time. 
D) It depends on whether the passenger is sitting at the front or the back of the boxcar. 
A) the flash going from back to front 
B) the flash going from front to back 
C) They both took the same time. 
D) It depends on whether the passenger is sitting at the front or the back of the boxcar.

Question 7

A particle is moving the +x direction at speed c/2.Another particle is moving in the -x direction at speed c/2 toward the first particle.Which of the following best describes the speed of one particle as seen by an observer moving with the other particle?

Accepted Answer

A) c 
B) some value less than 3c/4 
C) some value more than 3c/4 
D) 3c/4 
A) c 
B) some value less than 3c/4 
C) some value more than 3c/4 
D) 3c/4

Question 8

​An unstable particle initially at rest breaks up into two fragments.The mass of one fragment is 1.75 × 10-28 kg and the mass of the other fragment is 1.25 × 10-27 kg.The lighter fragment has a speed of speed 0.850c.What is the speed of the heavier fragment?

Accepted Answer

A) ​0.229c 
B) ​0.119c 
C) ​0.127c 
D) ​0.220c 
A) ​0.229c 
B) ​0.119c 
C) ​0.127c 
D) ​0.220c

Question 9

A tuning fork has a frequency of 300 Hz and hence a period of 3.33 × 10−3 s.If the tuning fork is in an inertial frame of reference moving by the observer at speed of 0.620 c,what is the frequency of the fork as measured by the observer? (Assume that measurements are strictly by optical means and that the speed of sound waves in air is not pertinent here).

Accepted Answer

A) 235 Hz 
B) 382 Hz 
C) 185 Hz 
D) 185 Hz. 
E) ​487 Hz 
A) 235 Hz 
B) 382 Hz 
C) 185 Hz 
D) 185 Hz. 
E) ​487 Hz

Question 10

A proton with mass 1.67 × 10−27 kg moves in an accelerator with a speed of 0.780c.What is its total energy? (c = 3.00 × 108 m/s)

Accepted Answer

A) 1.50E-10 J 
B) 3.90E-10 J 
C) 2.40E-10 J 
D) 7.51E-19 J 
E) ​1.28E-18 J 
A) 1.50E-10 J 
B) 3.90E-10 J 
C) 2.40E-10 J 
D) 7.51E-19 J 
E) ​1.28E-18 J

Question 11

If the nonzero momentum of a particle with mass is doubled,what happens to its total energy?

Accepted Answer

A) It also doubles. 
B) It increases,more than doubling. 
C) It stays the same since total energy is a constant for a given particle. 
D) It increases,but less than doubling. 
A) It also doubles. 
B) It increases,more than doubling. 
C) It stays the same since total energy is a constant for a given particle. 
D) It increases,but less than doubling.

Question 12

Which form of relativity applies for observers who are accelerating?

Accepted Answer

A) Special relativity applies. 
B) General relativity applies. 
C) Both special relativity and general relativity apply. 
D) Neither applies since the observer must be in an inertial frame to use either one. 
A) Special relativity applies. 
B) General relativity applies. 
C) Both special relativity and general relativity apply. 
D) Neither applies since the observer must be in an inertial frame to use either one.

Question 13

A proton with mass 1.67 × 10−27 kg moves with a speed of 0.560c in an accelerator.What is its kinetic energy? (c = 3.00 × 108 m/s)

Accepted Answer

A) 1.50E-10 J 
B) 1.81E-10 J 
C) 3.11E-11 J 
D) 1.03E-10 J 
E) ​4.71E-11 J 
A) 1.50E-10 J 
B) 1.81E-10 J 
C) 3.11E-11 J 
D) 1.03E-10 J 
E) ​4.71E-11 J

Question 14

A space probe is 15.6 m in length when measured at rest.What length does an observer at rest measure when the probe is going by at a speed of 0.740c?

Accepted Answer

A) 23.2 m 
B) 10.5 m 
C) 8.0 m 
D) 11.5 m 
E) ​21.1 m 
A) 23.2 m 
B) 10.5 m 
C) 8.0 m 
D) 11.5 m 
E) ​21.1 m

Question 15

Muons at speed 0.9995c are sent round and round a circular storage ring of radius 550 m.If a muon at rest decays into other particles after an average T =2.2 × 10−6 s,how many trips around the storage ring do we expect the 0.9995c muons to make before they decay?

Accepted Answer

A) 1 
B) 2 
C) 12 
D) 6 
E) ​131 
A) 1 
B) 2 
C) 12 
D) 6 
E) ​131

Question 16

A lump of uranium has a mass of 2.0 kg,and begins at rest.Half of the lump's mass is going to be totally converted into kinetic energy of the other half.After this is done,how fast is the remaining half going?

Accepted Answer

A) 0.60c 
B) 0.80c 
C) 0.87c 
D) 1.0c 
A) 0.60c 
B) 0.80c 
C) 0.87c 
D) 1.0c

Question 17

A knight on horseback holds a 9.0-m lance.The horse can run at 0.75c.(It wins most of its races!)How long will the lance appear to a person that is standing still on the ground as the horse runs past?

Accepted Answer

A) 6.0 m 
B) 14 m 
C) 9 m 
D) 6.8 m 
E) ​4.5 m 
A) 6.0 m 
B) 14 m 
C) 9 m 
D) 6.8 m 
E) ​4.5 m

Question 18

A spaceship is moving away from an observer at relativistic speed.Its length at rest is 100 m,but the observer measures its length as 60 m.A time interval of 84 s on the spaceship would be measured by the observer to be which of the following?

Accepted Answer

A) 50.4 s 
B) 30.2 s 
C) 134 s 
D) 140 s 
E) ​84 s 
A) 50.4 s 
B) 30.2 s 
C) 134 s 
D) 140 s 
E) ​84 s

Question 19

When one compares the relativistic kinetic energy to the classically calculated kinetic energy for a moving object,at which of the speeds listed below does the classical calculation give a greater value than the relativistic calculation?

Accepted Answer

A) 0.2c 
B) 0.5c 
C) 0.707c 
D) None of the above values will give such a result. 
A) 0.2c 
B) 0.5c 
C) 0.707c 
D) None of the above values will give such a result.

Question 20

The gravitational field is equivalent to:

Accepted Answer

A) the inertial mass. 
B) an accelerated frame of reference. 
C) an event horizon. 
D) a clock running slowly. 
A) the inertial mass. 
B) an accelerated frame of reference. 
C) an event horizon. 
D) a clock running slowly.

Exam 26: Relativity

The astronaut whose heart rate on Earth is 63 beats/min increases his velocity to v = 0.70c.Now what is his heart rate as measured by an Earth observer?

The mass of a proton at rest is m. If the proton is moving so fast that its total energy is three times its rest energy,then what is the kinetic energy of the proton?

A satellite is powered by a small nuclear generator that puts out 10 W.How much matter is converted into energy over the 20-year life span of the generator?

As measured from the Earth,a spacecraft is moving at speed 0.80c toward a second spacecraft moving at speed 0.60c back toward the first spacecraft.What is the speed of the first spacecraft as viewed from the second spacecraft?

At what speed must an object be moving in order that it has a kinetic energy 2.6 times its rest energy? (c = 3.00 × 108 m/s)

A particle is moving the +x direction at speed c/2.Another particle is moving in the -x direction at speed c/2 toward the first particle.Which of the following best describes the speed of one particle as seen by an observer moving with the other particle?

​An unstable particle initially at rest breaks up into two fragments.The mass of one fragment is 1.75 × 10-28 kg and the mass of the other fragment is 1.25 × 10-27 kg.The lighter fragment has a speed of speed 0.850c.What is the speed of the heavier fragment?

A proton with mass 1.67 × 10−27 kg moves in an accelerator with a speed of 0.780c.What is its total energy? (c = 3.00 × 108 m/s)

If the nonzero momentum of a particle with mass is doubled,what happens to its total energy?

Which form of relativity applies for observers who are accelerating?

A proton with mass 1.67 × 10−27 kg moves with a speed of 0.560c in an accelerator.What is its kinetic energy? (c = 3.00 × 108 m/s)

A space probe is 15.6 m in length when measured at rest.What length does an observer at rest measure when the probe is going by at a speed of 0.740c?

Muons at speed 0.9995c are sent round and round a circular storage ring of radius 550 m.If a muon at rest decays into other particles after an average T =2.2 × 10−6 s,how many trips around the storage ring do we expect the 0.9995c muons to make before they decay?

A lump of uranium has a mass of 2.0 kg,and begins at rest.Half of the lump's mass is going to be totally converted into kinetic energy of the other half.After this is done,how fast is the remaining half going?

A knight on horseback holds a 9.0-m lance.The horse can run at 0.75c.(It wins most of its races!)How long will the lance appear to a person that is standing still on the ground as the horse runs past?

A spaceship is moving away from an observer at relativistic speed.Its length at rest is 100 m,but the observer measures its length as 60 m.A time interval of 84 s on the spaceship would be measured by the observer to be which of the following?

When one compares the relativistic kinetic energy to the classically calculated kinetic energy for a moving object,at which of the speeds listed below does the classical calculation give a greater value than the relativistic calculation?

The gravitational field is equivalent to:

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The mass of a proton at rest is m_. If the proton is moving so fast that its total energy is three times its rest energy,then what is the kinetic energy of the proton?

At what speed must an object be moving in order that it has a kinetic energy 2.6 times its rest energy? (c = 3.00 × 10⁸ m/s)

An unstable particle initially at rest breaks up into two fragments.The mass of one fragment is 1.75 × 10^-28 kg and the mass of the other fragment is 1.25 × 10^-27 kg.The lighter fragment has a speed of speed 0.850c.What is the speed of the heavier fragment?

A proton with mass 1.67 × 10−²⁷ kg moves in an accelerator with a speed of 0.780c.What is its total energy? (c = 3.00 × 10⁸ m/s)

A proton with mass 1.67 × 10−²⁷ kg moves with a speed of 0.560c in an accelerator.What is its kinetic energy? (c = 3.00 × 10⁸ m/s)

Muons at speed 0.9995c are sent round and round a circular storage ring of radius 550 m.If a muon at rest decays into other particles after an average T =2.2 × 10−⁶ s,how many trips around the storage ring do we expect the 0.9995c muons to make before they decay?