Explanation 1) Concept: By using the classical equation, we can first find the radius and the period. After that, by using the relativistic correction, we can find the corrected radius and the period. 2) Formula: i) r = m v | q | | B | ii) T = 2 π r / v iii) K = m c 2 γ - 1 3) Given: i) The particle of charge q and mass m will move in circle of radius r. ii) K = 10.0 M e V iii) B = 2.20 T 4) Calculations: a) By using the classical orbital radius formula, r 0 = m v | q | | B | And the period is T 0 = 2 π r 0 / v Now by using the relativistic limit as r = p | q | | B | r = γ m v | q | | B | i.e., r = γ r 0 The period in the relativistic limit is T = 2 π r / v T = 2 π γ r 0 / v But from the above equation, r 0 is r 0 = m v | q | | B | By substituting this value in the above equation, T = 2 π γ v m v | q | | B | So, T = 2 π m γ | q | | B | T = γ T 0 … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … . . ( 1 ) b) From equation (1), we can conclude that the period is independent of v . c) Now we have to find the correct radius; for that, we use the kinetic energy formula as K = 1 2 m v 2 K = 1 2 m c 2 v 2 c 2 Where, β = v 2 c 2 K = 1 2 m c 2 β From that, we can find the value of β . β = 2 K m c 2 where m c 2 is the rest mass energy of the particle m c 2 = 0.511 M e V So, β = 2 × 10 0.511 β = 6.256 Now according to the formula of radius, we can calculate the radius as r = m v | q | | B | r = m v c c | q | | B | r = m β c e B r = 9

10th Edition

ISBN: 9781118230718

Author: David Halliday

Publisher: Wiley, John & Sons, Incorporated

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Chapter 37, Problem 53P

To determine

To find:

a) The expression for the period

b) Is the period independent of v?

c) The radius using classical method

d) The correct radius

e) The period using classical method

f) The correct period

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Chapter 37, Problem 52P

Chapter 37, Problem 54P

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Chapter 37 Solutions

Fundamentals of Physics

Ch. 37 - A rod is to move at constant speed v along the x...Ch. 37 - Figure 37-16 shows a ship attached to reference...Ch. 37 - Reference frame S' is to pass reference frame S at...Ch. 37 - Figure 37-17 shows two clocks in stationary frame...Ch. 37 - Figure 37-18 shows two clocks in stationary frame...Ch. 37 - Sam leaves Venus in a spaceship headed to Mars and...Ch. 37 - The plane of clocks and measuring rods in Fig....Ch. 37 - The rest energy and total energy, respectively, of...Ch. 37 - Figure 37-20 shows the triangle of Fig 37-14 for...Ch. 37 - While on board a starship, you intercept signals...

Ch. 37 - Figure 37-21 shows one of four star cruisers that...Ch. 37 - The mean lifetime of stationary muons is measured...Ch. 37 - To eight significant figures, what is speed...Ch. 37 - You wish to make a round trip from Earth in a...Ch. 37 - Come back to the future. Suppose that a father is...Ch. 37 - ILW An unstable high-energy particle enters a...Ch. 37 - GO Reference frame S' is to pass reference frame S...Ch. 37 - The premise of the Planet of the Apes movies and...Ch. 37 - An electron of = 0.999 987 moves along the axis...Ch. 37 - SSM A spaceship of rest length 130 m races past a...Ch. 37 - A meter stick in frame S' makes an angle of 30...Ch. 37 - A rod lies parallel to the x axis of reference...Ch. 37 - The length of a spaceship is measured to be...Ch. 37 - GO A space traveler takes off from Earth and moves...Ch. 37 - A rod is to move at constant speed v along the x...Ch. 37 - GO The center of our Milky Way galaxy is about 23...Ch. 37 - Observer S reports that an event occurred on the x...Ch. 37 - SSM WWW In Fig. 37-9, the origins of the two...Ch. 37 - Inertial frame S' moves at a speed of 0.60c with...Ch. 37 - An experimenter arranges to trigger two flashbulbs...Ch. 37 - GO As in Fig. 37-9, reference frame S' passes...Ch. 37 - Relativistic reversal of events. Figures 37-25a...Ch. 37 - For the passing reference frames in Fig. 37-25,...Ch. 37 - ILW A clock moves along an x axis at a speed of...Ch. 37 - Bullwinkle in reference frame S' passes you in...Ch. 37 - In Fig. 37-9, observer S detects two flashes of...Ch. 37 - In Fig. 37-9, observer 5 detects two flashes of...Ch. 37 - SSM A particle moves along the x' axis of frame S'...Ch. 37 - In Fig. 37-11, frame S' moves relative to frame S...Ch. 37 - Galaxy A is reported to be receding from us with a...Ch. 37 - Stellar system Q1 moves away from us at a speed of...Ch. 37 - SSM WWW ILW A spaceship whose rest length is 350 m...Ch. 37 - GO In Fig. 37-26a, particle P is to move parallel...Ch. 37 - GO An armada of spaceships that is 1.00 ly long as...Ch. 37 - A sodium light source moves in a horizontal circle...Ch. 37 - SSM A spaceship, moving away from Earth at a speed...Ch. 37 - Prob. 36P Ch. 37 - Assuming that Eq. 37-36 holds, find how fast you...Ch. 37 - Figure 37-27 is a graph of intensity versus...Ch. 37 - SSM A spaceship is moving away from Earth at speed...Ch. 37 - How much work must be done to increase the speed...Ch. 37 - SSM WWW The mass of an electron is 9.109 381 88 ...Ch. 37 - Prob. 42P Ch. 37 - How much work must be done to increase the speed...Ch. 37 - In the reaction p 19F 16O, the masses are mp =...Ch. 37 - In a high-energy collision between a cosmic-ray...Ch. 37 - Prob. 46P Ch. 37 - Prob. 47P Ch. 37 - GO The mass of a muon is 207 times the electron...Ch. 37 - GO As you read this page on paper or monitor...Ch. 37 - To four significant figures, find the following...Ch. 37 - ILW What must be the momentum of a particle with...Ch. 37 - Apply the binomial theorem Appendix E to the last...Ch. 37 - Prob. 53P Ch. 37 - GO What is for a particle with a K = 2.00E0 and b...Ch. 37 - Prob. 55P Ch. 37 - a The energy released in the explosion of 1.00 mol...Ch. 37 - Quasars are thought to be the nuclei of active...Ch. 37 - The mass of an electron is 9.109 381 88 1031 kg....Ch. 37 - GO An alpha particle with kinetic energy 7.70 MeV...Ch. 37 - Temporal separation between two events. Events A...Ch. 37 - Spatial separation between two events. For the...Ch. 37 - GO In Fig. 37-28a, particle P is to move parallel...Ch. 37 - Superluminal jets. Figure 37-29a shows the path...Ch. 37 - GO Reference frame S' passes reference frame S...Ch. 37 - Another approach to velocity transformations. In...Ch. 37 - Continuation of Problem 65. Use the result of part...Ch. 37 - Continuation of Problem 65. Let reference frame C...Ch. 37 - Figure 37-16 shows a ship attached to reference...Ch. 37 - Prob. 69P Ch. 37 - An airplane has rest length 40.0 m and speed 630...Ch. 37 - SSM To circle Earth in low orbit, a satellite must...Ch. 37 - Prob. 72P Ch. 37 - SSM How much work is needed to accelerate a proton...Ch. 37 - A pion is created in the higher reaches of Earths...Ch. 37 - SSM If we intercept an electron having total...Ch. 37 - Prob. 76P Ch. 37 - A spaceship at rest in a certain reference frame S...Ch. 37 - Prob. 78P Ch. 37 - SSM What is the momentum in MeV/c of an electron...Ch. 37 - The radius of Earth is 6370 km, and its orbital...Ch. 37 - A particle with mass m has speed c/2 relative to...Ch. 37 - An elementary particle produced in a laboratory...Ch. 37 - What are a K, b E, and c p in GeV/c for a proton...Ch. 37 - A radar transmitter T is fixed to a reference...Ch. 37 - One cosmic-ray particle approaches northsouth axis...Ch. 37 - How much energy is released in the explosion of a...Ch. 37 - What potential difference would accelerate an...Ch. 37 - A Foron cruiser moving directly toward a Reptulian...Ch. 37 - In Fig. 37-35, three spaceships are in a chase....Ch. 37 - Space cruisers A and B are moving parallel to the...Ch. 37 - In Fig. 37-36, two cruisers fly toward a space...Ch. 37 - A relativistic train of proper length 200 m...Ch. 37 - Particle A with rest energy 200 MeV is at rest in...Ch. 37 - Figure 37-37 shows three situations in which a...Ch. 37 - Ionization measurements show that a particular...Ch. 37 - Prob. 96P Ch. 37 - Prob. 97P Ch. 37 - An astronaut exercising on a treadmill maintains a...Ch. 37 - A spaceship approaches Earth at a speed of 0.42c....Ch. 37 - Prob. 100P Ch. 37 - In one year the United States consumption of...Ch. 37 - Quite apart from effects due to Earths rotational...Ch. 37 - Prob. 103P

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a) The expression for the period b) Is the period independent of v ? c) The radius using classical method d) The correct radius e) The period using classical method f) The correct period

Solution Summary: The author explains how the classical equation and relativistic correction can be used to find the radius and period.

Concept explainers

To find:

a) The expression for the period

b) Is the period independent of v?

c) The radius using classical method

d) The correct radius

e) The period using classical method

f) The correct period

Want to see the full answer?

Chapter 37 Solutions

a) The expression for the period b) Is the period independent of v ? c) The radius using classical method d) The correct radius e) The period using classical method f) The correct period

Solution Summary: The author explains how the classical equation and relativistic correction can be used to find the radius and period.

Concept explainers

To find: a) The expression for the period b) Is the period independent of v? c) The radius using classical method d) The correct radius e) The period using classical method f) The correct period

Want to see the full answer?

Chapter 37 Solutions

To find:

a) The expression for the period

b) Is the period independent of v?

c) The radius using classical method

d) The correct radius

e) The period using classical method

f) The correct period