Explanation 1) Concept: Squaring Eq.37-47 and equating it with Eq.37-55, we can show the relation m = p c 2 - K 2 2 K c 2 . If v ≪ c , then using Newtonian physics expression, we can show right side of the relation reduces to m . Substituting the given values in relation with m = p c 2 - K 2 2 K c 2 . Also using the information from Table 37-3, we can find the ratio m m e . 2) Formula: i) From Eq.37-47, the total energy is given by E = m c 2 + K ii) From Eq.37-55, we have E 2 = p c 2 + m c 2 2 iii) The momentum is p = m v iv) The kinetic energy is K = 1 2 m v 2 3) Given: i) The kinetic energy is K = 55.0 M e V ii) The momentum p = 121 M e V / c 4) Calculations: a) From Eq.37-47, the total energy is given by E = m c 2 + K Squaring both the sides, we get E 2 = m c 2 + K 2 E 2 = m c 2 2 + 2 m c 2 K + K 2 Now, from Eq.37-55, we get E 2 = p c 2 + m c 2 2 Substituting in the above equation, we get p c 2 + m c 2 2 = m c 2 2 + 2 m c 2 K + K 2 p c 2 = 2 m c 2 K + K 2 Therefore, m = p c 2 - K 2 2 K c 2 … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … ( 1 ) Hence, the proof. b) At low speed compared to c , Newtonian physics expression is p = m v … … … … … … … … … . . … … … … … … … … … … … … … … … … … … … … … … … … … ( 2 ) And K = 1 2 m v 2 … … … … … … … … … … … … … … … … … … … … … … … … … … … … …

10th Edition

ISBN: 9781118230718

Author: David Halliday

Publisher: Wiley, John & Sons, Incorporated

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Relativistic Energy and Momentum

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Question

Chapter 37, Problem 46P

To determine

To find:

a) The relation

m=pc2-K22Kc2

b) The right side of the relation reduces to m.

c) The ratio mme.

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Chapter 37, Problem 45P

Chapter 37, Problem 47P

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 relation m = p c 2 - K 2 2 K c 2 b) The right side of the relation reduces to m . c) The ratio m m e .

Solution Summary: The author explains how the relation m=left and the ratio are shown.

Concept explainers

To find:

a) The relation

m=pc2-K22Kc2

b) The right side of the relation reduces to m.

c) The ratio mme.

Want to see the full answer?

Chapter 37 Solutions

a) The relation m = p c 2 - K 2 2 K c 2 b) The right side of the relation reduces to m . c) The ratio m m e .

Solution Summary: The author explains how the relation m=left and the ratio are shown.

Concept explainers

To find: a) The relation m=pc2-K22Kc2 b) The right side of the relation reduces to m. c) The ratio mme.

Want to see the full answer?

Chapter 37 Solutions

To find:

a) The relation

m=pc2-K22Kc2

b) The right side of the relation reduces to m.

c) The ratio mme.