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: 9781118230725

Author: David Halliday, Robert Resnick, Jearl Walker

Publisher: Wiley, John & Sons, Incorporated

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Relativistic Energy and Momentum

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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

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Chapter 37 Solutions

Fundamentals of Physics Extended

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. 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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.