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 … … … … … … … … … … … … … … … … … … … … … … … … … … … … …

12th Edition

ISBN: 9781119773511

Author: Halliday

Publisher: WILEY

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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

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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.