The expression for relativistic kinetic energy is similar to classical kinetic energy in the limit of low speeds.

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Answer 1

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Chapter 12, Problem 1C

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The expression for relativistic kinetic energy is similar to classical kinetic energy in the limit of low speeds.

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Consider a highly relativistic particle. Discuss what is meant by the term “highly relativistic.” (Note that, in part, it means that the particle cannot be massless.) Construct a problem in which you calculate the wavelength of such a particle and show that it is very nearly the same as the wavelength of amassless particle, such as a photon, with the same energy.Among the things to be considered are the rest energy of the particle (it should be a known particle) and its total energy, which should be large compared to its rest energy.

(a) Prepare a graph of the relativistic kinetic energy and the classical kinetic energy, both as a function of speed, for an object with a mass of your choice. (b) At what speed does the classical kinetic energy underestimate the experimental value by 1%? (c) By 5%? (d) By 50%?

(Low velocity limit of relativistic kinetic energy.) Starting from the relativistic expression for the kinetic energy of a particle, show that when the particle’s velocity is small compared to c, the kinetic energy is approximately equal to the classical value. Hint: you’ll need to use the binomial approximation.

Answer 2

Question

Chapter 12, Problem 1C

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To show:

The expression for relativistic kinetic energy is similar to classical kinetic energy in the limit of low speeds.

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Answer 3

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Chapter 12, Problem 1C

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The expression for relativistic kinetic energy is similar to classical kinetic energy in the limit of low speeds.

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Answer 4

Question

Chapter 12, Problem 1C

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To show:

The expression for relativistic kinetic energy is similar to classical kinetic energy in the limit of low speeds.

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Answer 5

Chapter 12, Problem 1C

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To show:

The expression for relativistic kinetic energy is similar to classical kinetic energy in the limit of low speeds.

Answer 6

Chapter 12, Problem 1C

To determine

To show:

The expression for relativistic kinetic energy is similar to classical kinetic energy in the limit of low speeds.

Answer 7

Chapter 12, Problem 1C

To determine

To show:

The expression for relativistic kinetic energy is similar to classical kinetic energy in the limit of low speeds.

Answer 8

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Answer 9

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Answer 10

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Answer 11

Ch. 12 - Prob. 1AA Ch. 12 - Prob. 2AA Ch. 12 - Prob. 1PIP Ch. 12 - Prob. 1MIO Ch. 12 - Prob. 2MIO Ch. 12 - Prob. 1Q Ch. 12 - Prob. 2Q Ch. 12 - Prob. 3Q Ch. 12 - Prob. 4Q Ch. 12 - Prob. 5Q

The expression for relativistic kinetic energy is similar to classical kinetic energy in the limit of low speeds.

Solution Summary: The author explains that relativistic kinetic energy is similar to classical energy in the limit of low speeds.

Concept explainers

To show:

The expression for relativistic kinetic energy is similar to classical kinetic energy in the limit of low speeds.

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Chapter 12 Solutions

The expression for relativistic kinetic energy is similar to classical kinetic energy in the limit of low speeds.

Solution Summary: The author explains that relativistic kinetic energy is similar to classical energy in the limit of low speeds.

Concept explainers

To show: The expression for relativistic kinetic energy is similar to classical kinetic energy in the limit of low speeds.

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Chapter 12 Solutions

To show:

The expression for relativistic kinetic energy is similar to classical kinetic energy in the limit of low speeds.