   Chapter 12, Problem 1C

Chapter
Section
Textbook Problem

Show that in the limit of low speeds the expression for the relativistic kinetic energy (see Important Equations) reduces to the familiar one from classical mechanics, [Hint: For speeds v much smaller than c, the quantity is approximately equal to You should check this for yourself using typical speeds given inthe exercises in Chapter 3.]

To determine

To show:

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

Explanation

Given data:

Rest mass of an object = mo

Speed of the object = v.

Calculation:

Relativistic kinetic energy is written as

K=moc2 1 v 2 c 2 moc2K=moc2(1 1 v 2 c 2 1)K=moc2( ( 1 v 2 c 2 ) 1 2 1)by binomial approximation,  (1+

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