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Inquiry into Physics

8th Edition
Ostdiek
ISBN: 9781337515863
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 in
the 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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