Chapter 12, Problem 1C

### Inquiry into Physics

8th Edition
Ostdiek
ISBN: 9781337515863

Chapter
Section

### 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 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 1âˆ’ v 2 c 2 âˆ’moc2K=moc2(1 1âˆ’ v 2 c 2 âˆ’1)K=â€‰moc2( ( 1âˆ’ v 2 c 2 ) âˆ’ 1 2 â€‰âˆ’1)byÂ binomialÂ approximation,Â Â (1+

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