94. The expression (1+x)" can be approximated as 1 + nx, provided |x|<1. Here, the exponent n does not have to be an integer. Use this approximation to show that Equation 20.11's expression for relativistic kinetic energy reduces to K=mv² for v < c.

94. The expression (1+x)" can be approximated as 1 + nx, provided |x|<1. Here, the exponent n does not have to be an integer. Use this approximation to show that Equation 20.11's expression for relativistic kinetic energy reduces to K=mv² for v < c.

Glencoe Physics: Principles and Problems, Student Edition

1st Edition

ISBN:9780078807213

Author:Paul W. Zitzewitz

Publisher:Paul W. Zitzewitz

Chapter11: Energy And Its Conservation

Section: Chapter Questions

Problem 35A

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Concept explainers

Relativistic Energy and Momentum

According to classical physics, time flow is the same for every observer. But according to einstein's theory, time flow is different for different observers. The idea that time flow is not the same for all may sound strange because we may not experience this effect in everyday life. This effect is only observed when an object moves with some velocity comparable to the velocity of light. This velocity is termed relativistic velocity.

Question

Do Problem 20-94.
(the exact kinetic energy is )
(the approximate kinetic energy is )

94. The expression (1+x)" can be approximated as 1 + nx, provided
|x|<1. Here, the exponent n does not have to be an integer. Use this
approximation to show that Equation 20.11's expression for relativistic
kinetic energy reduces to K=mv² for v < c.

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Step 1: Introduce the formula of relativistic mass

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Step 2: Determine the exact kinetic energy

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Step 3: Calculate the approximate kinetic energy

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