Book cover for Physics

Physics

John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler

ISBN #9781118486894

10th Edition

2,562 Questions

Group icon
29,070 Students Helped

Homework Questions

Right arrow
Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

Special relativity fundamentally alters our classical notions of space and time. By recognizing that all inertial frames are equivalent (the relativity postulate) and that the speed of light is invariant (the speed-of-light postulate), we obtain phenomena such as time dilation and length contraction. These effects have practical implications, from ensuring the accuracy of GPS systems to understanding high-speed particle behavior, and introduce new expressions for momentum and energy that converge to classical mechanics at everyday speeds but diverge significantly at speeds approaching light.

Learning Objectives

1

-

2

2.

3

D

4

e

5

f

Key Concepts

CONCEPT

DEFINITION

No concepts available

No definitions available for this book.

Example Problems

Example 1

A particle known as a pion lives for a short time before breaking apart into other particles. Suppose that a pion is moving at a speed of $0.990 c,$ and an observer who is stationary in a laboratory measures the pion's lifetime to be $3.5 \times 10^{-8} \mathrm{s}$. (a) What is the lifetime according to a hypothetical person who is riding along with the pion? (b) According to this hypothetical person, how far does the laboratory move before the pion breaks apart?

Example 2

A radar antenna is rotating and makes one revolution every $25 \mathrm{s}$, as measured on earth. However, instruments on a spaceship moving with respect to the earth at a speed $v$ measure that the antenna makes one revolution every $42 \mathrm{s}$. What is the ratio $v / c$ of the speed $v$ to the speed $c$ of light in a vacuum?

Example 3

Suppose that you are planning a trip in which a spacecraft is to travel at a constant velocity for exactly six months, as measured by a clock on board the spacecraft, and then return home at the same speed. Upon your return, the people on earth will have advanced exactly one hundred years into the future. According to special relativity, how fast must you travel? Express your answer to five significant figures as a multiple of $c-$ for example, $0.95585 \mathrm{c}$

Example 4

Suppose that you are traveling on board a spacecraft that is moving with respect to the earth at a speed of $0.975 c .$ You are breathing at a rate of 8.0 breaths per minute. As monitored on earth, what is your breathing rate?

Example 5

A $6.00-\mathrm{kg}$ object oscillates back and forth at the end of a spring whose spring constant is $76.0 \mathrm{N} / \mathrm{m}$. An observer is traveling at a speed of $1.90 \times 10^{8} \mathrm{m} / \mathrm{s}$ relative to the fixed end of the spring. What does this observer measure for the period of oscillation?
Scroll left
Scroll right

Step-by-Step Explanations

Scroll left
Scroll right

Common Mistakes

  • -
  • 2.
  • C
  • o
  • n