Six Ideas that Shaped Physics: Unit R: The Laws of Physics are Frame-Independent [2 ed.] 9780072397147, 0072397144, 2002024404

Citation preview

Some Physical Constants Speed of light Gravitational constant Coulomb's constant Planck's constant Boltzmann's constant Elementary charge Electron mass Proton mass Neutron mass

c G k h h e me mp m„

Standard Metric Prefixes 3.00 X 10s m/s 6.67 X 10-11 N m2/kg: 8.99 X 109 N m2/C2 6.63 X 10"34 J s 1.38 X io~23j/k 1.60 X 10"19 C 9.11 X 10~31 kg 1.67 X 10"27 kg 1.68 X io-27 kg

For powers of 10 Power 1018 1015 1012

109 106 103 10"2 10"3

Commonly Used Physical Data

10-6 10~9

Gravitational field strength g Mass of the earth M c Radius of the earth R e Mass of the sun MsRadius of the sun R s Distance to moon Distance to sun Density of water+ Density of air+ Absolute zero Freezing point of water* Room temperature Boiling point of water* Normal atmospheric pressure

9.80 J kg 1 m 1 = 9.80 m/s2 5.98 x 1024 kg 6380 km (equatorial) 1.99 x 1030 kg 696,000 km 3.84 x 108 m 1.50 x 10u m 1000.0 kg/m3 = 1 g/cm3 1.2 kg/m3 0 K = —273.15°C = —459.67°F 273.15 K = 0°C = 32°F 295 K = 22°C = 72°F 373 K = 100°C = 212°F 101.3 kPa

10-12 10"15

10-18

Prefix

exa peta tera giga mega kilo centi milli micro nano pico femto atto

Symbol

E P T G M k c m n P f a

Useful Conversion Factors 1 meter = lm= 100 cm = 39.4 in. = 3.28 ft 1 mile = 1 mi = 1609 m = 1.609 km = 5280 ft 1 inch = 1 in. = 2.54 cm 1 light-year = 1 ly = 9.46 Pm = 0.946 x 1016 m 1 hour = 1 h = 60 min = 3600 s 1 day = 1 d = 24 h = 86.4 ks = 86,400 s 1 year = 1 y = 365.25 d = 31.6 Ms = 3.16 x 107 s 1 J = 1 kg m2/s2 1 N-m = 0.239 cal leal = 4.186 J 1 W = 1 J/s 1 kW-h = 3.6 MJ 1 K (temperature difference) = 1°C = 1.8°F (1 K \ [F[q + 273.15°C] 1 rad = 57.3° = 0.1592 rev fAt

normal pressure, 20°C.

*At normal atmospheric pressure.

1 m/s = 2.24 mi/h 1 mi/h = 1.61 km/h 1 ft3 = 0.02832 m3 1 gallon = 1 gal = 3.79 x 10~3 m3 « 3.8 kg H20 1 N = 1 kg m/s2 = 1 J/m = 0.225 lb 1 lb = 4.45 N Weight of 1-kg object near earth = 9.8 N = 2.2 lb 1 cal = energy to raise temperature of 1 g of H20 by 1 K 1 food calorie = 1 Cal = 1 kcal = 1000 cal 1 horsepower = 1 hp = 746 W 1 Pa = 1 N/m2 Tic] = (~)(T l F ] — 32°F) \ 9°F T = 5 K (T[f] + 459.67°F) 9°F *

— 360° — 2tt radians = 6.28 rad

Useful Astronomical Data (1 AU = mean distance from earth to sun = 1.50 x 1011 m)

Object

Mass

Radius

Mean Orbital Radius

Orbital Period

Orbital Eccentricity

Sun Moon Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Pluto/Charon

1.99 x 103° kg 7.36 x 1022 kg 0.0558M£ 0.815Me 5.98 x 1024 kg = ME 0.107M£ 318Me 95.1Me 14.5M£ 17.2Me 0.0025M£

696,000 km 1,740 km 2,439 km 6,060 km 6,380 km 3,370 km 69,900 km 58,500 km 23,300 km 22,100 km 3500/1800 km

384,000 km = 1.28 s 0.387 AU = 3.23 min 0.723 AU = 6.03 min 1.000 AU = 8.33 min 1.524 AU = 12.7 min 5.203 AU = 43.4 min 9.539 AU = 1.32 h 19.182 AU = 2.66 h 30.058 AU = 4.17 h 39.785 AU = 5.53 h

27.3 days 0.241 y 0.615 y 1.000 y 1.88 y 11.9 y 29.5 y 84.0 y 165 y 248 y

0.055 0.206 0.007 0.017 0.093 0.048 0.056 0.047 0.009 0.254

_

Based mostly on data in D. Halliday and R. Resnick, Fundamentals of Physics, 3d ed., New York: Wiley, p. A6.

1 min = 18 x 106 km 1 h = 1.08 Tm = 1.08 x 109 km 1 day = 2.59 x 1013 m = 25.9 x 109 km

Boston Burr Ridge, IL Dubuque, IA Madison, Wl New York San Francisco St. Louis Bangkok Bogota Caracas Kuala Lumpur Lisbon London Madrid Mexico City Milan Montreal New Delhi Santiago Seoul Singapore Sydney Taipei Toronto

McGraw-Hill Higher Education g A Division of The McGraw-Hill Companies SIX IDEAS THAT SHAPED PHYSICS, UNIT R: THE LAWS OF PHYSICS ARE FRAME-INDEPENDENT, SECOND EDITION Published by McGraw-Hill, a business unit of The McGraw-Hill Companies, Inc., 1221 Avenue of the Americas, New York, NY 10020. Copyright © 2003, 1998 by The McGraw-Hill Companies, Inc. All rights reserved. No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written consent of The McGraw-Hill Companies, Inc., including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning. ' Some ancillaries, including electronic and print components, may not be available to customers outside the United States. This book is printed on recycled, acid-free paper containing 10% postconsumer waste. 4 5 6 7 8 9 0 QPD/QPD 0 9 8 7 6 ISBN 978-0-07-239714-7 MHID 0-07-239714-4 Publisher: Kent A. Peterson Sponsoring editor: Daryl Bruflodt Developmental editor: Spencer J. Cotkin, Ph.D. Marketing manager: Debra B. Hash Senior project manager: Susan ]. Brusch Lead production supervisor: Sandy Ludovissy Media project manager: Sandra M. Schnee Lead media technology producer: Judi David Designer: David W. Hash Cover/interior designer: Rokusek Design Cover image: © CERN Senior photo research coordinator: Lori Hancock Photo research: Chris Hammond/PhotoFind LLC Supplement producer: BrendaA. Ernzen Compositor: Interactive Composition Corporation Typeface: 10/12 Palatino Printer: Quebecor World Dubuque, IA

Figure R22: From A. Brillet and J.L. Hall, "Improved Laser Test of the Isotropy Space," Physical

PhuZltTcilp aT 9' Feb'ul26'1979' PP• 5i9~552- C0pyright ® 1979 hy the Amcrican

Stanford Univerlity"

permission of the Stanford Linear Accelerator Center,

^d't"St: Time h Comparing Frames

Why Is This Text Different?

[> Relativistic Dynamics

Research consistently shows that people learn physics most effectively if they participate in activities that help them practice applying physical reason­ ing in realistic situations. This is because physics is not a collection of facts to absorb, but rather is a set of thinking skills requiring practice to master. You cannot learn such skills by going to factual lectures any more than you can learn to play the piano by going to concerts! This text is designed, therefore, to support active learning both inside and outside the classroom by providing (1) resources for various kinds of learning activities, (2) features that encourage active reading, and (3) features that make it easier for the text (as opposed to lectures) to serve as the primary source of information, so that more class time is available for active learning.

The Text as Primary Source To serve the last goal, I have adopted a conversational style that I hope will be easy to read, and I tried to be concise without being so terse that you need a lecture to fill in the gaps. There are also many text features designed to help you keep track of the big picture. The unit's central idea is summarized on the front cover where you can see it daily. Each chapter is designed to corre­ spond to one 50-minute class session, so that each session is a logically com­ plete unit. The two-page chapter overview at the beginning of each chapter provides a compact summary of that chapter's contents to consider before you are submerged by the details (it also provides a useful summary when you review for exams). An accompanying chapter-location diagram uses a computer menu metaphor to display how the current chapter fits into the unit (see the example at the upper right). Major unit subdivisions appear as gray boxes, with the current subdivision highlighted in color. Chapters in the current subdivision appear in a submenu with the current chapter high­ lighted in black and indicated by an arrow. All technical terms are highlighted using a bold type when they first ap­ pear, and a glossary at the end of the text summarizes their definitions. Please also note the tables of useful information, including definitions of common symbols, that appear inside the front cover. A physics formula is both a mathematical equation and a context that gives the equation meaning. Every important formula in this text appears in a formula box. Each contains the equation, a Purpose (describing the formula's

L

Features that help the text serve as the primary source of information

XVIII

Introduction for Students

meaning and utility), a definition of the Symbols used in the equation a description of any Limitations on the formula's applicability and possibly some other useful Notes. Treat everything in such a box as an indivisible unit to be remembered and used together.

Active Reading What it means to be an active reader

^SS!VSly Hf^ to;5 lecture' Passively scanning a text does not really help you learn. Active readmg is a crucial study skill for effectively learning from this text (and other types of technical literature as well). An active reader stops frequently to pose internal questions such as these: Does this make sense. Is this consistent with my experience? Am I following the logic here? o I see how I might use this idea in realistic situations? This text provides two important tools to make this easier. provides two

Tools to help you become an active reader

Use the wide margins to (1) record questions that occur to you as vou read « Srmrsrber ,o

se*,hen answ

steps and ' ?8 ™p°rtant Passa§es' (4) fill in missing mathematics steps and (5) record insights. Doing these things helps keep you actively enCOmments are generally helpful as you revTet Note Jhaf'lh 7°Ur f provided some marginal notes that summarize the points of crucial paragraphs and help you find things quickly. e rn-text exercises help you develop the habits of (1) filling in missing mathematics steps and (2) posing questions that help you practice using thf

The single most important thing you can do

" r • ftZ of / ? homework or exam£problems, some of these appear iS the form of m-text exercises (as you are more likely to learn from aS example* you work on it a bit yourself instead of just scanning someone else's solu turn). Answers to all exercises appear at the end of each chapter so vou can a

h

sh ,his

frci™tTreeaeddbaCk

has

are doin§-

corne an active^aden

at least some of the ex-

^imp0rtmt **y0H can to

Active reading does take effort. Scanning the 5200 words of a tvpiral .

t

T

b

u

ally!

!

a

c

t

™

r e a d

^ » «

, d B

k

e

-

-

A

l0W a fuse

ln my head after

S

xrrL i , about 20 minutes of ing to fOH m8' S° ^ f°? breaks t0 do something else to keep alert Pausg to fill in missing math also helps me to stay focused longer. p

Class Activities and Homework End-of-chapter problems support active learning

f° y°Ur instructor') types of problems are primaiSv other USG 3S homework ou^ide class, Basic problems are simnle drill!-? u, straightforward applications of a ^glTf, emS,that help you Practice in Synthetic problems are more chaTZn! bring together multiple formulas and/or Jl,'1 "T ^ recluire you

context problems are yet more challenging^roblems^hal ar °oftenlvritten in

Introduction for Students

xix

a narrative format and ask you to answer a practical, real-life question rather than explicitly asking for a numerical result. Like situations you will en­ counter in real life, many provide too little information and/or too much in­ formation, requiring you to make estimates and/or discard irrelevant data (this is true of some synthetic problems as well). Rich-context problems are generally too difficult for most students to solve alone; they are designed for group problem-solving sessions. Advanced problems are very sophisticated problems that provide supplemental discussion of subtle or advanced issues related to the material discussed in the chapter. These problems are for in­ structors and truly exceptional students.

Read the Text Before Class! You will be able to participate in the kinds of activities that promote real learning only if you come to each class having already read and thought about the assigned chapter. This is likely to be much more important in a class using this text than in science courses you may have taken before! Class time can also (if you are prepared) provide a great opportunity to get your partic­ ular questions about the material answered.

Class time works best if you are prepared

The Principle of Relativity Foundations |

The Principle of Relativity

_j Synchronizing Clocks

[>

Time

0 Comparing Frames 0 Relativistic Dynamics

Chapter Overview Introduction In units C and N, we have explored the newtonian model of mechanics. In this unit we will explore a different model, called the special theory of relativity, that better lieht3 Th h ^Vlr ,°b'(eCtS' esPecially objects moving at close to the speed of £ the /?• ^ foundations for that exploration by describing the core dea of the theory and linking it to newtonian mechanics.

Section

R1.1:

follows: mf0rma"y

Introduction to the Principle St3te

^ Sreat

id6a

°f

thiS Unit' the

PrinciPle of relativity, as

The laws of physics are the same inside a laboratory moving at a constant velocity as they are inside a laboratory at rest. The theory of special relativity essentially spells out the logical consequences of this This unit is divided into four subdivisions. The first (chapters R1 and R2) dis-

S

(S^RfRrSdSf ^ deVu0PS imP°rtant t00ls for future use. The second relativistic concept of time. The third (chapters R6 R7 and r d u R6 R7, and R8) discusses how observers in different reference frames will view a se(Ch3PterS M 3nd M0)

^ —

Section R1.2: Events and Spacetime Coordinates What exactty does the principle mean by a "laboratory"? The first step to under standing this better is to describe operationally how we measure a particle's motion An event is something that happens at a well-defined place andtime A^ent s spacetime coordinates are a set of four numbers that locate the event in^ace and time. A particle s motion is a series of events.

ismsmm Section

R 1 . 3:

Reference Frames

sAua£anreefpframe13 ^

ast^nS sPacetime

coordinates to events. We can vi-

Section R1.4:

I nertial Reference Frames

An inertial reference frame is a frame in which an isolated object is always and every­ where observed to move at a constant velocity. We can check whether a frame is inertial by distributing first-law detectors around the frame to test for violations of Newton's first law. A consequence of this definition is that two inertial frames in the same region of space must move at a constant velocity relative to each other. Conversely, if a given frame moves at a constant velocity relative to another inertial frame in the same re­ gion of space, the first must be inertial also.

Section R1.5:

The Final Principle of Relativity

Note that in our original statement of the principle of relativity, the "laboratory mov­ ing at a constant velocity" and the "laboratory at rest" are both inertial frames. More­ over, the principle itself implies that there is no physical way to distinguish a frame in motion from one at rest: only the relative velocity between two inertial reference frames is measurable. Our final, polished statement of the principle therefore ex­ presses the core issue without referring to "moving" or being at "rest": The laws of physics are the same in all inertial reference frames.

Section R1.6:

Newtonian Relativity

What does the phrase "the laws of physics are the same" mean? We can examine this issue in the context of newtonian physics if we temporarily embrace Newton's hy­ pothesis about time, which is that time is universal and absolute and thus independent of reference frame. Consider two inertial frames that have constant relative velocity fi and which are in standard orientation relative to each other; that is, the axes of both point in the same directions in space and the Other (primed) Frame moves in the +x direction relative to the Home (unprimed) Frame. The concept of universal time im­ plies that time measured in both frames is the same (f = f); this, together with some simple vector addition and some calculus, implies that r'(f') = r(t) - fit

(Rl.l)

v'(t') = 5(f) - p

(R1.3)

a'(t') = a(t)

(R1.4)

Purpose: These equations describe how to compute an object's position r', velocity 5', and acceleration a' at any given time f in the Other Frame, given the object's position, position r, velocity 5, and acceleration a at the same time t in the Home Frame. Symbols: p is the velocity of the Other Frame relative to the Home Frame. Limitations: _ These equations assume that t = f, which is not true unless both v