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Unformatted text preview: THIS SOLUTIONS MANUAL INCLUDES: • Step-by-step Solutions to 25% of the text's end-of-chapter Problems • Solutions in same two-column format as the worked examples in the text and the Problems and Solutions in the Study Guide • Carefully rendered art to help you visualize each Problem and its Solution Visit our Web site at STUDENT SOLUTIONS MANUAL TO ACCOMPANY PHYSICS FOR SCIENTISTS AND ENGINEERS FIFTH EDITION . T his solutions manual doesn't just give you the answers. It shows you how to work your way through the problems. T he Solutions Manual includes: • Detailed step-by-step Solutions to 25% of the text's end-okhapter problems. • Solutions in the same two-column format as the worked examples in the text and in the • Carefully rendered art to help you visualize each Problem and its Solution. Study Guide. David Mills retired in May 2000 after a teaching career of 42 years at the College of the Redwoods in Eureka, California. During that time, he worked with the Physical Science Study Committee, the Harvard Project, Personalized System of Instruction, and interactivlHlngagement movements in physics education. In 1996,a National Science Foundation grant allowed him to transform the way physics was taught at his school-from a traditional lecture-laboratory system into a microcomputer-based system that employed interac­ tive teaching and learning strategies. He is currently an Adjunct Professor at the Community College of Southern Nevada. Charles Adler is a professor of physics at St. Mary's College of Maryland. He received his undergraduate, masters, and doctoral degrees in physics from Brown University before doing his postdoctoral work at the Naval Research Laboratory in Washington, D.C. His research covers a wide variety of fields, including nonlin­ ear optics, electrooptics, acoustics, cavity quantum electrodynamics, and pure mathematics. His current inter­ ests concern problems in: light scattering, inverse scattering, and atmospheric optics. Dr. Adler is the author of over 30 publications. Other great resources to help you with your course work: Study Guide Gene Mosca, United States Naval Academy Todd Ruskell, Colorado School of Mines Vol. 1,0-7167-8332-0,Vols. 2 & 3,0-7167-8331-2 • Begins with a review of Key Ideas and Equations for each chapter. • Tests your knowledge of the chapter's material with True and False Exercises and Short Questions and Answers. • Provides additional Problems and Solutions to help you master your understanding of the chapter content. Be sure to visit the Tipler/Mosca Student Companion Web site at: .whfreeman.com/tipler5e. Accessible free of charge, the site offers: www • Online Quizzing • "Master the Concept" Worked Examples • Concept Tester Interactive simulations • Concept Tester Quick Questions • Solution Builders • Applied Physics video clips • Demonstration Physics video clips Student Solutions Manual for Tipler and Mosca's Physics for Scientists and Engineers Fifth Edition DAVID MILLS Professor Emeritus College of the Redwoods CHARLES L. ADLER Saint Mary's College of Maryland W. H. Freeman and Company New York Copyright © 2003 by W. H. Freeman and Company All rights reserved. Printed in the United States of America ISBN: 0-7167-8333-9 First printing 2003 W. H. Freeman and Company 41 Madison Avenue New York, NY 10010 Houndmills, Basingstoke RG2l 6XS, England CONTENTS Chapter 1 Systems of Measurement, 1 Chapter 2 Motion in One Dimension, 13 Chapter 3 Motion in Two and Three Dimensions, 47 Chapter 4 Newton's Laws, 75 Chapter 5 Applications of Newton's Laws, 105 Chapter 6 Work and Energy, 155 Chapter 7 Conservation of Energy, 181 Chapter 8 Systems of Particles and Conservation of Linear Momentum, 209 Chapter 9 Rotation, 259 Chapter 10 Conservation of Angular Momentum, 299 Chapter R Special Relativity, 329 Chapter 1 1 Gravity, 345 Chapter 12 Static Equilibrium and Elasticity, 371 Chapter 13 Fluids, 399 Chapter 14 Oscillations, 421 Chapter 15 Wave Motion, 447 Chapter 16 Superposition and Standing Waves, 469 Chapter 17 Temperature and the Kinetic Theory of Gases, 489 Chapter 18 Heat and the First Law of Thermodynamics, 505 Chapter 19 The Second Law of Thermodynamics, 535 Chapter 20 Thermal Properties and Processes, 555 To the Student This solution manual accompanies Physics for Scientists and Engineers, 5e, by Paul Tipler and Gene Mosca. Following the structure ofthe solutions to the Worked Examples in the text, we begin the solutions to the back-of-the-chapter numerical problems with a brief discussion of the physics of the problem, represent the problem pictorially whenever appropriate, express the physics of the solution in the fonn of a mathematical model, fill in any intennediate steps as needed, make the appropriate substitutions and algebraic simplifications, and complete the solution with the substitution of numerical values (including their units) and the evaluation of whatever physical quantity was called for in the problem. This is the problem-solving strategy used by experienced learners of physics and it is our hope that you will see the value in such an approach to problem solving and learn to use it consistently. Believing that it will maximize your learning of physics, we encourage you to create your own solution before referring to the solutions in this manual. You may find that, by following this approach, you will find different, but equally valid, solutions to some of the problems. In any event, studying the solutions contained herein without having first attempted the problems will do little to help you learn physics. You'll find that nearly all problems with numerical answers have their answers given to three significant figures. Most of the exceptions to this rule are in the solutions to the problems for Section 1-5 on Significant Figures and Order of Magnitude. When the nature of the problem makes it desirable to do so, we keep more than three significant figures in the answers to intennediate steps and then round to three significant figures for the final answer. Some of the Estimation and Approximation Problems have answers to fewer than three significant figures. Physics for Scientists and Engineers, 5e includes numerous spreadsheet problems. Most of them call for the plotting of one or more graphs. The solutions to these problems were also generated using Microsoft Excel and its "paste special" feature, so that you can easily make changes to the graphical parts of the solutions. Acknowledgments Charles L. Adler (Saint Mary's College of Maryland) is the author of the new problems appearing in the Fifth Edition. Chuck saved me (dm) many hours of work by p roviding rough-draft solutions to these new problems, and I thank him for this help. Gene Mosca (United States Naval Academy and the co-author of the Fifth Edition) helped me tremendously by reviewing my early work in great detail, helping me clarify many of my solutions, and providing solutions when I was unsure how best to proceed. It was a pleasure to collaborate with both Chuck and Gene in the creation of this solutions manual. They share my hope that you will find these solutions useful in learning physics. We want to thank Lay Nam Chang (Virginia Polytechnic Institute), Brent A. Corbin (UCLA), Alan Cresswell (Shippensburg University), Ricardo S. Decca (Indiana University-Purdue University), Michael Dubson (The University of Colorado at Boulder), David Faust (Mount Hood Community College), Philip Fraundorf (The University of Missouri-Saint Louis), Clint Harper (Moorpark College), Kristi R. G. Hendrickson (University of Puget Sound), Michael Hildreth (The University of Notre Dame), David Ingram (Ohio University), James J. Kolata (The University of Notre Dame), Eric Lane (The University of Tennessee­ Chattanooga), Jerome Licini (Lehigh University), Laura McCullough (The University of Wisconsin-Stout), Carl Mungan (United States Naval Academy), Jeffrey S. Olafsen (University of Kansas), Robert Pompi (The State University of New York at Binghamton), R. J. Rollefson (Wesleyan University), Andrew Scherbakov (Georgia Institute of Technology), Bruce A. Schumm (University of Chicago), Dan Styer (Oberlin College), Daniel Marlow (Princeton University), Jeffrey Sundquist (Palm Beach Community College-South), Cyrus Taylor (Case Western Reserve University), and Fulin Zuo (University of Miami), for their reviews of the problems and their solutions. Jerome Licini (Lehigh University), Michael Crivello (San Diego Mesa College), Paul Quinn (University of Kansas), and Daniel Lucas (University of Wisconsin-Madison) error checked the solutions. Without their thorough and critical work, many errors would have remained to be discovered by the users of this solutions manual. Their assistance is greatly appreciated. In spite of their best efforts, there may still be errors in some of the solutions, and for those I (dm) assume full responsibility. Should you find errors or think of alternative solutions that you would like to call to my attention, I would appreciate it if you would communicate them to me by sending them to [email protected] It was a pleasure to work with Brian Donnellan, Media and Supplements Editor for Physics, who guided us through the creation of this solutions manual. Our thanks to Amanda McCorquodale and Eileen McGinnis for organizing the reviewing and error-checking process. February 2003 David Mills Professor Emeritus College of the Redwoods Charles L. Adler Saint Mary IS College of Maryland Chapter 1 Systems of Measurement Conceptual Problems *1 Which of the following is not one of the fundamental physical quantities in the SI system? (a) mass. (b) length. (c) force. (d) time. (e) All of the above are fundamental physical quantities. • The fundamental physical quantities in the SI system include mass, length, and time. Force, being the product of mass and acceleration, Determine the Concept is not a fundamental quantity. Determine the Concept , (c) is correct. , Consulting Table means 1 0-12 . , ( a) is correct. ' 1-1 we note that the prefix pico Estimation and Approximation *10 ·· The angle subtended by the moon's diameter at a point on the earth is about 0.524°. Use this and the fact that the moon is about 384 Mm away to find the diameter of the moon. (The angle Bsubtended by the moon is approximately Dlrm, where D is the diameter of the moon and rm is the distance to the moon.) Figure 1-2 Problem 10 Because Bis small, we can approximate it by B � Dlrm provided that it is in radian measure. We can solve this relationship for the diameter of the moon. Picture the Problem D=Brm Express the moon's diameter D in terms of the angle it subtends 1 2 Chapter 1 at the earth Band the earth-moon distance rm: Find Bin radians: Substitute and evaluate D: B = 0.5240 x D = = 21l'rad 3600 = 0.009 1 5 rad (0.0091 5 rad)(384Mm) I3.5 1 x 1 06 m I The sun has a mass of 1 .99 x 1 0 30 kg and is composed mostly of hydrogen, with only a small fraction being heavier elements. The hydrogen atom 27 has a mass of 1 .67 x 1 0- kg. Estimate the number of hydrogen atoms in the sun. *11 •• We'll assume that the sun is made up entirely of hydrogen. Then we can relate the mass of the sun to the number of hydrogen atoms and the mass of each. Picture the Problem Express the mass of the sun Ms as the product of the number of hydrogen atoms NH and the mass of each atom M H: NH Substitute numerical values and evaluate NH: *14 ·· NH = = Ms MH 1 .99 X 1 030 kg 1 .67 X 1 0-27 kg = 1 1 .1 9 X 1 057 1 (a) Estimate the number of gallons of gasoline used per day by automobiles in the United States and the total amount of money spent on it. (b) If 1 9.4 gallons of gasoline can be made from one barrel of crude oil, estimate the total number of barrels of oil imported into the United States per year to make gasoline. How many barrels per day is this? 8 The population of the United States is roughly 3 x 1 0 people. Assuming that the average family has four people, with an average of two 8 cars per family, there are about 1 .5xl0 cars in the United States. If we double 8 that number to include trucks, cabs, etc., we have 3 x 1 0 vehicles. Let's assume that each vehicle uses, on average, about 1 2 gallons of gasoline per week. Picture the Problem Systems of Measurement ( )(2 galJd) (a) Find the daily consumption of gasoline G: G = 3 xl0 8 vehicles 8 = 6 x 1 0 galJd Assuming a price per gallon P = $1 .50, find the daily cost C of gasoline: C (b) Relate the number of barrels of crude oil required annually to the yearly consumption of gasoline Yand the number of gallons of gasoline n that can be made from one barrel of crude oil: N Substitute numerical values and estimate N: 3 ( ) )( 8 GP = 6 x 1 0 galJd $ 1 .50/ gal 8 = $9 x 1 0 I d � $1 billion dollars/d = N = Y = Gh.t N = (6 � n I I n X )( 1 08 gall d 365.24 d1y 1 9.4 gal/barrel ) 1 1 010 barr els/y I Estimate the yearly toll revenue of the George Washington Bridge in New York. At last glance, the toll is $6 to go into New York from New Jersey; going from New York into New Jersey is free. There are a total of 1 4 lanes. *17 ·· Assume that, on average, four cars go through each toll station per minute. Let R represent the yearly revenue from the tolls. We can estimate the yearly revenue from the number of lanes N, the number of cars per minute n, and the $6 toll per car C. Picture the Problem R = NnC = 1 4 lanes x 4 cars x 60 min x 24-x h 365 .24 -x d $6 I $177M . I y car mm h d - - - = Units Write out the following (which are not SI units) without using abbreviations. For example, 1 03 meters = 1 kilometer: (a) 1 0-12 boo, (b) 1 09 low, (c) 1 0-6 phone, (d) 1 0-18 boy, (e) 1 06 phone, (f) 1 0-9 goat, (g) 1 012 bull . *20 · We can use the definitions of the metric prefixes listed in Table 1 -1 to express each of these quantities without abbreviations. Picture the Problem Chapter 1 4 (a) 1 0-12 boo = 1 1 picoboo I (e) (b) 1 09 low = 1 1 gigalow I (f) 10-9 goat = 1 1 nanogoat I (c) 10-6 phone = 1 1 microphone I 106 phone = 1 1 megaphone I (g) 101 2 bull =1 1 terabull I (d) 1 0-18 boy = 1 1 attoboy I Conversion of Units *25 · A basketball player is 6 ft l O t in tall. What is his height in centimeters? We'll first express his height in inches and then use the conversion factor 1 in = 2.54 cm. Picture the Problem Express the player's height in inches: h 6ftx 12in 10.5 in = 82.5in ft Convert h into cm: h 82.5inx 2.5.4cm = = + m = I 210cm I *28 · Find the conversion factor to convert from miles per hour into kilometers per hour. Let v be the speed of an object in miIh. We can use the conversion factor 1 mi = 1 .61 km to convert this speed to kmIh. Picture the Problem Multiply v milh by 1.61 kmlmi to convert v into kmIh: v mi = v mix 1 . 61� = 1 1.61vkmlh I h h ml In the following, x is in meters, t is in seconds, v is in meters per second, and the acceleration a is in meters per second squared. Find the SI units of each combination: (a) V2/X, (b)�x/a, (c) tat2 . *33 ·· We can treat the SI units as though they are algebraic quantities to simplify each of these combinations of physical quantities and constants. Picture the Problem Systems of Measurement 5 (a) Express and simplify the units of v 2Ix: (b) Express and simplify the units of �x/a: (c) Noting that the constant factor + has no units, express and simplify the units of 1- at 2 : Dimensions of Physical Quantities 2 The SI unit of force, the kilogram-meter per second squared (kg·mls ) is called the newton (N). Find the dimensions and the SI units of the constant G in Newton's law of gravitation F = Gmlmll? *36 ·· We can solve Newton's law of gravitation for G and substitute the dimensions of the variables. Treating them as algebraic quantities will allow us to express the dimensions in their simplest form. Finally, we can substitute the SI units for the dimensions to fmd the units of G. Picture the Problem Solve Newton's law of gravitation for G tovobtain: Substitute the dimensions of the variables: �3 3 � xL2 2 G= T 2 = MJ' 2 M ML - _ Use the SI units for *41 L, M, and T: Units of G are _ kg · s2 ·· When an object falls through air, there is a drag force that depends on the product of the surface area of the object and the square of its velocity, that is, 2 Fair = CAv , where C is a constant. Determine the dimensions of C. We can find the dimensions of C by solving the drag force equation for C and substituting the dimensions of force, area, and velocity. Picture the Problem Solve the drag force equation for the constant C: 6 Chapter 1 Express this equation dimensionally: Substitute the dimensions of force, area, and velocity and simplify to obtain: Scientific Notation and Significant Figures *43 · Express as a decimal number without using powers of 1 0 notation: (a) 3 x 1 04, (b) 6.2x 1 0-3, (c) 4 x 1 0-6, (d) 2. 1 7x 1 05. We can use the rules governing scientific notation to express each of these numbers as a decimal number. Picture the Problem 1 04 (a) 3 (b) 6.2x1 0-3 *47 x = 1 30,000 1 = (c) 1 0.0062 1 4 X 1 0-6 = (d) 2. 1 7 X 1 05 1 0.000004 1 = 1 2 1 7,000 1 · A cell membrane has a thickness of about 7 nm. How many cell membranes would it take to make a stack 1 in high? Let N represent the required number of membranes and express Nin terms of the thickness of each cell membrane. Picture the Problem Express Nin terms of the thickness of a single membrane: N= Convert the units into SI units and simplify to obtain: N = · 7nm lin 7 nm = *49 lin 14 x x 2.54 cm 1 06 in x 1m x 1 00cm I nm 1 0-9 m 1 Perform the following calculations and round off the answers to the correct number of significant figures: (a) 3 . 1 4 1 592654 x (23.2 , (b) 2 x 3.141 592654 x 0.76, (c) (413) 7rX (l.l , (d) (2.0)5 13. 1 4 1 592654. i i Apply the general rules concerning the multiplication, division, addition, and subtraction of measurements to evaluate each of the Picture the Problem Systems of Measurement 7 . . glven expresslOns. (a) The second factor and the result have three significant figures: 3.141592654 x (23.2f = \1 .69 x 103 \ (b) We'll assume that 2 is exact. Therefore, the result will have two significant figures: 2 x 3.141592654 x 0.76 = @] (c) We'll assume that 4/3 is �7r x (1.1) exact. Therefore the result will have two significant figures: (d) Because 2.0 has two significant figures, the result has two significant figures: = l}I] (2 . 0, 1iOl 3.141592654 � = General Problems *51 count · 1 If you could count $1 per second, how many years would it take to billion dollars (1 billion = 1 09)? We can use a series of conversion factors to convert billion seconds into years. Picture the Problem Multiply years: 1 billion seconds by the appropriate conversion factors to convert it into 109 s 1 09 S X = *57 1 1h X 1d -X 1y 3600s 24h 365.24d = \ 31.7 y \ ·· The astronomical unit (AU) is defmed in terms of the distance from the earth to the sun, namely 1 .496 x 1011 m. The parsec is the radius of a circle for which a central angle of 1 s intercepts an arc of length 1 AU. The light-year is the distance that light travels in one year. (a) How many parsecs are there in one astronomical unit? (b) How many meters are in a parsec? (c) How many meters in a light-year? (d) How many astronomical units in a light-year? (e) How many light-years in a parsec? We can use the relationship between an angle B, measured in radians, subtended at the center of a circle, the radius R of the circle, and the Picture the Problem 8 Chapter 1 length L of the arc to answer these questions concerning the astronomical units of measure. (a) Relate the angle Bsubtended S by an arc of length to the distance R: Solve for and evaluate S: ()=�R (1) S=RB min = (lParsec)(l s)( l60s ) 10 )( 21l'rad ) ( 60min 3600 =14.85 10-6 parsec 1 R=SB 1.496 l Ollm (ISl(�)(60::m)(23::;:) =13.09 1016 m 1 =e/).t (3 10' ,�;}Yl(3.156 10' ;) =19.47 1015m 1 x x (b) Solve equation evaluate R: (1) for and X � x (e) Relate the distance D light travels in a given interval of time /).t to its speed e and evaluate D for /)....
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