Student's Guide Physics in the Modern World Jerry B. Marion University of Maryland College Park Academic Press New York / San Francisco / London A Subsidiary of Harcourt Brace Jovanovich, Publishers COPYRIGHT © 1976, BY ACADEMIC PRESS, INC. ALL RIGHTS RESERVED. NO PART OF THIS PUBLICATION MAY BE REPRODUCED OR TRANSMITTED IN ANY FORM OR BY ANY MEANS, ELECTRONIC OR MECHANICAL, INCLUDING PHOTOCOPY, RECORDING, OR ANY INFORMATION STORAGE AND RETRIEVAL SYSTEM, WITHOUT PERMISSION IN WRITING FROM THE PUBLISHER. ACADEMIC PRESS, INC. Ill Fifth Avenue, New York, New York 10003 United Kingdom Edition published by ACADEMIC PRESS, INC. (LONDON) LTD. 24/28 Oval Road, London NW1 ISBN: 0-12-472278-4 PRINTED IN THE UNITED STATES OF AMERICA To The Student This Guide is designed to help you in your study of the science of physics using Physios in the Modem World. As you proceed through the text material, you may wonder which are the really important topics, ideas, equa­ tions, and numbers. In this Guide you will find, for each chapter, a list of the Objectives for that chapter. You should look carefully at these lists as you read the chapters so that you will be able to identify the important points. You can test your understanding of the material by answering the supplementary questions and working the supplementary exercises that are given for each chapter. The answers to the various questions are given at the end of each chapter. If you are pursuing a self-paced course, the lists of objectives and the questions and exercises for each chapter should assist you in preparing for the unit examinations that your instructor will use to gauge your progress. Also in this Guide you will find, for each chapter, a list of Readings. These are not merely references to other textbooks — you will have no dif­ ficulty locating such material. Instead, the books listed here emphasize historical, biographical, and popular accounts of the topics in the text. A large fraction of the books are available in paperback editions. There are also numerous magazine articles that are useful sources of supplementary reading material. However, the lists here include only articles in Scientific American because this magazine is widely available and contains articles on a great variety of scientific topics, and because the level of presentation is such that students in introductory physics courses will be able to understand most of every article. vii Chapter 1 Introduction to Physical Ideas Objectives Things you should understand and know how to do in Chapter 1: 1. You should know that the fundamental units of measure in science are those of length, time, and mass* All other quantities (such as den­ sity, energy, force, pressure, and so forth) can be expressed in terms of these three fundamental quantities. 2. You should know that the metric system of measure is based on the standard units of the meter, the kilogram, and the second (the MKS system). 3. You should remember these metric multiples: 1 m = 100 cm 1 cm = 10 mm 1 km = 1000 m 1 kg = 1000 g 4. You should remember these conversion factors: 1 in. = 2.54 cm 1 lb = 0.454 kg (or 1 kg = 2.2 lb) 5. You should be able to convert from any British unit of length or mass to the equivalent metric unit and vice versa. For example, from miles to meters by using 1 mi = 5280 ft, 1 ft = 12 in., 1 in. = 2.54 cm, and 100 cm = 1 m. 6. You should be able to express any number in terms of powers of ten. 5 4 For example, 140 000 = 1.4 χ 10 and 0.00013 = 1.3 χ 10" . 7* You should be able to multiply and divide using powers of ten. For 3 4 7 4 6 example, (2 χ 10 ) χ (3 χ 10 ) = 6 χ 10 , (4 χ 10 ) χ (2 χ 1θ") = 2 6 2 4 8 χ 10" , and (6 x 10) * (3 χ 10) = 2 χ 10 . 1 CHAPTER 1 8. You should be able to estimate and express the sizes of some everyday things in terms of metric units and powers of ten. -2 For example, the width of a finger is about 1 cm = 10 m; the volume 3 of an ordinary bedroom is about 4 m x 4 m x 3 m = 4 8m . 9. You should understand the reason for the adoption of atomic standards of measure for length and time. You should understand why the kilogram cannot yet be specified in terms of an atomic standard. 10. You should remember the definition of density; density is mass per unit volume, ρ = M/V. If you are given any two of the three quantities in this expression, you should be able to calculate the remaining quantity. 11. You should have a rough idea of the density of some everyday things. 3 (It is probably easier to think about densities in g/cm because the 3 density of water is 1 g/cm . Remember this value.) Important Equations and Numbers Conversion factors: 1 in. = 2.54 cm 1 lb = 0.454 kg M Density: ρ = ~ 2 CHAPTE R 1 Examples 1 . I n etpahC r 6 w e wil l nif d aht t ht e anoitativarg l crof e o n a n cejbo t o f mas s ecudorp d b y a n cejbo t o f mas s i s M M ± 2 F = G wher e r i s ht e cnatsid e betwee n na d M^. hT e inu t o f F i s ht e 2 kg-m/s . ahW t i s ht e inu t o f GÏ noituloS : nivloS g of r G w e vah e 9 2 F χ r G = MM 12 so that the unit of G is the 2 2 (kg-m/s) χ m 3 2 ^-f——|-* = m 7/ lkg-s kg x kg 2. Express 1 cm/s in miles per year (mi/y) Solution : 1 cm _ ., cm * 1 in. Ί ft 1 mi ' s 1 s— X 2 .54 cm 12 in. 5280 ft 3600 s 24 h 365 days X 1 h 1 day ι y = 197 mi/y 3 CHAPTER 1 3. Calculate the height of a cylinder of radius 3 cm, which has a mass of 3 500 g and a density of 4 g/cm . Solution; ρ = y and V = ττν η so 9 TW h = — Ρ Therefore, ^2 = — ——2 — ... . . ,,^ι -, „ ^2Ρ. 3 ~ 4.43 cm τπτ»ρ (3.14) (3 cm)(4 g/cm ) J. Β. Conant, Science and Common Sense (Yale University Press, New Haven, Conn., 1951). G. Gamow, One, Two, Three ... Infinity (Viking, New York, 1962). C. C. Gillespie, The Edge of Objectivity (Princeton University Press, Princeton, N. J., 1960). S. A. Goudsmit and R. Claiborne, Time (Time, Inc., New York, 1966). H. Margenau and D. Bergamini, The Scientist (Time, Inc., New York, 1964). M. A. Rothman, Discovering the Natural Laws (Doubleday, Garden City, Ν. Y., 1972). P. Tompkins, Secrets of the Great Pyramid (Harper and Row, New York, 1971). An interesting commentary on ancient Egyptian metrology; the last few chapters, however, are sheer numerology. A. M. Weinberg, Reflections on Big Science (M.I.T. Press, Cambridge, Mass., 1967). Scientific American articles: Α. V. Astin, "Standards of Measurement," June 1968. J. Cohen, "Psychological Time," November 1964. H. Lyons, "Atomic Clocks," February 1957. Lord Ritchie-Calder, "Conversion to the Metric System," July 1970. 4 CHAPTER 1 Supplementary Questions and Exercises 1. In the metric system, length, time, and mass are measured in (a) foot, second, and pound* (b) foot, second, and kilogram· (c) meter, minute, and kilogram. (d) meter, second, and kilogram. 2. Which of the following is not correct? 2 4 (a) 0.014 = 1.4 χ 10 (b) 13760 = 1.3760 x 10 4 6 4 (c) 127 x 10 = 1.27 χ 10 (d) 0.000078 = 0.78 x 1θ" 3. Write the following in powers-of-ten notation: (a) 137650 (b) 162.78 (c) 0.00037 (d) 100 000 000 000 4. Since 1967 the international standard of time has been based on (a) rapidly vibrating quartz crystals . (b) the light emitted by krypton atoms . (c) vibrations of cesium atoms. (d) a vibrating tuning fork. 5. How old are you in seconds? (Do not neglect leap years.) 6. A facetious unit of speed is furlongs/fortnight. Express this in mi/h and in cm/s. (A furlong is 220 yards and a fortnight is 2 weeks.) 5 CHAPTER 1 What is the advantage of having atomic standards for length and time, compared with arbitrarily defined standards? 8. How many grams are in a ton? (1 ton = 2000 lb) 9. Which of the following is approximately correct? 4 (a) 1 day = 10 s (b) 5 kg = 11 lb (c) 3 mi = 2 km (d) 1 ft = 15 cm 3 4 3 10. What is the mass of 100 cm of mercury (p = 1.36 x 10 kg/m )? 11. Density is defined as the ratio ζ ν mass ν volume (a) —- (b) /Λ volume mass m (U ;\ ass }volume K length length 12. Arrange the following list according to increasing density: steel, oil, cork, lead, rock. 6 CHAPTER 1 13. Given two objects and told that the objects have the same density, which one of these statements must be true? (a) The volume is the same for both objects. (b) The mass is the same for both objects. (c) If the objects are cylindrical, they have the same diameter. (d) If one object has twice the volume of the other object, it also has twice the mass. 14. A crystal cube has sides which are 11.5 mm long. If the mass of the 3 crystal is 3.5 g, what is its density expressed in g/cm ? 15. Suppose that you have 2 blocks of gold, one with a mass of 2 kg and the other with a mass of 5 kg. What is the density of each? 7