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GEORGE GAMOW University of Colorado JOHN M CLEVELAND University of Colorado Foundations and Frontiers PRENTICE-HALL OF INDIA (PRIVATE) LIMITED NEW DELHI Rs.

PRENTICE-HALL INTERNATIONAL, INC Englewood Chiffs PRENTICE-HALL OF INDIA (PRIVATE) LTD New Delhi PRENTICE-HALL INTERNATIONAL, INC. London PRENTICE-HALL OF AUSTRALIA PTY. LTD. Sydney PRENTICE-HALL OF CANADA LTD Toronto PRENTICE-HALL OF JAPAN, INC Tokyo PRENTICE-HALL DE MEXICO, SA Mexico City by Prentice-Hall, Inc., Englewood Chiffs, NJ, US.A All rights reserved.

No part of this book may be reproduced in any form, by mumeograph or any other means, without permission m writing from the publishers.

Gamow biography of physics pdf book download sites Dr. Gamow has written a view of physics which does not teach basic facts exclusively or dwell completely on biographical data, but rather, Dr. Gamow does both, for each chapter presents one or two great physicts and then discusses the nature and content of their work Includes sources (page ) and index.

Reprinted m India by special arrangement with Prentice-Hall, Inc., Englewood Chiffs, NJ, US.A Copynght by PRENTICE-HALL OF INDIA (PRIVATE) LTD., New Delhi First Printing - - November Second Printing October This book has been published with the assistance of the Joint Indian-American Standard Works Programme Printed by W.

H Smith at Ganges Printng Company, Howrah, and published by Prentice-Hall of India (Private) Ltd., New Delhi. EPreface In an introduction to physics at the col lege level, the authors feel that the physics of today should be strongly emphasized Modern physics 1s the key to understanding the atom and the nucleus and the quantum, which play so large a part in our hves—even relativity 1s good news- paper copy Behind these frontiers of science, however, the foundations laid down by Galileo and Faraday and others cannot be shghted The Jaws of Newton are still vital m every satelhte and rocket We have tried to make both the foun- dations and the frontiers alive and interesting.

Magnetism, Magnets and Fields The Nature of the Electromagnetic Field Electromagnetic Interaction Solenoids and Electromagnets Currents in a Magnetic Freld Galvanometer, Voltmeter, Ammeter Interactions between Currents Generation of Electric Currents Changing Flux Transformers and Alternating Current Electronics, Vacuum Tubes Oscillations and Oscillators Electronic Oscillator Radio and TV Radar Electronic Computers Reflection and Refraction of Light, Reflection of Light Plane Mirrors Concave and Convex Miriors Refraction of Light Why Is Light Refracted?

Prisms Lenses Lens Combinations Optical Instruments The Prism Spectroscope The Rambow18 19 2O The Wave Nature of Light, Interference of Light Waves Optical Gratings The Electron Microscope Light Emission by Hot Bodies Infrared and Ultraviolet Radiation Line Spectra Fraunhofer Lines Why Solids Emit a Continuous Spectrum Spectral Lines and Atomic Structure Polarization of Light Doubly Refracting Crystals Velocity of Light The Special Theory of Relativity, The Paradox of the “World Ether” Ether Wind?

So Spoke Etnstein Equivalence of Mass and Energy Relativistic Mechanics Space-Time Transformation Mr. Upside-down Mountams Floatmg Continents The Rise of Mountams Terrestnal Magnetism Physics of the Atmosphere -CONTENTS = >i! vail 33 GONTENTS. Astrophysics, Planetary Atmospheres Stellar Atmospheres Other Spectroscopic Information Properties of Matter inside the Sun Energy Production in the Sun Carbon Cycle and H-H Reaction The Future of Our Sun Cenversion Tables, Answers to Problems, Index, : Foundations and Frontiers PHYSICS:Our Place in the Universe —\ The Large and the Small In our everyday hfe we encounter objects of widely differing sizes Some of them are as large as a barn and others are as small as a pin- head When we go beyond these hmuts, either n the direction of much larger objects or in the direction of much smaller ones, it becomes m- creasingly difficult to grasp their actual sizes Objects that are much larger than mountams, such as our earth itself, the moon, the sun, the stais, and stellar systems, constitute what 1s known as the macrocosm (1e., “large world” in Gieck) Very small objects, such as bacteria, atoms, and electrons belong to the microcosm (.e, “small world” in Greek).

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If we use one of the standard scientific umts, the meter ( inches) or the centimeter ( meter or 0 inch), for measurmg sizes, objects belongmg to the macrocosm will be described by very large numbers, and those formmg the microcosm by very small ones Thus, the diameter of the sun is ,,, cm, while the diameter of a hydrogen atom 1s only om. Scien- tists customarily express such numbers in terms of positive or negative powers of ten To see how this “exponential notation” works, let us quickly review some of the rules for work- ing with exponents Suppose we want to multiply 10?

by 10°. Smce 10?=10x10=, and = 10 x 10 x 10 x 10 x 10 = ,, these two numbers multiphed together give us 10,- ,, which is It 1s easier, however, just to write 10? x 10° = 19", thus, to multiply ex- ponential numbers we simply add exponents From this explanation you might guess, and cor-rectly, that to divide you subtract exponents You can easily check this by dividing 10* by 10°, which gives 1,, or 10?

But suppose we had wanted to divide 10? by 10°? Following the rule for division, we would subtract 5 from 2 and get the answer, 10—*, which represents the number 1/1,, or 1/ As an example, let us work out how many times larger than a hydrogen atom the sun is We can write ,,,/0 , but m dividing this 1t would be very hard to keep the decimal pomt straight, f we write mstead x 10" and x , ths calculation becomes relatively simple $ B81, = X = x Sometimes, for convenience, special very large or very small units are used Thus, in the macrocosm we use the so-called astronomical unit (symbol A U ), which 1s defined as the mean distance of the earth from the sun and 1s equal to x % cm, or a stil] larger umt known as a light-year (symbol ly ), which as defined as the distance traveled by light m the course of one year and 1s equal to x 10%” cm In the mucrocosm we often use microns (symbol ,), defined as * cm, or meter, and Angstroms (symbol A), defined as cm In Fig the relative sizes of vaiious objects in everyday hfe, m the macrocosm, and im the microcosm are shown in a decimal logarithmic scale, 1.e, mm the scale in which each factor of ten 1s represented by one division of the yardstick We are accustomed, in most graphs, to have each scale division represent the addition of some number.

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In Fig , each scale division represents a multiplication by 10 The sizes range from the diameter of an election—and other elementary particles that are about one hundred-thousandth of an Angstrom—to the diameter of giant stellar galaxies, which often measure a hundred thousand hght- years across It 1s mteresting to notice that the size of the human head is yust about halfway between the size of an atom and the size of the sun, or halfway between the size of an atomec nucleus and the diameter of the planetary system (on the logarithmic scale m both cases, of course).

Simular vast variations will be found in the time intervals encountered an the study of the microcosm and the macrocosm In human history we ordinarily speak about centunes, in geology the eras are usually measured in hundreds of milhons of years, while the age of the universe itself is believed to be about five bilhon years. The time required for an electron to make one revolution around the nucleus of a hydrogen atom, on the other hand, 1s sec, and the oscillations of particles constitutmg atomic nucle: have a period of only % sec A compamison (on the logarithmic scale agam) ‘of various durations encountered in the macro- cosm, microcosm, and in our everyday hfe 1s also given in‘Fig Notice 2 OUR PLACE IN THE UNIVERSETSN SSANSNN NES Size of © & & Clusters of galaxies 10% Our galaxy Planetary 1o'6 system LAWS The sun The earth Empire State Buriding Mount Everest [Mf Sec sty Duration of Mean Irfe of U29* %ZF The Universe S .

Lee ———— es Human head AB Fingernail 7 Pinhead Dust particles 10% BD Bacteria eo, Virus 4%) particles a BX Atoms Atomic nuclet Electrons and other elementary particles, 10'S rex Life onthe earth LZ Mammais 0 Sy Human race % Written history 1 BF Awink Period of } Audible sound 10°? Life of T*-on lo“ LGR Period of Visible light tore 2.

Life of Ton Period of Medical X-rays 19°.

Gamow biography of physics pdf book download Biography of physics Biography of physics by George Gamow. Publication date Publisher Pdf_module_version Ppi Rcs_key.

Period of (rays) Fig. Space ard time scales of the universe. In the year the French Academy of Sciences recommended the adoption of an inter- national standard of length and suggested that the unit of length be based on the size of the eaith This unit, called a meter, was to be equal to one ten-milionth of the distance from the pole to the equator.

To prepare a standaid meter it became necessary to measure, with all possible pre- cision, at least a part of the earth’s mendian, and two French scientists, M Delambre and M Mécham, were charged with the task. It took them seven years to measure, by an improved tnangulation method, a stretch of meridian from Barcelona in Spain to Dunkirk in Normandy On the basis of these measurements the academy prepared a “standard meter”— a platmum-ridium bar with two marks on it that was supposed to repre- sent one ten-millionth part of a quarter of the earth’s meridian The origmal meter 1s kept at the Bureau des Poids et Mesures in Sévres (not far from Paris), and faithful copies are distributed among all the coun- tnes in the world Although the United States, along with Great Britain, has chosen not to accept the metric system as all other countries do, it possesses a copy of the standard meter at the National Bureau of Standards m Washington, D GC.

(Fig ). While in stores and factories in this country, length is customarily measured in yards, feet, and inches, scientific measure- ments are always expressed in kilometers (one thousand meters or 0 62 mules), meters, decrmaters (one-tenth of a meter), centrmeters (one- 4 OUR PLACE JN THE UNIVERSEFig. Subsequent, more exact, measurements have shown that the length of a quarter of the eaxth’s meridian is actually 10,, 8 meters The error does not matter, however, as long as we know the exact amount of discrepancy.

a unit of time A day 1s divided mto 24 hours, and each hour 1s subdivided mto 60 mmutes, with each minute further divided into 60 seconds This system of time measurement 1s based upon that used mm ancient Babylon and Egypt, and even the French Revolution (not to mention the Russian one) was unable to convert it nto a decimal system Since we use a decimal system for length and weights, we should logically divide a day into “decidays” (24 hours each), “centidays” ( minutes each), and “milhdays ( seconds each) This would neces- sitate, however, the introduction of “decadays” (10 days each), “hecto- days” ( months each) and “kilodays” (26 years each), and would lead to chaos in about years and seasons In the scientific measure- ment of time intervals much shorter than a second, however, the decimal system 1s used, and we speak about milliseconds (one-thousandth of a second) and microseconds (one-millionth of a second).

Having defined the units for length, mass, and time, we can express through them the units for all other physical quantities Thus, one unit of velocity could be a centimeter per second (cm/sec), the umt of ma- terial density, a gram per cubic centimeter (gm/cm*), etc The above have been expressed in the system of units known as the “CGS system” (for centumeter-gram-second).

The MKS system (meter-kilogram-sec- ond) is also commg into common use These two decimal systems, related to each other by simple powers of ten, are accepted by scientists all over the world, and represent a defimte advantage over the Anglo-American system of units where the velocity, for example, may be expressed at will in “feet per seconé,,” “mites per hour,” or even in “furlongs per fortnight.2 Adnillis 1/8 in m diameter Express this in centimeters 8 If sheets of paper make a stack 1 m high, what 1s the thickness of a sheet of paper, in centimeters?

4 Light of a certain color 1s composed of a tram of waves, each 5, A long How many of these waves are there m an inch? 5 What are the values of the followmg fractions? 6 x 10° x 4 x b) x x 3, 2x * x 3 x 10% ( x x x 6 The mass (which roughly means the amount of matter) of an electron 1s x gm How many electrons would be required to make 1 gm? 7 About how many oscillations would a nuclear particle make while an election made 1 revolution?

8 (a) What is the mass of a particle midway between a mass of 1 Ib and a mass of 16 Ib on the ordinary, or “arithmetical,” scale? on a logarithmic scale? (b) What 1s the mass of a particle midway between a mass of 1 oz and a mass of 16 Jb on the arithmetical scale? on a loganthmuc scale? 9 How many »? (cubic microns) are there in 1 cm’ (cubic centumeter)?

10 (a) What 1s the procedure you would follow to raise to some power a number expressed in exponential notation? (b) What is (3 x 10—°)3? (c) What as (46 x )2? (d) (46,) 3? 11 Suppose you are given a number (such as, say, 27 X ) and are asked to take its cube root (a) Can you determme the rule that tells how to deal with the exponent?

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(b) How would you take the cube root of 9 x ? (c) What as the square root of 51 x 10—5? A simple method, demon- strated by Mrs S Barry, for finding the center of gravity of a golf club Courtesy Convair, San Diego, Calif. To make the experiment more quantitative, we may use a hght but sturdy aluminum tube whose weight may be neglected, and at the two ends of which different weights can be attached When equal weights are placed on both ends, the tube will remain in equhbrium if xt 1s supported an the middle (Fig a) If, however, the weight on the left 1s twice as héavy as the weight on the right, the tube must be supported at a pomt located closer to the heavier weight in such a way that the length AB is equal to one-half the length BC (Fig b) Similarly, if the ratio of weights 1s 8 to 1 (Fig c), the ratio of lengths AB and BC should be 1to 8 Thus, we arnve at the conclusion that the distances of the center of gravity from the two ends of a stick stand in inverse proportion to the weights attached at these ends.

A reverse situation 1s encountered in the case of two men carrying a heavy load that is suspended from a stick but not from the middle of it (Fig. d) In this case, the distribution of the total load between two carriers will be inversely proportional to the dis- tances between the point of suspension and the two ends of the stick. In the case of an object of more complicated shape, the center of gravity can always be found by suspending it on a string attached first at one point and then at another pomt on its surface An object always comes to rest with its center of gravity directly under the point of suspension Sup- pose we cut an object out of plywood with the shape shown in Fig If we suspend it at the pomt, A, it will hang in the way shown in Fig SOLIDS, LIQUIDS, AND GASES) 17(left), and its center of gravity must be located somewhere on the hne AB If we suspend it at another point, C, the object will hang as shown m Fig (nght), and the center of gravity must be somewhere on the lme CD Thus, the exact loca- tion of the center of gravity 1s de- : termed by the intersection, E, © of the lines AB and CD !

To continue our discussion con- cernmg the center of gravity, let us consider the following interest- ee ing problem Suppose we have a 5 Lr large number of books of equal eae Scrat etch aged size and want to pile them at the objects edge of a table in such a way that the top book will protrude as much as possible beyond the table's edge How can we do it?

If the bottom book 1s placed so that 3t protrudes by almost one-half its length, the second and all the followmg books cannot project any more without falling, and nothing will be gained by pilng up more of them Suppose that, mstead of starting the arrangement with the bottom book, we first consider the book that 1s on top. Since all that is required from it 1s that it not fall from the pile below it, 1t can project out by just a little less than half its length By inspecting Fig we see that the common center of gravity of the first and the second books will be located a quarter-book length to the night of the edge of the second book Thus, if these two books are placed on top of the third one and overhang it a quarter length (or just a little bit less), they will not fall.

Let us go one step further and find the center of gravity of the system of the thee top books The way the books are stacked, the center of gravity of the first two 1s halfway between them, and the center of gravity of the third book is, of course, m its middle Since the combmation of the first two books 1s twice as heavy as the third book, according to the law illustrated in Fig b, we should expect the center of gravity of all three books to be located twice as close to the center of gravity of the first two as it is to the center of gravity of the third one A glance at Fig.

shows that the overhang of the third book should be one-sixth of its total length. If we proceed m the same way down the pile, we will find that the next two overhangs will be one-eighth and one-tenth, respectively. With five books, the distance of the outer edge of the top book from the edge of the table will be. (+ Ay) book lengths = book lengths S 12 soins, LIQUIDS, AND GASES‘Thus, by pihng books up m a rational way, we can do much better than a half-book overhang, in fact, better than a full-book overhang If we use more than five books, the sum in the bracket above must be extended by adding ys, 7x, rs, etc., and it can be proven mathematically that the sum of a series of terms of this kind can become as large as we want, provided that we add enough terms By stacking an unlimited number of books, therefore, we can make the top book protrude any desired distance be- yond the edge of the table Because of the rapidly decreasing contribu- ton of each new book, however, we will need the entire Library of Con- gress to make the overhang equal to three or four book lengths!

(5) Fig. The best way to pile books that edge beyond a table The pont (1 42) 1s the center of gravity of the two top books The point (1 + 2+ 3) is the center of gravity of the three top books and 1s located one-third of the way between the double weight applied at (I +2) and the single weight applied at (3). In Fig. we see a photograph of five books actually piled up in the above described manner Although, in piling up these books, the photog- rapher placed the centers of gravity well within the underlying edges, the top book protrudes beyond the edge of the table by slightly more than its full length.

Levers If we look again at the balanced rods and weights in Fig. , we can figure out sqme of the laws of levers If the rods are not to crash to the earth or fly up to the sky, it is clear that the forces pushmg them SOLIDS, LIQUIDS, AND Gases) 13,Fig A photograph of an actual protruding column of books Photo- graph by Dr Philpot upward must exactly balance the forces pulling them down So im a, b, and ¢, the sharp fulcrum at B must be pushing up agamst the rod with forces equal to the weight of 2 kg, 3 kg, and 4 kg, respectively This balance of forces, however, 1s not enough to ensure that the rods are in equilibrium, because we must also make certain that they do not be- gin to spm ke pmwheels The rotating effect of a force depends not only Fig.

The torque produced by force depends on the length of the lever orm. on how big the force 1s, but also on where it 1s apphed. In Fig a, for example, it will be very hard to turn the rusted nut The turning effect, or torque, 1s the force F multiphed by the dis- tance d, By shpping a piece of pipe over the wrench handle, as m Fig b, the distance, or lever arm, 1s increased to do, and the torque, Fds, 1s made much greater without any mcrease in the force We must note here that the lever arm is always measured from the center of rotation per- pendicular to the le of action of the force F This 1s seen to be he case for d, and dz m Fig 26a and b.

In Fig c, how- 2ver, the ‘situation is different, and ds must be measured fromthe center of the pipe in the direction shown, which 1s perpendicular to the dashed Iine of action of F, 1, the prolongation of the arrow or vec- tor representing the pull of the hand Figure replaces the picture of Fig c by a simple chagram of forces and distances If we unagine the bar trying to turn about B, force A will have a torque of 3 X 1= 3 umts counterclockwise and will be just bal- anced by the clockwise torque of force C, which equals 1 x 3 = 3 units The 4-kg force at B will have no torque about B as a center of rotation, because its lever arm 1s zero.

If you check the torques around A and C m the same way, you will get the same results—namely that the clock- wise torque equals the counterclockwise. If we use + and — signs to indicate upward and downward forces, and counterclockwise and clockwise torques, the conditions for equilibrium can be put in a very brief mathematical form Oo 0 and.

kg Fig For a body in equilibrium, the forces upward equal the forces down. ward and the clockwise torques equal the counterclockwise torques The & is the Greek capital letter sigma and is used by mathematicians to mean “the sum of” The lever in Fig would check out as EF =4—-3—-1=0 2r=3xXxX3=0 Suppose we try this out on a Ib plank, 12 ft long, which projects 4 ft beyond the rail of a ship (Fig ) How far out can a Ib man walk?

Here we must take into account the Ib weight of the plank, which can be taken as acting at the plank’s center of gravity When the man has gone out as far as he can, the plank will be teetering on the rail, and the rail will have to push upward with a force of Ib Taking the torques (or moments, as they are often called) of the forces about the rail, we have x counterclockwise, which must equal x 2 clock- wise.

This gives us. SOLIDS, LIQUIDS, AND GASES 15, = X 2 = or: z= HG = it These prmaiples can be apphed to the use of various kinds of levers If the ratio of lever arms is sufficiently large, a small effort applied at the end of the longer lever arm can easily move a heavy rock at the other end (Fig a). The ancient Greek scientist, Archimedes ( 8c ), who was the first to formulate the basic mechanical prmciples involved m the use of levers, exclaimed once “Give me a point of support and I can turn over the entire world” (Fig b) Friction In discussing the way that the center of gravity of a golf club or other object always stays between the two supporting fingers on which it sldes, we have seen that as the force between two objects becomes larger, the force of friction between them also becomes larger.

More de- tailed studies have shown that the frictional force retarding one object slidmg on another is proportional to the force that 1s pressmg them to- gether The proportionality constant is called the coefficient of friction between the surfaces, and in most textbooks 1s assigned the symbol » (the Greek letter mu), so that. Foie = » X F Fig.

The counterclockwise torque of the pirate 1s balanced by the clock- wise forque of the massive plankFig “Pressure” here is not the same thing as “force” It 1s the force per unit area, that 1s, the total force di- vided by the area over which 1t 1s exerted Figure shows a tank contammg an imaginary column of liquid 1 cm square and extending h cm from the bottom to the top free surface.

The volume of this column is h cm? and its weight will be h times what a single cubic centimeter weighs. This latter figure, the weight of 1 cm* (or 1 ft, or 1 m8) of any substance, is called the density of the substance, and we can let it be represented by the letter d The weight of the column of liquid then will be hd gm, and this weight 1s supported by 1 cm?

of the Liquid of density ‘J gm/em? a h Fig. Each square centimeter of the bottom of the tonk supports a col- a umn of liquid that weighs hd gm. The total force on the tonk bottom is pressure A eet X area = abhd. bottom Since force per umt area 1s what we mean by pressure, we can use this general formula for the pressure at any depth m a liquid.

P=hd ‘We used the bottom of the tank in making our calculation, but the same arguments will hold for the pressure at any depth Water, or any other fluid, since it does not have a mgid shape, cannot resist a pressure exerted on it in only one direction, the way, for example, a block of steel can when it resists being squeezed in a vise Instead, liquids squash out in all directions and will exert an The pressure in vessels of equal pressure against the walls lta tometer arereemeterTeoel of the contamer.

So our formula, depths. P=hd, is equally useful to tell the pressure against the wall of a container at any depth, no matter at what angle the wall happens to be For this reason, the shape of the contamer makes no difference. In Fig. , 1f both vessels are filled with a hquid of density d, the pressure at the bottom 1s Jud for both, and at the pomts marked A the pressure m both is had Pascal’s Law Since the pressure on any small piece of a fluid is the same in all directions, any increase of pressure on a fluid in a closed contamer will be transmitted equally to every part of the fluid.

This basic law was dis- covered by the French physicist, Blaise Pascal (), and carnes his name. Imagme a closed vessel with two vertical cyhnders of different diameters protruding from its upper part (Fig.

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) These cylmders are fitted with pistons that can be loaded with various numbers of heavy weights If we place one weight on the piston in the narrower cylnder, it will produce a pressure within the liquid, and this same pressure will be transmitted to all parts of the vessel ancluding the surface of the larger piston Since, however, the area of that piston is larger, the total force acting on it will be larger, too In the example shown in Fig , the cylinder on the right is twice as large m diameter so the areas of the two pistons stand in the ratio 4 to 1 Since the total force of hydrostatic pres- sure acing on the night piston will also be four times larger, we will have to place four weights on it to maintain the equilibrium The above de- scribed principle forms the basis of the hydraulic press in which the pres- SOLIDS.

LIQUIDS, AND Gases sure created within a liquid by a comparatively small force acting on a small piston exerts a much stronger force on another piston of consider- ably larger diameter. Archimedes’ Law We turn now to the im- portant subject of solids floating in liquids Everybody knows that a piece of wood will float in water because its density 1s smaller than that of water (ie, it has less weight per unit vol- ume), and that a piece of metal will sink because its density is Fig.

A demonstration of Pas- greater There is a story, how- oe ever, of a student in a freshman course in physics who was asked whether a solid iron sphere would float in mercury and who could not give the answer. “I can tell you this much,” said the professor, trying to help him, “the density of iron relative to water is 8, and the density of mercury is ” “Oh!” said the lad brightly, “then almost two iron spheres can float in merc Although a solid metal object will not be supported by water and will sink to the bottom, the fact that 1t 1s submerged m a liquid will diminish its apparent weight This phenomenon can be easily seen m Fig On the left 1s a spoon suspended m water on a string.

On the right there is no spoon, but the volume that was previously occupied by the spoon and now is, of course, filled by water is shown by dotted lines If we consider this part of the water separately from the rest of the water in the glass (think of it as a thin-walled plastic container which has the shape of a spoon and is filled with water ), we can see that it is completely supported by the surrounding water and moves neither up nor down If the “water spoon” is replaced by a silver spoon, the net force acting on the spoon will be the difference between the weight of the silver spoon and the weight of the water spoon.

Thus, we can conclude that any material body suspended within a liquid is acted on by an upward buoyant force and hence apparently loses weight in the amount equal to the weight of the liquid it displaces. ‘This famous law was discovered by Archimedes, who, as the story goes, thought of it while sitting in a bathtub, and then, in his excitement, rushed through the streets of Alexandria shouting “Eureka, Eureka!” (“I have found it, I have found it,” in Greek).

The populace of the city was 20 =soLms, LIQUIDS, AND GASE! not impressed by the great discovery, however, un- doubtedly they thought he had found a missing cake of soap in the tub Whether the above account 1s true or not, a more credible story 1s that Archimedes used this law while checking the authen- tuaity of a golden crown that Fig.

Archimedes’ law apphes also, of course, to objects floating on water and only partially submerged In this case, the weight of a floating object such as a ship 1s the same as the weight of the water it displaces ‘We can try another example, a bit more complicated Suppose a gm stone weighs gm when submerged m water and gm when sub- merged in oil Because the stone loses 60 gm m weight when it 1s n water, xt must displace 60 gm of water, and its volume 1s therefore 60 cm?

This gives a density of /60 = gm/cm for the stone In the oil, the 60 em stone loses only 50 gm of weight, so 60 cm of oil must weigh 50 gm, and the density of the oil 1s 50/60 = gm/cm’. Bernoulli's Principle Pascal’s and Archimedes’ laws pertam to fhe field of hydrostatics, 1e, the study of equibbrium of hquids We will now take up one of the important items from the field of hydrodynamics, ie, the study of hq- soups, igus, AND cases 21uids im motion Consider water flowing through a pipe with a varymg chameter (Fig ) In the narrow part of the pipe, the water-flow is faster than it 1s m the wider part because the same amount of water must go through it per umit time as goes through the wide part Since the water speeds up when it enters the narrow section, there must be a force that makes it move faster, and the force can be due only to the pressure dif- ference between the wider part of the pipe on the left and the narrower muddle part Thus, mm the narrower part of the pipe the pressure 1s lower than in the wider part Similarly, when the water enters the wider part Fig The pressure 1s lower in the narrow part of the tube whe: the water moves fast on the right, it is slowed down in its motion and we can see that the pres- sure again must be higher.

This fact can be easily demonstrated by at- tachmg narrow vertical pipes to the three parts of our honzontal pipe, as shown in Fig The water in the middle pipe will stand lower and thus indicate a lower pressure The statement that in the regions where the velocity of fluid is smaller, the pressure 1s higher, and vice-versa, 1s known as the principle of Bernoulli, after a Swiss physicist, Damel Ber- noulli (), who discovered 1t In Chapter 5 we will examine Bernoulh’s prmciple agam, quantitatively.

Surface Tension and Capillarity Before we leave the subject of liquids, we must say a few words about the phenomenon of surface tension As we imphed above when we reminded you of dewdrops, liquids show some tendency to assume a characteristic shape which, for small quantihes of the quid, competes with the force of gravity that forces liquids to assume the shape of their containers.

We may think of droplets of water falling from a faucet or from the sky, small water droplets resting on an oily surface, drops of mercury on a glass plate, etc Another example is provided by a glass heaping full of water m which the water level stands slightly above the rim of the glass and ssopes down towards the edges The behavior of liquid m all these cases 1s caused by certain forces acting along the hquid surface that tend to shrink that surface to the smallest possible size.

The 22 souips, LIQUIDS, AND GASES. liquid behaves as though its surface were covered with a sort of elastic membrane that has a tendency to constantly shrmk mm size. The strength of this “membrane” 1s the meas- $ ure of the surface tension, and can be measured easily by measuring the force, F, needed to pull a fine wire up from the surface of a quid on which it as lymg flat (Fig ).

In or- der to pull the wire free, you must first break the two sheets of water surface, one on each side of the wire, that tend to hold xt back. If each sheet has a length I (the length of the wire), the surface tension of Fig Measurement of surface the liquid surface must be F/21 tee) for each umt of length “For water, this surface tension is about 73 dynes/cm at room temperature, and for mercury, about dynes/em Since, for a given volume, a sphere possesses the smallest surface, these surface tension forces will give to hquid bodies a regular spherical shape, af not interfered with by other forces.

If a liquid drop rests on a surface that does not “wet,” (we will return to this notion m a minute), a conflict Fig. Capillary forces de- press mercury in a glass tube (a) and raise water in the same fube (b). arises between gravity forces, which tend to spread it thmly over the en- ture surface, and the surface tension forces, which tend to keep it spheri- cal As a result, the drop assumes the shape of a flattened ellipsoid.

* We have not yer defined the dyne, which 1s a very importan? umt for measuring forces. One dyne is equal to about 1/ of the weight of a gram SOLIDS LIQUIDS, AND GASES 23Closely connected with surface tension are the capillary forces that act on the boundanes between solid and liquid (or two liquid) bodies If we put a narrow glass tube ito a dish of mercury (Fig.

a), we will find that, although the hquid enters the tube, its level on the inside is somewhat lower than that on the outside In addition, the surface in- side the tube will have the shape of a convex meniscus. This phenomenon as the result of another competition between forces, one in which the molecules of the mercury adhere more strongly to each other than they do to the molecules of the glass tube.

The mercury therefore does not wet the glass, and surface tension squeezes the mercury down below its natural level. In Fig. b, the same glass tube 1s put into a dish of water, and the Glass tube ‘Normal level of hquid inside tube Fig Surface tension is the cause of capillary action. If the radius of the tube 1s r cm, the volume of this raised hquid is «1h cm and its weight is x1*hd gm, where d is its density in gm/cm* We want to set this weight equal to the pull of surface tension, which 1s T dynes/cem along the cir- cumference, times the length of the circumference, 2wr, or a total of QurT dynes.

Gamow biography of physics pdf book download library: Dr. Gamow has written a view of physics which does not teach basic facts exclusively or dwell completely on biographical data, but rather, Dr. Gamow does both, for each chapter presents one or two great physicts and then discusses the nature and content of their work.

‘We come now to a rather important pomt We cannot, as they are now, set these two expressions for surface tension pull and the weight of the liquid equal to each other, because one is in dynes and the other in grams. upside-down test tube with some air mn it (Fig a) By pressmg on the rubber membrane, we push water into the test tube, thus compressing the air in it and malang the diver heavier than the surrounding fluid As a result, he sinks to the bottom If we release the pressure, the air m the tube will expand and push the water out of it, and the diver will float up Figure b illustrates a modification of the diver ex- perment that 1s both much more striking and easier to perform Take an ordmary bottle with not too wide a neck and fill it heapmg full of water Then take three paper matches, break each in two near the middle to get the proper buoyancy, and drop the ends with the heads into the water The matches will float at the surface of the bottle because the buoyancy of ther paper bodies will support their heavy heads Fig.

The classical “Cartesian But if you cover the openmg diver” (a) and its more modern tightly with your thumb and baat) push m to build up some pressure (it requires some but not much practice), you will see the matches dive to the bottom Release the pressure and up they come! The explanation 1s that the submerged matches still contain some arr, either in capillaries in the paper or an the form of small ar bubbles attached to thew surfaces Under the pressure produced by your thumb, this air com- presses—yust as the air did mside the Cartesian diver—and the matches lose their buoyancy and sink When you release the pressure, the bubbles expand, the buoyancy 1s regained, and the matches rise.

The interesting point of this exper:ment is that it 1s always possible to adjust the pres- sure in such a way that one match stays at the bottom, one at the surface, and the third in the middle of the bottle This is due, of course, to the fact that there is always enough difference in the air content of the three matches (under a properly adjusted pressure) to make one of them buoyant, one sinkable, and the third just in between.

Atmospheric Pressure The gaseous envelope, or atmosphere, that surrounds our globe is essentially a mixture of nitrogen ( per cent) and ozygen ( 26 sous, LiyUms, AND CASESper cent) plus small amounts of carbon dionde, argon, and some other gases At lower altitudes, 1t also contains variable amounts of water vapor, which can be more convemently considered as an admixture rather than as a permanent mgredient of the atmospheric air The total weight of the texrestrial atmosphere 1s 5 x 10'5 tons, which amounts to about one kulo- gram for every cm?

Fig. The mercury barometer. A mechanical device for measuring atmosphenc pressure is the aneroid barometer which records varying atmospheric pressures by the deforma- tions of a thm-walled metal box The microbarograph in Fig. is an aneroid barometer that records the pressure on a revolving graph. ‘As we rise above the earth's surface (or rather, above sea level) by climbing ugh mountains or in a balloon or airplane, less and less air is left above our heads, and the atmospheric pressure decreases correspond- ingly, the amount of air over the top of Mt.

Everest is only one-third of that above sea level, and chmbers on it are forced to carry oxygen tanks with them in order to breathe. Boyle’s Law Returning to the compressibilty of gases, we will formulate the basic law discovered by an Irish physicist, Robert Boyle (). Take a closed glass tube with some air trapped m it and an open tube and connect them with a mercury-filled rubber tube a couple of meters long, as shown m Fig.

Start the experiment with the two glass tubes in the relative positions shown in Fig a, in which the mercury stands at the same level in both of them. Under these conditions the trapped aur is under normal atmospheric pressure. Now move the open tube up 28 soums, Liguips, AND GASESFig An aneroid microbarograph, which records, by means of the pen, pressure changes on the graduated chart that revolves on a drum The large cylinder that looks like a coiled spring is a metal chamber with corrugated walls It lengthens and shortens as the pressure of the atmosphere varies George F Taylor, Elementary Meteorology (Englewood Cliffs, NJ: Prentice.

Hall, inc, ) Courtesy Bendix-Friez until the trapped aur 1s compressed to one-half of its onginal volume You will find that, in this case, 1f we have been careful to keep the tempera- ture constant, the difference m the mercury levels will be about mm (Fig b)* Move the open tube higher until the trapped air 1s squeezed to one-third of 1ts origmal volume and you will find that the difference in the mercury levels 1s now 1, mm, or 2 x mm (Fig c).

In case (a) the trapped aw was subject to atmospheric pressure, 1e, mm of mercury In case (b) the pressure was mcreased mm to a total of two atmospheres. In case (c) the pressure was that of three atmospheres Since the volumes of trapped air were m the ratios 1 4 4, we can conclude that the volume of gas at constant temperature is in- versely proportional to the pressure to which it is subjected, which 1s the classical Boyle’s law of gases Air and other gases follow this law fawly precisely, but at very high compressions deviations are observed toward * It wall vary shghtly, depending on the atmosphenc pressure SOLIDS, LIQUIDS, AND GASES 29lower compressibility This 1s quite understandable smce m these cases the density of gas approaches that of hquids, which possess very low compressibihty.

States of Matter The three states of matter described above— sohd, liquid, and gaseous—do not, of course, represent a ‘umique attribute of any given maternal While water, as we all know, 1s ordmanily a fluid, it freezes into a sohd block of 1ce at a low temperature and turns into a vapor at a suffi- ciently high temperature. (We avoid here the use of the word “steam” for water vapor, be- cause the popular notion 1s that the steam commg from a teapot or a steam engine is something that can be seen as white puffs The white color- ing, however, as in the case of clouds or fog, 1s caused by tiny water droplets and not by the water vapor itself ) Other substances can also be found m all these three states, but ther meltmg and evaporation points vary quite widely.

Iron, for example, melts only at 3,°F and does not tum into vapor, under atmospheric pressure, until its temperature reaches 5,°F Nitrogen, on the other hand, the mam com- ¥ pressure —~ Q g 5 6 42 £o BS 5° 2 83 £3 a £? ES <= an Fig. An apparatus for deter- mining the compressibility of gases ponent of air, does not hquefy until its temperature drops to —°F and does not become sohd until its temperature goes down to —°F 30 soLms, LIQUIDS, AND GASESQUESTIONS 1 A man has caught a large fish which he wishes to weigh He has two spring scales, each able to weigh up to 10 Ib, but the fish weighs more than 10 Ib So he takes a light stick 8 ft long, suspends each end of the stick from one of the scales, and hangs the fish on the stick The two scales now read 6 Ib and 8 Ib, respectively (a) What does the fish weigh?

(b) At what pomt on the stick did he hang the fish? (c) If he had hung the fish from a pomt on the stick just 1 ft from one of the scales, what would each of the scales have read? 2 A tapering bamboo pole is 6 ft long and weighs 10 Ib It is found to bal- ance at a pomt 2'5 ft from the large end How much weight must be hung from the small end of the pole to make it balance at its mdpomt?

8 It takes a push of 25 kg to move a kg wooden crate along a smooth oe floor What 1s the coefficient of friction between the crate and the oor’ 4 Akg man finds he cannot push the crate im the above question because his leather shoe-soles shp on the floor When he changes to rubber-soled shoes, he 1s able to push the crate along What can you say, from this above informa- tion, about the coefficients of fmction between leather and the floor, and rubber and the floor?

5 What 1s the density of the iron block mentioned m the section on Fric- tion? 6 Knowmg that water has a density very close to 1 gm/cm3, compute the density of water in Ib/ft 7 ~What 1s the volume of the fish m Question 1? What assumption must you make m order to figure this? 8 A bottle weighs gm, and has an internal volume of just cm?

The bottle 1s filled with oul, and 1s then found to weigh gm What is the density of the ol? 9 If, m Question 8, you did not know the volume of the bottle, what would be an easy and accurate way of finding 1t? 10 At the bottom of a swimmmg pool 10 ft deep, what is the pressure (in Tb/in2) due to the water? 11 A corked bottle can withstand a pressure of 50 Ib/m 2 without crushng How deep 1m the ocean can this bottle be lowered before 1t 1s crushed?

(Assume sea water has a density 1 05 times as great as pure water ) 12 A tank 5 m high 1s half filled with water, and then 1s filled to the top with oil of density gm/cm, What 1s the pressure at the bottom of the tank due to these hquids m 1t? 18 A hydrauhe jack has a piston 05 cm mm diameter on which a force 1s apphed, and a piston 6 om in diameter which raises a load How much force must be apphed to hft a load of 2, kg?

14 A stone weighmg gm appears to weigh pnly gm when it is submerged in water (a) What is the volume of the stone? (b) its density? 15 In order to find the density of some acid, we fisst weigh a glass stopper m air ( gm), then m water ( gm), and then mm the acid ( gm) (a) SOLIDS LIQUIDS, AND GAsES 31