Laboratory exercises to accompany Carhart and Chute's First principles of physics

Preface

In the preparation of a Physics laboratory manual, it is necessary to take into account the diversity of courses and equipment in different schools. The individuality of the teacher and the limitations of equipment have been recognized in the selection and treatment of topics, in these Exercises, and a wide choice of experiments has been provided, only a few of which require highly specialized apparatus. Where such apparatus is decidedly superior to that commonly used, specific directions for its preparation have been given in footnotes. Experiments which have proved their value in generally accepted courses have been retained with such simplifications as seem desirable to secure directness. Other experiments which represent the more modern trend in Physics teaching are introduced in considerable number to enrich the course.

Many students lose the value of the laboratory period because it is spent in following directions in a purely mechanical way, while they wonder why the particular problem on which they are engaged should be done at all. In order to settle this question in the student's mind, the authors have been in the habit of furnishing their students with .an introductory paragraph for each experiment. This introduction connects the experiment with the pupiFs experience and furnishes definitions of such terms as are necessary to the understanding of the directions. This introductory paragraph also permits the laboratory experiment on a particular topic to be given either before or after the subject is discussed in class, as the instructor may desire.

Following the plan of the best laboratory manuals, definite provision has been made for recording observations and calculated results either in tabulations or in simple diagrams. This plan permits the student's record to be made in a minimum time and leaves a larger proportion of the period available for actual laboratory work and the consideration of results than is possible w r hen a running record is made. It also reduces the iv PREFACE

time necessary for the instructor to judge the accuracy of the student's results, as well as his grasp. of the principles involved.

The Conclusion always calls for a definite answer to the question which- is raised in the Object of the experiment. Other important facts or principles which may be deduced in connection with the experimental work are subjects for questions in the Discussion. These may be answered orally as the instructor passes from student to student, or, in large classes particularly, the answers may be written in the note-book. In any case, these questions direct attention to the salient points of the experiment and should be taken up in the quiz on the laboratory work.

The authors wish to express their grateful appreciation of the assistance which they have received in the preparation of this book. Among their associates in the Stuyvesant High School they are particularly indebted to the principal, Dr. E. R. von Nardroff for valuable suggestions and for the stimulus which his interest in the experiments has afforded; to their colleagues in the Physical Science Department, particularly Mr. J. G. Baier and Mr. H. W. Mott, for many helpful criticisms and suggestions; and to Dr. H. E. Fritz, for valuable assistance in the preparation of the drawings. Many of the drawings have been made by the following students : Charles E. O'Rourke and Harold Jay, of the Stuyvesant High School, and John G. Smith, of the Geneseo Normal School. In connection with particular experiments, acknowledgment is made to the teachers who rendered assistance in these experiments. Thanks are tendered also to Professors Carhart and Chute for permission to use several cuts (Figs. 3, 35, 68, and 112) from the " First Principles of Physics " ; to Professor W. H. Timbie for the use of the Resistance Table (p. 315) from his "Elements of Electricity"; and to the L. E. Knott Apparatus Company for the use of several cuts.

The authors will gladly receive criticisms and suggestions from teachers who may use the Exercises in their classes.

R. W. F.

R. B. B.

February, 1913.

Sug

^gestions to the Instructor .....

Directions to Students ......

Mechanics

EXPE

RIMENT

Metric Units of Measurement ....

. 21

Measurement of Bodies .....

Volume Measurement of an Irregular Body

. 32

Elasticity — Hooke's Law . .

Tenacity of Wire . . . .

Relation between -Pressure and Depth

Archimedes' Principle .....

Law of Flotation ......

(Alternative) Law of Flotation

Specific Gravity of Solids .

Specific Gravity of a Liquid (Bottle Method)

Specific Gravity of a Liquid (Hydrometer Method)

Specific Gravity of a Liquid (Hare's Method)

(Alternative) Specific Gravity of Liquids (Balancing

• 58

Density of Air .......

(Alternative) Density of Air .

Boyle's Law ........

Measurement of Gas Pressure .

VI

18. Water Pumps

19. Principle of Moments

20. Lever Arm of a Force

21. Composition of Several Parallel Forces

22. Four Forces at Right Angles

23. Parallelogram of Forces .

24. Resolution of Forces

25. Force at the Center of Gravity of a Body

26. Pendulum

27. Inclined Plane

28. Pulleys ....

29. Wheel and Axle

30. Mechanical Efficiency of Machines

PAGE

Sound

32. Vibrations of a Tuning Fork

33. Velocity of Sound in Air .

34. Sympathetic Vibrations

35. Wave Length of a Sound .

36. Laws of Vibrating Strings

116 120 122 125 129

Light

Power -

37. Measurement of Candle

Photometer .....

37. (Alternative) Measurement of Candle Power

ford Photometer .....

38. Law of Reflection of Light

39. Images in a Plane Mirror

Jolly or Bunsen

• Rum-

136 139 142

Vll

40. Reflection in a Concave Mirror

41. Reflection in a Convex Mirror .

42. Refraction through a Glass Plate

43. Refraction through a Prism

44. Index of Refraction .

45. Total Reflection 46 A. Study of a Converging Lens . 46B. Focal Length of a Converging Lens

47. Conjugate Foci of a Converging Lens

48. Magnifying Power of a Lens 49A. Astronomical Telescope 49B. Compound Microscope .

50. Dispersion of Light by a Prism

Heat

51. Fixed Points of a Thermometer . . . .181

53. Coefficient of Linear Expansion . . . .190

54. Coefficient of Cubical Expansion . . . .193

55. Increase in Volume of a Gas at Constant Pressure . 197

56. Increase in Pressure of a Gas at Constant Volume . 201

57. Law of Heat Exchange ...... 205

58. Specific Heat of a Metal 209

59. Cooling through Change of State . . . .213

60. Melting Points and Boiling Points . . . .216

61. Heat Changes during Solution and Evaporation . . 220

62. Heat of Fusion of Ice . . . . 223

63. Heat of Vaporization ...... 226

64. Dew Point 230

Vlll

Magnetism and Electricity

EXPERIMENT PAGE

65. Magnetic Induction 232

66. Magnetic Lines of Force ...... 235

67. Development of an Electrostatic Series . . . 238

68. Simple Cell 241

69. Two-fluid Cell 244

70. Electroplating " 247

71. Electrotyping .250

72. Storage Cell 252

73. Laws of Resistance ...... 255

74. Effect of Temperature on Resistance . . . 258

75. Internal Resistance of a Cell 261

76. Grouping of Cells ....... 263

77. Resistance and Current in a Divided Circuit . . 266

78. Resistance by Substitution . . . . . 269 Heating Effect of an Electric Current . . . 272 Study of an Incandescent Lamp .... 276 Lines of Force around a Conductor .... 278 Electromagnet . . . . . . .281

83. Electric Bell 284

84. Telegraph Instruments ' . . . . . . 286

Operation of an .Electric Motor .... 288

Relation between Fall of Potential and Resistance . 296

Resistance by the Wheatstone Bridge . . . 298

Induced Currents ....... 302

Study of a Dynamo ....... 304

79 80 81 82

85 86 87 88 89 90

IX

PAGE

I. Important Numbers and Equivalents . . . 309

II. Properties of Materials 310

III. Density of Water 312

IV. Index of Refraction * 312

V. Electromotive Force of Cells . . . .312

VI. Table of Natural Sines and Tangents . . .313

VII. Size and Resistance of Annealed Copper Wire . 314

VIII. Specific Resistance and Temperature Coefficient . 315

SUGGESTIONS TO THE INSTRUCTOR

Selection of Experiments

Scope of the Experiments. — The experiments in this book provide a wide range of laboratory work for an elementary course in Physics. The exercises have been selected on the basis of their educational value to the student. Their aim is to impart to him certain fundamental principles, to acquaint him with some physical phenomena qualitative in character, and to show the operation and the use of practical devices or instruments that are applications of physical principles.

The authors have not hesitated to omit from their list certain well-known experiments which have persisted in many elementary courses, rather by inertia than because of any special interest or value to the beginner. On the other hand, it is impossible to include in a small book all the experiments of merit suitable to a first course in Physics. Yet, from those given, it will be possible for any instructor to make a selection of the experiments which the great majority of Physics teachers include in their courses, so as to afford a well-balanced laboratory training, both interesting and instructive to the student.

Recommended Lists. — Only the institutions most favored as to laboratory time will be able to complete in one scholastic year all the experiments outlined in this book. Any choice of experiments must depend upon the apparatus available and upon the laboratory conditions. To fit the usual laboratory equipment and to meet the time limitations of most first courses in the subject, the authors suggest the following list of thirty-five experiments as affording a good training in those fundamentals of the science most suitable for laboratory in struction :

Fundamental Course

The following ten exercises will supplement the above, particularly for those students whose ability enables them to do a maximum amount of work :

Mechanics, 6, 13 or 14, 28, 29 ; Heat, 57 ; Sound, 34 ; Magnetism and Electricity, 72,

Light, 44; 78 (or other experiment

on resistance), 90.

The following sixty exercises are suggested as a more extended course for those institutions favored with about double the laboratory time usually allotted to the first course :

Extended Course

Sound : Exercises 32, 34, 35.

The authors recommend the following list of experiments for girls, especially for those not intending to go beyond the high school. Most of these experiments have been selected because of their close relationship to the practical affairs of life.

TO THE INSTRUCTOR 3

Sound: Exercises 34 (or 35), 36.

Magnetism and Electricity : Exercises 65, 68, 70, 79, 80, 82, 83, 84.

A number of interesting and valuable experiments do not appear in any of the preceding lists, but it is hoped that some of them will be taken from time to time either as substituted or as additional exercises. A limited amount of variation from year to year adds interest and vitality to any laboratory course. Many of the experiments just referred to will meet the needs of those instructors who desire to give more time to certain divisions of the subject.

Order of Experiments. — The order in which the divisions of the subject are taken should depend upon the aim of the course and the conditions under which it is given. In their own work the authors find the most satisfactory order to be Mechanics, Heat, Sound, Electricity, and Light. In most syllabi, however, the subject of Light precedes that of Electricity. In the view of many, the experiments on Heat are best adapted to the student's powers after he has finished the experiments in Mechanics.

Time required for Experiments. — A majority of the experiments are designed to take from 80 to 90 minutes of laboratory time, including the writing of the note-book record. Some of the shorter ones will require but half of that time, or a single school period. Even if a double laboratory period is not available for the longer experiments, the directions have been written so that the experiments can be done successfully in two single periods. The system recommended for the note-book record saves time in securing the observational data. Especial care has been taken not to overload the student with more manipulations and observations than would be reasonable for an average rate of work within the time allotment.

The Experimental Directions

Aim. — At first sight it may seem that the directions for the experiments have been written in a rigid form which may hamper the individuality of the teacher using them. With the possible exception of the placing of the tables of observations and calculated results, it will be found that the directions and their requirements are in accord with the usages which have become generally established as leading to intelligent and efficient laboratory work.

The five main divisions of the printed directions are "Introductory," "Experimental," "Calculated Eesults," "Discussion," and "Conclusion." Certain suggestions as to these divisions appear in the paragraphs that follow.

Introductory. — The paragraphs under this heading in the printed directions serve several purposes. First, they awaken the student's interest in the problem to be studied by reference to applications of Physics more or less familiar to him. Secondly, the introductory statements show the relation between the practical applications and the laboratory problem to be solved. In some cases the paragraphs furnish a little theoretical information, necessary for the intelligent performance of the experiment. All that is required of the student is that he read and understand this introductory matter — usually a task of a few minutes. It is not expected nor is it desired that the introductory matter be copied into the note-book.

The authors offer no apology for the paragraphs introductory to the experiments. They have simply put in written form those preliminary remarks that many instructors find desirable to make when the class assembles for the experiment. It is felt that the written form has the advantage of being always available for the student's reference.

Experimental. — Whenever the length and character of the experiment permits, the laboratory problem is presented as a whole to the student. With the general plan in mind, he is able to do the experiment with greater self-reliance and effi-

TO THE INSTRUCTOR 5

ciency than can be obtained from the slavish following of detailed directions with little grasp of their intent.

In some experiments, however, detailed directions must be given to secure the successful imparting of a series of experimental facts. In such cases the divisions are made as few as possible and their meaning made clear by brief directions, a little supplementary information, and questions that the average student should be able to answer from his experimental observations.

The students are directed to place the data gathered in the experiment in a table of observations near the top of the left-hand page of the note-book record. The form for this table is usually furnished, and it is strongly recommended that the student write the form in the note-book before making any of the measurements. This procedure provides for the orderly recording of the data as soon as it is obtained, and insures the completion of the experimentation within the laboratory hour. There is economy also of the instructor's time, as he can quickly note the rate of progress of the individual and check inaccuracies in the readings.

^Yith most experiments only one set of readings is indicated in the tables of observations, but the instructor desiring more can increase the number of columns at the right. In the opinion of the authors, much time is wasted by requiring the duplication of readings by the elementary student of Physics, unless in work where personal errors are large.

Drawings. — After the observations are completed, the student is directed to make sectional or outline drawings from his apparatus so as to show that he understands its arrangement and operation. Many of the illustrations in this book have been made from drawings made by students in the regular course of their laboratory work. Such drawings will indicate to the users of this book the methods of representing laboratory apparatus by simple outline drawings. The development of a simple scheme of sectional representation is within the power of any student and will prove most useful to him.

Descriptions. — The table of observations and the sectional drawings render unnecessary long and elaborate descriptions of the experimental work. All that is asked is a brief but clear statement of the general method of the experiment and the recording of any experimental facts not shown by the drawings nor provided for in the table of observations. In the last few years it has become more and more recognized that the chief function of the laboratory note-book is to show the essentials of an experiment and not to provide useless drudgery for the student.

Calculated Results. — Preceding the table of calculated results occurring in many experiments, are found directions for making the calculations. The authors have not hesitated to furnish information to aid the student in making the calculations when these are rendered more intelligible thereby.

The directions call for the placing of the table of calculated results at the top of the right-hand page of the note-book record. The calculations themselves should be made directly # below the table. These requirements secure prominent and convenient locations for the making of the computations and the orderly recording of the results. The student can tell from the tabular form what is expected of him in the way of calculations and know? when his work is finished. The instructor is enabled to check quickly the recorded results and to point out during the laboratory period sources of error.

Discussions. — Under this division the student is directed to answer any italicized questions occurring in the experimental directions or the questions under the printed heading, Discussion. Thus the theoretical considerations of the experiment are brought together ready for reference or correction.

Conclusions. — The student is either required to state for himself the formal conclusion justified by the experimental facts, or to complete a partial statement by filling in the indicated blanks. The latter method is preferred in those cases where a complete and well-worded conclusion is difficult for

TO THE INSTRUCTOR 7

the student to formulate. The vital part of the statement must be furnished by the student and requires thought on his part.

Method of Laboratory Work. — Many of the advantages of having the note-book record follow a definite plan have been discussed under the topics preceding this. Tabular forms for the observations and the calculated results are appreciated by many instructors as leading to that economy of laboratory time which gives the best opportunity for experimentation and reflection. The forms for such tabulations may be written in the note-book prior to the laboratory hour and the general plan of the experiment studied.

The authors believe that it is not only permissible, but highly desirable, for the student to know before he comes into the laboratory what he is to do. They require their own students to carefully study the experiment and to write the blank table of observations in the note-book before coming to the laboratory. Except in the case of very complicated experiments, the student is not allowed to have the experimental directions before him until he has taken all readings and completed his drawing and description. He is then allowed to refer to his direction sheet for guidance as to his calculations and conclusions. It has been found that under this plan the work in the laboratory is more intelligent and less of the " cook-book " order. Furthermore, schools having only single laboratory periods may be certain of having the readings taken and the experiment described during the laboratory period, while calculated results and conclusions may be worked out the next day either in laboratory or classroom, or, if desired, done as part of the home lesson for the day following that of the laboratory period.

No factor contributes more to the success of a laboratory course than having the apparatus tested and entirely ready for the student when he enters the laboratory. Then only is it possible for him to put the apparatus together and start its operation without loss of time, so that the readings can be made comfortably within the period.

}iiNafce*book Directions. — On page 16 there will be found brief instructions intended for the student and relating to the form of the note-book record. Any orderly plan must have definiteness ; so it becomes necessary to designate left-hand and right-hand pages for certain purposes. These directions may reverse the usage of some instructors, but it is hoped that they will realize it makes little difference whether the left-hand page or the right-hand page serves a certain purpose, so long as there is a definite systematic plan to make the note-book record a help to the student, and to make the ever present and laborious task of note-boot correction easier for the instructor.

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DIRECTIONS TO STUDENTS

Balances

Construction of Platform Balances. — The platform balance ot trip scale is a simple, equal arm lever in which the vertical displacement of either arm is indicated by a pointer swinging across a horizontal scale. When the pointer swings approximately equal distances on each side of the? center division on the horizontal scale, the two lever arms are balanced and the scale is said to be in equilibrium,

Fig. I. Platform Balance.

The construction of the trip scale is shown in Figs. 1 and 2 on this and the following page. This convenient instrument for weighing is too often misused in the physical laboratory and poor results obtained with it. With the observance, however, of a few simple precautions, rapid, accurate weighings can be made with this piece of apparatus.

Adjustment of Platform Balances. — Before weighing always see that both platforms are clean Then touch lightly one

Fig. 2. Sectional View of Balance.

platform and note whether or not the pointer swings freely and equally on each side of the center line of the scale. The pointer should oscillate at least two divisions to the right and to the left. In too short swings the friction in the bearings

makes the scale relatively less sensitive.

Therefore the pointer's coming to rest at the center point is no sure indication that the two arms of the scale are balanced or in equilibrium.

In case the pointer swings to a distinctly greater distance on one side of center, turn the thumb nut which is just below the center, so that the nut moves a little distance towards the side of the lesser swing. Again note the swings. When they are approximately equal on both sides of center, the scale is adjusted for weighing.

Handling of Weights. — Place the object to be weighed on the left-hand platform .or pan and the weights on the right-hand platform. In adding or removing weights, prevent with the left hand the movement of the pans until the change of weights has been made. In this way avoid jarring the balance and injuring the knife-edges.

For the first weight select the one which in your opinion is about equal to the object being weighed. If this weight is too small, take it off and replace it with the next larger one. Continue in this way until you have the largest weight which is lighter than the object. Then add the next smaller weight. Time-saving weighing means the systematic use of the next smaller or the next larger weight, as the case may be, until the scale is balanced.

In practice the graduated beam with its rider enables one to

TO STUDENTS 11

dispense with the smaller weights. If the beam is graduated for 5 grams, the 1-gram and the 2-gram weights are not used ; with a 10-gram beam, the weights below 10 grams are not necessary. By means of the graduated beam, these smaller weights are found by moving the rider to the right until the balance is in equilibrium. Note carefully on which side of the rider the reading should be made, and remember that the reading can be made to tenths of a gram.

When the correct weight is obtained, count carefully the weights on the right-hand pan and add the weight indicated on the beam. Record this total weight at once in the laboratory note-book.

Return the weights to their block, or case, counting as you do so. Add the weight indicated on the beam and check the weight recorded in the note-book. Remove the object from its scale pan. A scale left with the arms unequally balanced soon loses its sensitiveness, owing to unnecessary wear on the bearings.

Beam Balances. — Another form of balance much used in the physical laboratory is the beam balance. The beam in this case rests at its center point on a knife-edge, or a wedge, supported on a vertical stand. Pans are suspended on the ends of the beam either by hooks, or in the more expensive kinds by stirrups which rest on knife-edges. A vertical pointer indicates on a small graduated scale the oscillations of the beam. Some beam balances have on one arm of the beam a rider, which slides along a graduated scale and thus indicates the smaller weights. To avoid dulling the knife-edges, there is often a device which lifts the beam off the knife-edges when the balance is not in use. The pan arrest similarly lifts the bow and stirrup suspension from off the knife-edges on the ends of the beam.

The specific gravity balance is usually a beam balance which has a shorter suspension for one of the pans. From a hook on the under side of this pan are suspended objects which are to be weighed in a liquid.

The hornpan balance is simply a beam balance, which is supported yertically from a hook hung on a ring stand or held by the hand. 01 woJfed ■ bl

Spring Balances. — A spring balance measures the mass of a body by the elongation of a spiral spring. The weight is indicated on a graduated scale by a pointer attached to a drawon the free end of the spring. Attached to the drawbar is a hook on which is suspended the object to be weighed.

The spring balance is made to read correctly in vertical position, with the hook downward. The weight of the drawbar and hook should be sufficient to bring the pointer to the zero mark on the graduated scale. If the pointer does not stand at zero with no load on the balance, a correction must be made to the weight registered on the scale in order to get the true weight of the object. The inconvenience of making these corrections may sometimes be avoided by wrapping about the shank of the hook a strip of sheet lead, sufficient in weight to bring the pointer to the zero point of the scale.

The friction in a spring balance tends to make less accurate the readings in the first portion of the graduated scale. At the other end of the scale, when the spring is near its maximum stretch, the elongations are not quite proportional to the heavier weights added. Accordingly the most accurate readings with a spring balance are those obtained in about the middle portion of the graduated scale.

In some experiments the spring balance is used to measure the pull or force exerted upon its spring. When used for this purpose it is termed & dynamometer.

Sensitiveness of a Balance. — The sensitiveness of a balance may be defined as the smallest difference which is indicated by the balance with a given load. The trip scale should be sensitive to at least the tenth of a gram with an ordinary load, %.e. show a difference between 50.6 and 50.7 grams. A good hornpan balance indicates weights within the hundredth of a gram (1 centigram) while an accurate chemical balance is sensitive to a ten-thousandth of a gram (tenth of a milligram).

TO STUDENTS 30 13

Relative Advantages of Platform and Beam Balances. — The

platform balance, while it is easy to keep clean and can stand much usage, is usually not so sensitive as the beam balance. The broad platforms, however, are very convenient for weighing bulky, unstable objects, and the oscillations of its bestaf are easily controlled.

The sensitiveness of a beam balance is gained at the expense of stability and durability, for the beam is easily displaced and the knife-edge suspension becomes dulled by use. On this account great care should be taken not to jar the balance nor allow the beam to oscillate too rapidly. The weights should be placed gently upon the pans and removed when the pans are at rest {i.e. supported by the pan arrest or by the hand).

Were it not for the awkwardness and carelessness of some

students, the beam balance would always be most desirable for

rapid, accurate weighings in the physical laboratory.

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Electrical Measuring Instruments row

ton

The instruments used for measuring the strength or the

pressure of an electric current have very delicate parts and may be easily ruined by either rough usage or excessive current

Before using any galvanometer or other meter the student should assure himself that it has the proper scale range and current-carrying capacity for the work in hand. He must further so connect his apparatus that the instrument will not be upset or pulled out of place by any change in connections made during the experiment. As the several instruments that the student may be called to use in his experiments differ in their sensitiveness, method of connection, and method of reading, each kind will be briefly discussed by itself. In reading all instruments, tenths of the smallest divisions, should be es^ mated.