Elementary Physics for High Schools

Contents

The numbers in square brackets [ ] are the numbers of the chapters in Merchant and Chant’s High School Physics in which the same subjects are treated.

Part I — Introduction CHAPTER PAGE

i‘. — Measurements [i] 1

Part II — Mechanics op Solids

ii. — Velocity, Acceleration [11] 14

hi. — Momentum, Force [m] 21

iv. — Gravitation [v] 28

v. — Work and Energy [vi] 31

vi. — Centre of Gravity [vnj 36

vn. — Friction [vm] 41

viii. — Machines [ix] ", 43

Part III — Mechanics of Fluids

ix. — Pressure of Liquids [x] 52

x. — Buoyancy of Fluids [xi] 60

xi. — Determination of Density [xii] 63

xii. — Pressure in Gases [xiii] 67

xiii. — Applications ot the Laws of Gases [xiv] 80

Part IV — Some Properties of Matter

xiv. — Molecules and their Motions [xv, xvi, xvii] ... 86

Part V — Sound

xv. — Production and Transmission of Sound [xix] ... 96

xvi. — Pitch, Musical Scales [xx] 101

xvii. — Musical Instruments [xxiii] 105

xviii. — Quality; Sympathetic Vibrations [xxn] . . . . Ill

2578000

Iv

CONTENTS

Part YI — Heat

CHAPTER PAGB

xix. — Sources of Heat ; Expansion through Heat [xxiv, xxv] 114

xx. — Temperature [xxvi] 120

xxi. — Expansion of Water : Expansion of Gases [xxvii] . 125

xxn. — Measurement of Heat [xxvm] 128

xxiii. — Change of State — Solids and Liquids [xxix] . . . 134

xxiv. — Change of State — Liquids and Yapours [xxix] . . 140

xxv. — Transference of Heat [xxxi] 149

Part YII — Light

xxvi. — Nature of Light ; Its Motion in Straight Lines [xxxn] 161

xxvii. — Reflection of Light [xxxv, xxxvi] . . . . . . 166

xxix. — The Spectrum ; Colour [xxxix] 181

Part YIII. — Electricity and Magnetism

xxx. — Magnetism [xli] 187

xxxi. — The Electric Current [xliii] 199

xxxii. — Chemical Effects of the Electric Current [xliv] . . 207

xxxiii. — Magnetic Effects of the Current [xlv] 210

xxxiv. — Induced Currents — The Dynamo and the Motor

[xlvi, xlvii] 218

xxxv. — Heating and Lighting Effects of the Electric Current

[xlviii] 224

Answers to Numerical Problems 226

CHAPTER I Measurements

1. Science in Daily Life. During the last fifty years science in all its branches has developed very rapidly, and at the present time its applications have become of the utmost importance in our every-day life. Some of the most prominent of these applications are to be seen in our means of transportation over the land and the water and through the air ; and also in the methods of generating, distributing, and utilizing electric energy. Many of to-day’s achievements were not even dreamt of by our grandfathers.

Now it may seem strange, but it is none the less true, that this great development came about through our learning to make accurate measurements of the various quantities which enter in our experiments.

2. Fundamental Units. Let us measure a piece of rope. We do so, and find that its length is (say) 52 feet. Here our unit is a foot, and it is contained 52 times in the given length. A loaf of bread is said to contain 3 pounds. In this case the unit of mass is a, pound. Again the strength of an electric current is stated as 25 amperes. The unit in this instance is called an ampere.

It is evident that there will be as many kinds of units as there are kinds of quantities to be measured ; and the magnitude of the units may be just what we choose. But there are three units which we speak of as fundamental, namely, the units of length, mass and time. Each is independent of the others and cannot be derived from them. It can also be shown that the measurement of any quantity (for instance,

l the power of a steam-engine) ultimately depends on the measurement of length, mass and time. Hence these units are properly considered fundamental.

3. Standards of Length, — the Yard. One of the commonest units of length is the foot. For centuries it has been used by many nations, but the same name did not always mean the same length. Even in a single nation there was considerable variation, which, however, became greater on passing from one nation to another.

At the present time there are two standards of length in use in English-speaking countries, namely, the yard and the metre.

The yard is said to have represented, originally, the length

of the arm of King Henry I., but such a definition will not suffice now. It is defined to be the distance between two lines ruled on two gold plugs in a bronze bar, which is preserved in

The bronze bar is 38 inches long and has a cross-section one inch square (Fig. 1). At a , a, wells are sunk to the mid-depth of the bar, and at the bottom of each well is a gold plug or pin, about TV inch in diameter, on which the line is engraved.

The inch, the foot, the rod, the mile, etc., are derived from the yard.

4. The Metre. At the end of the 18th century there were in France many standards of length, and it was decided to replace them all by a new unit which was named a metre. Its length was intended to be one ten-millionth part of the distance from the pole to the equator, measured through Paris.

London, England.

Fig. 1.— Bronze yard", 38 in. long-, 1 in. sq. in section. a , a are small wells in bar, sunk to mid-depth.

RELATION BETWEEN METRES AND YARDS

(HalfSige)

The bar, representing this, which was taken as the standard, was completed in 1799. It was made from platinum and is just a metre from end to end, 25 millimetres (about 1 inch) wide and 4 millimetres (about \ inch) thick.

As time passed, great difficulty was experienced in making exact copies of this platinum rod, and as the demand for such continually increased, it was -decided to construct a new standard bar of the same length, and to make duplicates for various nations.

The form of the new metre bars is shown in Fig. 2. The material used is a hard and durable alloy composed of platinum 90 parts and iridium 10 parts. The bars are 102 cm. in length over all and 20 square mm. in section.

Fig. 2. — View of end and cross-section of the new standard metre bars. The line defining the end of the metre is a short mark on the surface midway between the top and bottom of the bar.

5. Sub-divisions and Multiples of the Metre. The metre is divided decimally^thus : —

1 metre = 10 decimetres = 100 centimetres = 1,000 millimetres.

For greater length multiples of ten are used, thus : —

The decametre and hectometre are not often used.

6. Relation between Metres and Yards. In Great Britain the metre is officially stated to contain 39.370113 inches, but in changing from metric to English measures we need not use so many decimal places.

We may take

1 metre = 39.37 inches ; 1 inch = 2.54 centimetres.

'It is also useful to remember that, approximately,

10 centimetres = 4 inches ; 30 cm. = I foot ; 8 kilometres = 5 miles.

In Fig. 3 is shown a comparison between centimetres and inches.

Centimetres

7 .2

iiiiliijilliiiliililiiiil

iiiiliiiilm

5 1

iiiIiii

6 ,7

in.iIi.iii. mill

1 8

ill iiiiIii

T ] i j T| I 1 f 1 V | 1 Inches

Ml 1 I pr T| 1 i f i

r| i 1 1 i

Fig. 3.— Comparison of inches and centimetres.

7. Units of Surface and Volume. The ordinary units of surface and volume (sq. yd., sq. cm., cu. ft., cu. metre, etc.) are at once deduced from the lineal units. The litre is a cubic decimetre and hence contains 1,000 cu. cm. As a unit of volume we also use the imperial gallon , which is defined to be the volume of 10 pounds of water at' 62° F., which is found to be 277.274 cu. inches. (The U. S. or Winchester or wine gallon = 231 cu. in.) N

The following relations are also useful : —

1 cu. in. = 16.387 cu. cm. 1 litre = 1.76 quarts.

PROBLEMS.

1. How many millimetres in 2^ kilometres ?

2. Change 186,330 miles to kilometres. (Light travels 186,330 miles in 1 sec.).

3. How many sq. cm. in a rectangle 54 metres by 60 metres ?

4. Change 760 mm. into inches.

5. Reduce 1 cubic metre to litres and to cubic centimetres.

6. Lake Superior is 602 feet above sea level. Express this in metres.

7. Dredging is done at 50 cents per cubic yard. Find the cost per cubic metre.

8. Air weighs 1. 293 grams per litre. Find the weight of the air in a room 20 x 25 x 15 metres in dimensions.

9. Which is cheaper, milk at 7 cents per litre or 8 cents per quart 1

10. The speed of sound, at 61° F., is 341 metres per second ; express this in feet per second.

11. Express, correct to a hundreth of a millimetre, the difference between 12 inches and 30 centimetres.

STANDARDS OF MASS— UNIT OF TIME

Fig. 4.— Imperial Standard Pound Avoirdupois. Made of platinum.

Height 1.35 inches; diameter 1.15 inches.

“ P.S.” stands for parliamentary standard.

8. Standards of Mass. We may define the mass of a body as the quantity of matter in it. According to our present views, matter may change its form, but it can never be destroyed. A lump of matter might be transported to any place in the universe but its mass would remain the same ; it would still have the same quantity of matter in it.

There are two units of mass in ordinary use, namely, the pound and the kilogram.

The standard pound avoirdupois is a certain piece of platinum preserved in London, England, of the form shown in Fig. 4. The grain is ywov °f the pound and the ounce is XV of the pound or 437.5 grains.

The original standard kilogram was also constructed of

I- platinum, and it is still carefully pre-

served in Paris. It was intended to represent the mass of 1,000 c.c. (1 litre) of water when at its maximum density (at 4° C.). Thus 1 c.c. of water = 1 gram. Duplicate standard kilograms have been made for various nations out of the platinum-iridium alloy (Fig. 5).

Fig. 5. — Kilogram, made of an alloy of platinum and iridium. Height and diameter each 1.5 inches.

The relation of the pound to the kilogram is officially stated thus : —

1 kilogram (kg.) = 2.2046223 pounds avoir., but, as before, in changing from metric to English measures we need not use so many decimal places.

We may take

1 kg. = 2.20 pounds av.; 1 gram = 15.4 grains ; I oz. av. = 28.3 grams.

9. Unit of Time. If we reckon from the moment when the sun is on our meridian (noon), until it is on the meridian again, the interval is a solar day. But the solar days thus determined are not all exactly equal to each other. In order to get an invariable interval we take the average of all the solar days, and call the day thus obtained a mean solar day. Dividing this into 86,400 equal parts we obtain a mean solar second. This is the quantity which is “ticked off” by our watches and clocks. It is used universally as the fundamental unit of time.

10. Measurement of Length. A dry-goods merchant unrolls his cloth, and, placing it alongside his yard-stick, measures off the quantity ordered by the customer. Now the yard-stick is intended to be an accurate copy of the standard yard kept at the capital of the country, and this latter we know is an accurate copy of the original preserved in London, England. In order to ensure the accuracy of the merchant’s yard-stick a government official periodically inspects it, comparing it with a standard yard which he carries with him.

11. More Accurate Measurements. Suppose next we wish to find accurately the diameter of a ball or of a cylinder. We may use a calliper such as that shown in Fig. 6. The jaws are

Fig. 7.— Micrometer wire gauge.

pushed up until they just touch the object, and the diameter is read from the graduations on the instrument.

For a small ball or a wire the most convenient instrument is a screw gauge, one of which is illustrated in Fig. 7. A is the end of a screw which works in a nut inside of D. The screw can be moved back and forth by turning the cap G to which it is attached, and which slips over D. Upon D is a

MEASUREMENT OF MASS scale, and the end of the cap C is divided into a number of equal parts. By turning the cap the end A moves forward until it reaches the stop B. When this is the case the graduations on D and C both read zero.

In order to measure the diameter of a wire, the end A is screwed up until the wire is just held between A and B. Then from the scales on D and C we can find the diameter required. '

There are other devices for accurate measurement of lengths, but in every case the scale, or the screw, or whatever is the essential part of the instrument, must be carefully compared with a good standard before our measurements can be of real value.

12. Measurement of Mass.

The pans A and B are suspended from the ends of the beam CD, which can turn easily about a “ knife-edge ” at E. This is usually a sharp steel edge resting on a steel or an agate plate. The bearings at G and D are made with very little friction, so that the beam turns very freely. A long pointer P extends downwards from the middle of the beam, and its lower end moves over a scale 0. When the pans are balanced and the beam is level the pointer is opposite zero on the scale.

In Fig. 8 is shown a balance.

Pig. 8.— A simple and convenient balance. When in equilibrium the pointer P stands at zero on the scale 0. The nut n is for adjusting the balance and the small weights, fractions of a gram, are obtained by sliding the rider r along the beam which is graduated. The weight W, if substituted for the pan A, willbalancethe pan B.

At once it It goes downwards

Suppose a lump of matter is placed on pan A. descends and equilibrium is destroyed.

MEASUREMENT because the earth attracts the matter. Now put another lump on pan B. If the pan B still remains up we say the mass on A is heavier than that on B; if the pans come to the same level and the pointer stands at zero the two masses are equal.

It is the attraction of the earth upon the masses placed upon the pans which produces the motion of the balance. The attraction of the earth upon a mass is called its weight , and so in the balance it is the weights of the bodies which are compared. But if the weights of two bodies are equal their masses are equal, and so the balance allows us to compare masses.

13. Sets of Weights. We have agreed to take a lump of platinum-iridium as our standard of mass (§ 8).

In order to duplicate it we simply place it on one pan of the balance, and by careful filing we make another piece of matter which, when placed on the other pan, will just balance it.

Again, with patience and care two masses can be constructed which will be equal to each other, and which, taken together, will be equal to the original kilogram. Each will be 500 grams.

Continuing, we can produce masses of other denominations, and we may end by having a set consisting of 1,000,

500,

200,

200, 100

50,

20,

20, 10

5,

2,

2,

.5,

•2,

•2,

.1 grams

and even smaller weights.

If now a mass is placed on pan A of the balance, by proper combination of these weights we can balance it and thus at once determine its mass.

RULES FOR THE USE OF THE BALANCE

The balances and the weights used by merchants throughout the country are periodically inspected by a government officer.

14. Rules for the Use of the Balance. The balance should always be handled with care and the following rules be observed v..

1. Keep the balance dry and free from dust.

2. See that the balance is properly adjusted, so that it will, when unloaded, either rest in equilibrium with the pointer at the zero mark on the scale, or will swing equally on either side of zero.

3. Place the body, whose mass is to be ascertained in the left-hand scale-pan, and place the weights in the right-hand scale-pan. Until some experience in judging the mass of a body has been obtained, try all the weights in order, commencing with the largest and omitting none. When any weight causes the right-hand pan to descend remove it. Never select weights at random.

In the balance shown in the figure any addition under 10 grams is obtained by sliding the rider r along the beam. It gives ^ gram directly, and iV of this may be obtained by estimation.

Before beginning, the balance should be tested. Push the rider r over to its zero mark and then if the pans do not balance (as indicated by the pointer P ) turn the nut n until they do.

4. To determine the equilibrium do not wait until the balance comes to rest. When it swings equally on either side of zero, the mass in one pan equals that in the other.

5. Place the largest weight in the centre of the pan, and the others in the order of their denominations.

6. Keep the pans supported when weights are to be added or taken off.

7. Small weights should not be handled with the fingers. Use forceps.

8. Weigh in appropriate vessels substances liable to injure the pans. For counterpoise use shot and paper.

9. Never use the balance in a current of air.

Exercise— Find the value of 1 oz. in grams, 1 kilogram in pounds, 1 quart in c.c. and in litres.

Apparatus : — Balance, with, both British and metric weights, quart measure, glass vessel graduated in c.c.

(a) Place an ounce weight on the left-hand pan of the balance (Fig. 8) and place metric weights on the right-hand pan to balance it.

( b ) Next place the kilogram weight on the left pan, and keeping the rider at the zero point, add British weights on the right until they balance the kilogram. Express your result in pounds and decimals.

(c) Carefully pour water from the graduated vessel into the quart measure until it is just filled. Then add up the amount poured in. Or, fill the quart measure and empty the water into the. glass graduate. Express the quart in c.c. and also in litres. (1 1. = 1,000 c.c.)

15. Density. Let ns take equal volumes of lead, aluminium, wood, brass, cork. These may conveniently be cylinders about l inch in diameter .and 1| or 2 inches in length.

By simply holding them in the hand we recognize at once that these bodies have different weights and therefore different masses. With the balance and our set of weights we can accurately determine the masses.

We describe the difference between these bodies by saying that they are of different densities, and we define density thus : —

The density of a substance is the mass of unit volume of that substance.

If we use the foot and the pound as units of length and mass, respectively, the density will be expressed by the number of pounds in 1 cubic foot. For example, water at 4° C. has a density 62.4 ; iron, about 440 ; white pine, about 26, pounds per cubic foot.

Next let us take 1 cm. and 1 gram as our units of length and mass, respectively, and see what numbers will represent the densities of some substances.

RELATION BETWEEN DENSITY AND SPECIFIC GRAVITY H

We know that

1 litre of water = 1,000 c.c. = 1 kilogram = 1,000 grams, or 1 c.c. of water = 1 gram-,

and hence in this case the density of water is represented by 1.

The following are the densities of some other substances : — Cast-iron, 7.0 to 7.1 ; silver, 10.5 ; mercury, 13.6 ; white pine, 0.3 to 0.5 grams per c.c.

Note also that if we know the volume and the density of a body we can at once calculate its mass. For example, the volume of a piece of cast aluminium is 150 c.c. and its density is 2.56 grams per c.c. Then the

Exercise— Find the volume of a rectangular solid, also its density.

Apparatus : — Block of wood, metre stick, balance.

Apply the metre stick to each edge of the block, thus measuring each dimension of the block four times. Take the average ; and then, by multiplying the three dimensions together obtain the volume.

Take the measurements in inches as well as in cm., and from the volumes obtained calculate the number of c.c. in 1 cu. in.

Next, weigh the block with the balance, and calculate the number of grams in 1 c.c. of it.

16. Relation between Density and Specific Gravity. We

have seen that the number expressing the density- of a substance differs according to the units of length and mass which we use.

Specific gravity is defined to be the number of times the weight of a given volume of the substance contains the weight of an equal volume of water. This is expressed by a simple number, which is the same, no matter what units we use.

For example, suppose we have a cubic foot of a substance, and that it weighs 440 lbs. Now the weight of a cubic foot of water is 62.4 lbs.

Then specific gravity = = 7.05. [What substance is it ?]

If we took 2, 3, or any number of cu. ft. we would get the same number for the specific gravity, which we see, therefore, does not depend on the volume of the substance used.

Again, suppose we have 50 c.c. of the substance, which, by means of thex balance, we find weighs 352.5 grams. Now 50 c.c. of water weighs 50 grams.

352 5

Then specific gravity = ■ - = 7.05, ou

which is the weight of 1 c.c. of the substance, and is the same as the density when we use these units.

Hence, when we use a centimetre as the unit of length and a gram as the unit of mass, the number representing the specific gravity of a substance is the same as that representing its density.

1. Find the mass of 140 c.c. of silver if its density is 10.5 gm. per c.c.

2. The specific gravity of sulphuric acid is 1.85. How much will 100 c.c. weigh ? How many c.c. must one take to weigh 100 gm. ?

3. A rolled aluminium cylinder is 20 cm. long, 35 mm. in diameter, and its density is 2.7. Find the weight of the cylinder.

4. A piece of granite weighs 83. 7 gm. On dropping it into the water in a graduated vessel, the water rises from 130 c.c. to 161 c.c. (Fig. 9). Find the density of the granite.

5. A tank 50 cm. long, 20 cm. wide and 15 cm. deep is lpJn filled with alcohol of density 0.8. Find the weight of the

alcohol.

6. A rectangular block of wood 5 x 10 x 20 cm. in dimen- ^ sions weighs 770 grams. Find the density.

Q 7. The density of anthracite coal is about 54 lbs. and that

of bituminous coal about 49 lbs. , per cubic foot. A coal bin is 9 x 7^ x 4 ft. in dimensions. Find the number of tons it will hold ( a ) of anthracite, (6) of bituminous coal.

RELATION BETWEEN DENSITY AND SPECIFIC GRAVITY 13

8. Write out the following photographic formulas, changing the weights to the metric system : — •

Developer

Water 10 oz.

Metol 7 gr.

Hydroquinone 30 “

Sulphite of Soda (desiccated) 110 “

Carbonate of Soda (desiccated) 200 ‘ ‘

Ten per cent, solution Bromide of Potassium ....... 40 drops

Fixing Bath

-^Water 64 oz.

Hyposulphite of Soda 16 “

When above is dissolved add the following solution

Water 5 “

Sulphite of Soda (desiccated) \ “

Acetic Acid 3 “

Powdered Alum 1 <£.

PART II— MECHANICS OF SOLIDS -BODIES AT REST AND IN MOTION

CHAPTER II Velocity, Acceleration

17. Rest and Motion. When we get out in the open air and look about for a few minutes we see numerous examples of rest and motion. The houses, the fences and the trees are at rest ; while the carriages and motor-cars on the road, the railway-train in the distance, or the birds flying across the field, we declare to be in motion.

We agree at once that we can arrange bodies into the two classes, namely, those at rest and those in motion ; but a brief consideration will show that this arrangement is not so simple after all, — that, indeed, a body considered from one point of view may be at rest while from another it may be in motion.

Two persons sit together in a railway-train. Each is at rest with respect to the other, but both are in motion with respect to a third person on the ground outside. It is impossible to think of a single object as at rest, which, when looked at in another way, would not be considered to be in motion. Thus motion is quite as natural a state as rest.

18. Velocity or Speed. A body is in motion when it is changing its position ; and there is another idea which we usually associate with this change of position, namely, the time taken to do it. This brings in the notion of speed or velocity. The latter term is often used to include also the direction of the motion, while the former refers only to the rate at which the body moves. But in this work this distinction will not be insisted on.

Suppose you wish to go from Toronto to Montreal, a distance of 330 miles. You find that one train requires 10

ACCELERATION hours, while another one would take 48 hours. You do not hesitate long to choose the one you will use. The rate of motion is of great importance to us.

In the first case the average speed is 330 -MO = 33 miles per hour; in the second case, 330-f 48 = 6£ miles per hour.

Thus we see, Speed = ^?ace- ^ Time

Usually the speeds we have to deal with are not constant, the body moves faster at some times than at others. This is well illustrated in the motion of a railway-train. On a long level track the speed is approximately uniform, but on climbing a hill or approaching a station the speed changes.

1. A train leaves Winnipeg at 10.40 p.m. and reaches Regina next morning at 9.40 as shown by the same time-piece. The distance is 357 miles. Find the average speed.

2. A train leaves Montreal at 9.45 p.m. Monday and reaches Vancouver on Saturday at 9.10 a m., Pacific time, which is 3 hours slow of Montreal or Eastern time. The average speed, including stops, was 26j miles per hour. Find the distance.

3. A train travels at the rate of 60 miles per hour ; find the speed in feet per second.

4. An eagle flies at the rate of 30 metres per second ; find the speed in kilometres per hour.

5. A sledge party in the arctic regions travels northward, for ten successive days, 10, 12, 9, 16, 4, 15, 8, 16, 13, 7 miles, respectively. Find the average velocity.

4* Tf at the same time the ice is drifting southward at the rate of 10 ^ards per minute, find the average velocity northward.

19. Acceleration. We have all enjoyed the sport of coasting down hill on a sleigh or a toboggan. We start off* very gently but with every second the speed increases, until at the bottom it is very great. The sleigh then runs up the opposing hill, rapidly loses its speed and finally comes to rest.

When the velocity is not uniform we say the motion is accelerated. If there is an increase in the velocity, the

VELOCITY, ACCELERATION acceleration is positive ; if a decrease, it is negative. The latter is sometimes called a retardation. On going down hill the acceleration is positive, but when slowing up on the opposite hill it is negative.

Suppose the sleigh is allowed to start from rest/i.e., without being pushed), and that at the end of one second its speed is 2 feet per second ; if it continues to gain speed at the same rate, the speed at the end of 2 seconds will be 4 feet per second ; at the end of 3 seconds, 6 feet per second ; and so on. At the end of 20 seconds the speed will be 40 feet per second. In this case the rate of increase, or the acceleration , is uniform, namely, 2 feet per second in each second.