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EXAMPLES IN PHYSICS

INTRODUCTION

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1. Units.- In order to measure any physical quantity, we have first to select as our unit, or standard of reference, a quantity of the same kind as that to be measured. The ratio between the quantity and the selected unit is called the numerical value or measure of the quantity. Suppose that we have to measure a definite length l, and that we adopt as our unit a length L: the numerical value (n) of the length to be measured will be

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I' where n may be any number, whole or fractional.

2. Fundamental Units. — All physical quantities can be expressed in terms of three fundamental units, the choice of which depends upon the ease and certainty with which the standard quantities so selected can be compared with other quantities of the same kind. We might choose as our fundamental quantities a definite length, a definite force, and a definite interval of time : other units, such as those of mass and work, could be deduced from these. But on account of the difficulty of devising a permanent standard of force, the value of which would not change from place to place, such a choice would not be advisable.

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The fundamental units usually adopted are those of length, mass, and time; these three elements can be measured with great accuracy, and standards of length and mass can easily be copied, and compared with the original standards.

THE C.G.S. SYSTEM OF UNITS.

A committee of the British Association has recommended the adoption of the centimetre, the gramme, and the second as the three fundamental units. Other units derived from these are distinguished by the letters “ C.G.S.” prefixed, these being the initial letters of the three fundamental units.

3. Derived Units. Velocity.--The C.G.S. unit of velocity is the velocity

of a point which moves over one centimetre in a

second. Acceleration. - The C.G.S. unit of acceleration is

that of a point whose velocity increases by one unit per second. The numerical value of the acceleration due to gravity (8) is 978.10 at the equator, 980.94 at Paris, 981.17 at Greenwich,

and 983.11 at the pole. Force.—The C.G.S. unit of force is that force which,

acting upon a mass of one gramme for a second, generates in it a velocity of one centimetre per

second. Special names are given to some of these units ;

thus the C.G.S. unit of force is called the dyne. Assuming the value of g to be 981 (as we shall do throughout), we see that a dyne is gt of the

weight of a gramme. Work and Energy.—The C.G.S. unit of work is the

work done by a dyne acting through a distance of one centimetre, and is called an erg. The

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same name is applied to the unit of energy, for energy is measured by the amount of work which it represents. Since the weight of a gramme is 981 dynes, the work done in raising one gramme vertically through one centimetre against the

action of gravity is 981 ergs. Practical Units and Index Notation. - In any uniform

system some of the units must be inconveniently large, while others are so small that the quantities with which we have to deal are represented by very large numbers. Electricians find it convenient to use a system of “practical units,” each of which bears to the corresponding C.G.S. unit a ratio which is some multiple or submultiple of 10. Thus the volt is equal to 100,000,000 C.G.S. units of potential; the farad is

of

1,000,000,000 the C.G.S. unit of capacity. The prefixes mega- and micro- are used to signify

one million millionth part” respectively. Thus a megadyne is a force of one million dynes ; a microfarad denotes a capa

city of one-millionth of a farad. When very large or very small numbers have to be expressed,

it is convenient to adopt the index system of notation, in which numbers are expressed as the product of two factors, the second of which is a power of 10; and it is usual to choose the factors so that the first contains only one integral digit. Thus the velocity of light, which is 300,400 kilometres per second, is expressed as 3.004 * 1010 centimetres per second. A megadyne is 10dynes ; a farad is 10-9 (= m) and a microfarad is

10-15 C.G.S. unit of capacity. Power, Activity, or Rate of doing Work. The

C.G.S. unit of power is the power of doing work at the rate of one erg per second.

The corre sponding practical unit, called the Watt, is the power of doing work at the rate of 107 ergs per

second. A horse-power is equal to 746 watts. Pressure.—The C.G.S. unit of intensity of pressure

is a pressure of one dyne per square centimetre. It would be convenient if the pressure of a megadyne per square centimetre (100 C.G.S. units) were adopted as the normal atmospheric pressure : this standard would correspond to a barometric height of 75 centimetres, but, as compared with any barometric standard, would have the advantage of being independent of the value

of g:

Heat.-The C.G.S. unit of heat is the amount of heat

required to raise the temperature of a gramme of water through one degree centigrade. The dynamical equivalent of one heat-unit in ergs is 4.2 X 107: this quantity is called the mechanical equivalent of heat or “ Joule's equivalent,” and is usually represented by the letter J.

4. C.G.S. Electrostatic Units. Quantity.The unit quantity of electricity is that

quantity which, when placed (in air) at a distance of one centimetre from an equal and similar

quantity, repels it with a force of one dyne. Potential.—Unit difference of potential exists between

two points when the work done against the electrical forces in moving unit quantity of electricity

from the one point to the other is one erg. Capacity.A conductor is said to have unit capacity

when a charge of one unit of electricity raises its

potential from zero to unity. Magnetic Units. Strength of Pole. A magnetic pole is said to have

unit strength when it repels an equal and similar pole, placed at a distance of one centimetre from

it, with a force of one dyne. Strength of Field.A magnetic field is said to have

unit intensity (or strength) when a unit magnetic pole placed in it is acted upon by a force of one dyne.

Electro-magnetic Units.
Current.The unit of current is that current

which, when flowing along a wire one centi-
metre in length bent into the form of a circu-
lar arc of one centimetre radius, acts with a
force of one dyne upon a unit pole placed at the

centre of the circle. Quantity.—The electro-magnetic unit of quantity is

the quantity of electricity which in one second passes any section of a conductor in which unit

current is flowing. Electromotive Force or Difference of Potential.Unit

electromotive forcel exists between two points when the work done against the electrical forces in moving unit quantity of electricity from the

one point to the other is one erg. Resistance.A conductor is said to possess unit

resistance when unit difference of potential between its ends causes unit current to flow through

it. Capacity.—A conductor has unit capacity when a

charge of one unit of electricity raises its poten

tial from zero to unity. 5. Practical Units. The following system of units, based upon

the C.G.S. electro-magnetic units, was devised by the British Association committee, and is in general use among practical electricians. It will be noticed that in this system the units of current, electromotive force, and resistance have been chosen so as to be of suitable magnitude for the electrical measurements which most frequently occur. Current and Quantity.—The practical unit of current

is the ampère, and is one-tenth (10-1) of the C.G.S. electro-magnetic unit of current. It follows

1 Usually contracted into “E.M.F."

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