Showing posts with label Physics. Show all posts
Showing posts with label Physics. Show all posts

Thursday, 22 March 2018

System of Units of Measurements

March 22, 2018 0

The Standard of Length

The first international standard of length was a bar of a platinum -  iridium alloy called the standard meter, which was kept at the International Bureau of Weights and Measures near Paris. The distance between two fine lines engraved near the ends of the bar, when the bar was held at a temperature of 00C and supported mechanically in a prescribed way, was defined to be one meter. Historically, the meter was intended to be one ten-millionth of the distance from the north pole to the equator along the meridian line through Paris. However, accurate measurements showed that the standard meter bar differs slightly (bout 0.023%) from this value.
Figure 1: 
System of Units of Measurements

Because the standard meter is not very accessible, accurate master copies of it were made and sent to standardizing laboratories throughout the world. These secondary standards were used to calibrate other, still more accessible, measuring rods. Thus, until recently, every measuring rod or device derived its authority from the standard meter through a complicated chain of comparisons using microscopes and dividing engines. Since 1959 this statement had also been true for the yard, whose legal definition in the United States was adopted in that year to be

1 yard = 0.9144 meter (exactly)
Which is equivalent to
1 inch = 2.54 centimeters (exactly)

The accuracy with which the necessary intercomparisons of length can be made by the technique of comparing fine scratches using a microscope is no longer satisfactory for modern science and technology. A more precise and reproducible standard of length was obtained when the American physicist Albert A. Michelson in 1893 compared the length of the standard meter with the wavelength of the red light emitted by atoms of cadmium. Michelson carefully measured the length of the mater bar and found that the standard meter was equal to 1,553,163,5 of those wavelengths. Identical cadmium lamps could easily be obtained in any laboratory and thus Michelson found a way for scientists around the world to have a precise standard of length without relying on the standard meter bar.
Despite this technological advance, the metal bar remained the official standard until 1960, when the 11th General Conference on Weights and Measures adopted an atomic standard for the meter. The wavelength in vacuum of a certain orange-red light emitted by atoms of a particular isotope of krypton, 86Kr, in electrical discharge was chosen (see Fig. 2). Specifically, one meter was defined to be 1,650,763,73 wavelengths of this light. With the ability to make length measurements to a fraction of a wavelength, scientists could use this new standard to make comparisons of lengths to a precision below 1 part in 109.
The choice of an atomic standard offers advantages other than increased precision in length measurements. The 86 Kr atoms are available everywhere, are identical, and emit light of the same wavelength. The particular wavelength chosen is uniquely characteristic of 86Kr and is sharply defined. The isotope can readily be obtained in pure form.
By 1983, the demands for higher precision had reached such a point that even the 86Kr standard could not meet them and in that year a bold step was taken. The meter was redefined as the distance traveled by a light wave in a specified time interval. In the words of the 17th General Conference on Weights and Measures.
The meter is the length of the path traveled by light in vacuum during a time interval of 1/299, 792, 458 of a second.
This is equivalent to saying that the speed of light c is now defined as

c=299,792,458 m/s (exactly)
      Figure 2
System of Units of Measurements

This new definition of the meter was necessary because measurements of the speed of light had become so precise that the reproducibility of the 86Kr meter itself became the limiting factor. In view of this it then made sense to adopt the speed of light as a defined quantity and to use it along with the precisely defined standard of time (the second) to redefine the meter.
Below table shows the range of measured lengths that can be compared with the standard.
      Table Some Measured Lengths
System of Units of Measurements


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Sunday, 18 March 2018

STD Time Frames

March 18, 2018 4
The measurement of time has two aspects. For civil and for some scientific purposes we want to know the time of day so that we can order events in sequence. In most scientific work we want to know how long an event lasts (the time interval). Thus any time standard must be able to answer the questions "At what time does it occur?" and "How long does it last?" In the below table shows the range of time intervals that can be measured. They vary by a factor of about 1063.
We can use any phenomenon that repeats itself as a measure of time. The measurement consists of counting the repetitions, including the fractions thereof. We could use an oscillating pendulum, a mass - spring system, or a quartz crystal, for example. Of the many repetitive phenomena in nature the rotation of the Earth on its axis, which determines the length of the day, was used as a time standard for centuries. One (mean solar) second was defined to be 1/86,400 of a (mean solar) day.
STD Time Frames
Approximate Values
Quartz crystal clocks based on the electrically sustained periodic vibrations of a quartz crystal serve well as secondary time standards. A quartz clock can be calibrated against the rotating Earth by astronomical observations and used to measure time in the laboratory. The best of these have kept time for a year with a maximum accumulated error of 5 Âµs, but even this precision is not sufficient for modern science and technology.
To meet the need for a better time standard, atomic clocks have been developed in several countries. Figure 1 shows such a clock, based on a characteristic frequency of the microwave radiation emitted by atoms of the element cesium. This clock, maintained at the National Institute of Standards and Technology, forms the basis in this country for Coordinated universal Time (UTC), for which time signals are available by shortwave radio (stations WWV and WWVH) and by telephone.
Figure 2 shows, by comparison with a cesium clock, variations in the rate of rotation of the Earth over a 4-year period. These data show what a poor time standard the Earth's rotation provides for precise work. The variations that we see in Fig 2 can be ascribed to tidal effects caused by the Moon and seasonal variations in the atmospheric winds.
The second based on the cesium clock was adopted as the international standard by the 13th General Conference on Weights and Measures in 1967. The following definition was given. 
STD Time Frames
Figure 1: Cesium atomic frequency standard No. NBS-6 at the
 National Institute of Standards and Technology in Boulder, 
Colorado. This is the primary standard for the unit of time in the
United States. Dial (303) 499-7111 to calibrate your watch 
against the standard. Dial (900) 410.8463 for 
Naval Observatory time signals

One second is the time occupied by 9,192,631,770 vibrations of the radiation (of a specified wavelength) emitted by a cesium atom.
STD Time Frames
Figure 2: The variation in the length of the day over a 4 year period.
Note that the vertical scale is only 3 ms = 0.003 s. See "The Earth's Rotation Rate," 
by John Wahr, American Scientist. January-February 1985.

Two modern cesium clocks could run for 300,000 years before their readings would differ by more than 1 s. Hydrogen maser clocks have achieved the incredible precision of 1 s in 3,000,000 years. Clocks based on a single as much as 3 orders of magnitude. Figure 3 shows the impressive record of improvements in timekeeping that have occurred over the past 300 years or so, starting with the pendulum clock; invented by Christian Huygens in 1656, and ending with today's hydrogen maser.
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SI Unit Conversion Table pdf

March 18, 2018 0

The International System of Units

The General Conference on Weights and Measures, at meetings during the period 1954 - 1971, selected as base units the seven quantities displayed in table 1. This is the basis of the International System of Units, abbreviated SI from the French Le System International d Units and si unit conversion table pdf is below.
Throughout the book we give many examples of SI derived units, such as speed, force and electric resistance, that follow from table 1. Fore example, the SI unit of force, called the newton (abbreviation N), is defined in terms of the SI base units as.

1N=1kg m/S2

Table 1  SI Base Units

si unit conversion table pdf
If we express physical properties such as the output of a power plant or the time interval between two nuclear events in SI units, we often find very large or very small numbers. For convenience, the General Conference on Weights and Measures, at meetings during the period 1960 - 1975, recommended the prefixes shown in table 2. Thus we can write the output of a typical electrical power plant, 1.3×109 watts, as 1.3 gigawatts or 1.3 GW. Similarly, we can write time interval of the size often encountered in nuclear physics, 2.35 ×10-9 seconds, as 2.35 nanoseconds or 2.35 ns. Prefixes for factors greater than unity have Greek roots and those for factors less than unity have Latin roots (except femto and atto, which have Danish roots).
To fortify table 1 we need seven sets of operational procedures that tell us how to produce the seven SI base and mass in the next three sections.
Two other major systems of units compete with the International System (SI). One is the Gaussian system, in terms of which much of the literature of physics is expressed. We do not use this system in this book. Appendix G gives conversion factors to SI units.
The second is the British system, still in daily use in the United States. The basic units, in mechanics, are length (the foot), force (the pound) and time (the second). Again Appendix G gives conversion factors to SI Units. We use SI units but we sometimes give the British equivalents, to help those who are unaccustomed to SI units to acquire more familiarity with them. In only three countries {Myanmar (Burma), Liberia and the United States} is a system other than SI used as the accepted national standard of measurement.

Table 2 SI Prefixes

si unit conversion table pdf
In all cases, the first syllable is accented, as in na'-no-me'-ter. 

Solution

(a) For our conversion factors, we need (see Appendix G) 1 mi = 1609 m (so that 1 = 1609 m/1 mi) and 1 h= 3600s (so 1 = 1h/3600s). Thus
(b) One fluid gallon is 231 cubic inches and 1 in = 2.54cm.
Thus
Note in these two calculations how the unit conversion factors are inserted so that the unwanted units appear in one numerator and one denominator and thus cancel.
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Physical Quantities and Measurement

March 18, 2018 0

Measurement

Physical Quantities and Measurement
Physical Quantities and Measurement
Despite the mathematical beauty of some of its most complex and abstract theories, including those of elementary particles and general relativity, physics is above all an experimental science. It is therefore critical that those who make precise measurements be able to agree on standards in which to express the results of those measurements, so that they can be communicated from one laboratory to another and verified.


Introduction of Measurement

We start our study of physics by introducing some of the basic units of physical quantities and the standards that have been accepted for their measurement. We consider the pr
oper way to express the results of calculations and measurements, including the appropriate dimensions and number of significant figures. We discuss and illustrate the importance of paying attention to the dimensions of the quantities that appear in our equations. Later in the text, other basic units and may derived units are introduced as they are needed.

The Physical Quantities, Standards and Units

Physical Quantities and Measurement
The building blocks of physics are the quantities that we use to express the laws of physics. Among these are length, mass, time, force, speed, density, resistivity, temperature, luminous intensity, magnetic field strength and many more. Many of these words, such as length and force are part of our everyday meanings of these words. The precise scientific definitions of length and force have no connection at all with the uses of these words in the quoted sentence.
We can define an algebraic quantity for instance, L for length, any way we choose and we can assume it is exactly known. However when we try to assign a unit to a particular value of that quantity, we run into the difficulty of comparing one length with another will agree on the units of measurement. At one time, the basic unit of length was the yard, determined by the size of the king's waistline. You can easily see the problems with such a standard, it is hardly accessible to those who need to calibrate their own secondary standards and it is not invariable to change with the passage of time.
Fortunately, it is not necessary to define and agree on standards for every physical quantity. Some elementary quantities may be easier to establish as standards and more complex quantities can often be expressed in terms of the elementary units. Length and time for example, were for many years among the most precisely measurable physical quantities and were generally accepted as standards. Speed, on the other hand, was less precisely measurable and therefore was treated as a derived unit (speed = length/time). Today, however, measurements of the speed of light have reached a precision beyond that of the former standard of length, we still treat length as a fundamental unit, but the standard for its measurement is now derived from the standards of speed and time.
The basic problem is therefore to choose the smallest possible number of physical quantities as fundamental and to agree on standards for their measurement. These standards should be both accessible and invariable, which may be difficult to satisfy simultaneously. If the standard kilogram, for instance, is to be an invariable object, it must be inaccessible and must be kept isolated beyond the effects of handling and corrosion.
Agreement or standards has been accomplished through a series of international meetings of the General Conference on Weights and Measures beginning in 1889, the 19th meeting was held in 1991. Once a standard has been accepted, such as the second as a unit of time, then we can apply the unit to a vast range of measurements from the lifetime of the proton (greater than 1040 seconds) to the lifetime of the least stable particles that can be produced in our laboratories (about 10-23 seconds). When we express such a value as 1040 in units of seconds, what we mean is that the ratio between the lifetime of the proton and the time interval that is arbitrarily defined as the standard second is 1040. To  accomplish such a measurement, we must have a way of comparing laboratory measuring instruments with the standard. Many of these comparisons are indirect, for no single measuring instrument is capable of operating precisely over 40 orders of magnitude. Nevertheless, it is essential to the progress of science that, when a researcher records a particular time interval with a laboratory instrument, the reading can in some way be connected to a calibration based on the standard second.
The quest for more precise or accessible standards is itself an important scientific pursuit, involving physicists and other researchers in laboratories throughout the world. In the United States, laboratories of the National Institute of Standards and Technology (formerly the National Bureau of Standards) are devoted to maintaining, developing and testing standards for basic researchers as well as for scientists and engineers in industry. 

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