Showing posts with label dimensional analysis. Show all posts
Showing posts with label dimensional analysis. Show all posts

INTRODUCTION AND MEASUREMENT

PHYSICAL WORLD

Physics gives knowledge of nature and natural phenomenon and their quantitative measurements. Science is the knowledge acquired by man in an organised way. The way involved in acquiring knowledge includes systematic observation, reasoning, model making and theoretical prediction. This is called scientific method.

Advancements in Physics are directly related to the advancements in experimental observations and to the development of concepts. A wide diversity in physical world can be known on the basis of a few concepts. It is because of three reasons.
  
    a) Strict regularities and laws help in  quantitative measurements.

    b) There are small number of common and basic principles covering enormous diversities of    scales of phenomenon.

    c) It is easier to understand a phenomenon by separating important features from unimportant features.

The technological development of any society is very closely related with the application of Physics and other branches of science. Measurements are the heart of Physics. Motion, energy, gravitation, properties of matter in bulk and their atomic origin, study of details of mechanical oscillations and waves, description of matter with microscope all form a systematic study. There is a certain amount of overlapping among Physics, Chemistry and Biology.

SCIENCE : An organised effort of person to known and the knowledge he acquires is science.

SCIENTIFIC METHOD : Scientific method corresponds systematic observation, reasoning, model making and theoretical prediction all together.

SCIENTIFIC APPROACH : The scientific approach consists of observations in a proper way, hypothetical analysis and modification of the proposed theory without neglecting important points of views and reasons.

THEORY : A scientific theory is the explanation of natural phenomenon in terms of limited number of laws.

GEOCENTRIC THEORY : It is a theory in which Earth is supposed to bell at the centre of universe.

HELIOCENTRIC THEORY : The sun is at the centre of world consisting of Earth and solar planets.

CORPUSCULAR THEORY OF LIGHT : Newton assumed light to be made up of corpuscles or particles.

HYDROELECTRIC ENERGY : Conversion of gravitational energy into electric energy is called hydroelectric energy.

THERMAL POWER : Conversion of chemical energy of coal y burning it into electric energy.

GEOTHERMAL ENERGY : It is the heat in the depth of the Earth.

SCOPE OF PHYSICS

The scope of physics is very wide i.e, the domain of physics covers a very wide variety of natural phenomenon. For example, the range of distances we study in physics varies from 10-14m (size of nucleus) to 10 29 m (size of universe).

Similarly, the range of masses included in the study of physics varies from 10 -30 kg.(mass of electron) to 10 55 kg (mass of universe). Also the range of time varies from 10 -23 seconds(time taken by light to cross a nuclear distance) to 10 18 seconds (lifetime of the sun).

So the scope of the physics is very wide. It includes optics, electricity, waves and oscillations,heat and thermodynamics, magnetism, atoms and nuclear physics, computer and electronics.

DEVELOPMENT OF PHYSICS

Physics is a science took roots from the days of Copernicus i.e, nearly centuries ago when it was not well understood and it was considered as a  part of philosophy i.e, knowledge. Later on, with the development of knowledge about nature and its various activities,the knowledge was divided as physical and biological science. Some important developments like neutrons, law of gravitation, ideas about light were developed in the 18th century. 19th century saw some of the great discoveries in physics and at the end of century i.e. 1889, electromagnetic theory was developed, foundation of Einsteins and Plank's ideas were laid down, apart from laying the basis for industrial revolution. Physics progressed very fast in the first quarter of the 20th century.

Atomic structure, theory of relativity, quantum theory, nuclear physics, basics of laser theory and most of other developments took place in this period. Then come transistor, semiconductors, television, radar and few important discoveries during world war II. Further developments in quantum mechanics, thin films technology, computers, laser were developed from 1950 onwards. Today,we have no theoretical development beyond quantum mechanics. Unified theory is not being tried yet. This is the present status with achievement in applied fields.


UNITS AND MEASUREMENTS

Unit is defined as the reference standard used to measure a physical quantity. Fundamental units are defined as the units of fundamental quantities. They are independent of each other and are expressed by writing the letter of the fundamental quantity in a paranthesis. Derived units are defined as those units which can be derived from fundamental units . They are expressed by writing the symbols of a derive quantity in a paranthesis.

The SI units of measurements of seven physical quantities are known as fundamental units. They are
   
    metre(m) for length
    kilogram(kg) for mass
    second(s) for time
    ampere(A) for electric current.
    kelvin(K) for temperature
    candela(cd) for luminous intensity
    mole(mol) for amount of substances

The SI units of measurement of two or more quantities are known as supplementary units. They are radian(rad) for plane angle and steradian(sr) for solid angle. The order of accuracy obtained in adopting atomic standards of length and time is 1 part of 10 9.

Dimensions :

Dimensions of physical quantity are defined as the powers to which the fundamental units of mass, length and time have to be raised to obtain its units. Dimensional formula as an expression which shows that which of the fundamental units and with what powers appear into the derived unit of a physical quantity. Dimensional equation is defined as the equation obtained by equating the symbols of a physical quantity with its dimensional formula.

   Merits

     - conversion of one system of units into another
     -checking the correctness of a given physical relation.
     -derivation of formula.

   Demerits

     -does not help to derive the relations containing exponential and trigonometrical functions.
     -dimensionless constants involved in the physical relation cannot be determined.
     -tells no information about the physical correctness of the relation.

Difference between measured value and true value of a quantitiy represents error of measurement. The arithmetic mean of all the absolute error is known as mean absolute error. The relative error is the ratio of mean absolute error to the mean or true value of the quantity measured. Percentage error is the relative error expressed in percent. 

Significant figures  : 

In the measured value of a physical quantitiy, the digits about the correctness of which we are sure plus the last digit which is doubtful, are called significant figures. The rules for counting significant figures are

    a) All the non-zero digits are significant.
    b)All zeros occuring in between the two non-zero digits are significant.
    c) In a number without decimal, zero on the right of non-zero digits are significant.
    d)In a number with decimal,zeros on the last non-zero digit are significant.
    e)In a value less than one, zeros occuring between the decimal point and non-zero digit on the right are not significant.
    f)The change in the units of measurement of a quantity does not affect number of significant figures.
   g)When some value is expressed in an exponential form, the exponential form, the exponential term does not affect the number of significant figures.


In mathematical operations involving addition and substraction, the result should be correct upto minimum number of decimal places in any of the quantity involved. In mathematical operations involving significant figures in the result will be limited corresponding to the minimum number of significant figures in any of the quantities involved.

Method of Rounding off  :
  
To represent the result to a correct number of significant figures, we round off as per the following rules

   a) When the digit to be rounded offf to the more than 5, the preceding digit is increased by one.
   b) When the digit to be rounded off to the less than 5, the preceding digit is unaffected.
   c) When the digit to be rounded off is 5, then increased the preceding digit by 1 if it is odd and retain the preceding value if it is even.