Moments and their application

MOMENTS OF A FORCE:
It is the turning effect produced by a force,on the body,on which it acts,The moments of a force is equal ton the product of the force and the perpendicular distance of the point,about which the moment is required and the line of action of the force.

Mathematically,moment,
M=p x l
where p=force acting on the body,and
        l=perpendicular distance between the point,about which the moment is required and the line of                action of the tree.

UNITS OF MOMENTS: since the moment of a force is the product of force and distance,therefore the units of the moments will depend upon the units of force and distance.Thus ,if force is in Newton and the distance is in maters,then the units of moments will be Newton-meter (briefly written as N-m).similarly, the units of moments may be kN-m(i.e.kN x m ),N-mm (i.e. N x mm) etc.
TYPE OF MOMENTS
Broadly speaking,the moments are of the following two types:
1.Clockwise
2.Anticlockwise moments.

CLOCKWISE MOMENT:
It is moment of a force,whose effect is to turn or rotate the body,about the point in the same direction in which hands of  a clock move .

ANTICLOCKWISE MOMENT:
it is the moment of a force,whose effect is to turn or rotate the body,about the point in the opposite direction in which the hand of a clock move.

NOTE:
The general convention is to take clockwise moments as positive and anticlockwise  moment as negative.

VARIGNON'S PRINCIPLE OF MOMENTS (OR LAW OF MOMENTS)
It states, "If a number of coplanar forces are acting simultaneously on a particle,the algebraic sum of the moments of the forces about any point is equal to the moments of their resultant force about the same point

What is forces

The force is an important factor  in the field of mechanics,which may be broadly *defined as an agent which produces or tends to produce,destroys or tends to destroy motion e.g., a horse applies force to pull a cart and to set it in motion.Force is also required to work on a bicycle pump.In this case,the force is supplied by the muscular power of our arms and shoulders.

  It may be noted that the force may have either of the two functions i.e., produces or tends to produce motion. The second part of the definition is an application of the first part. In statics,we consider the second function of the force only i.e.,'tends to produces motion.'

sometimes,the applied force may not be sufficient to move a body,e.g if we try to lift a stone weighing 2 or 3 quintals,we  fail to do so. In this case we exert a force, no doubt,but no motion is produced.This shows that a force may not necessarily produce a motion in a body ;but it may, simply, tend to do so.In a tug-of-war the two parties, when balanced,neutralize each other's force .But the moment one party gets weaker,the other party pills off,in spite of first party's best effort to destroy motion.

EFFECTS OF A FORCE
A force may produces the following effects in a body,on which it acts:
1. It may change the motion of a body ,i.e if a body is at rest,the force may set it in motion.And if the body is already in motion,the force may accelerate it.
2. It may retard the motion of a body.
3.It may retard the forces,already acting on a body,thus bringing it to rest or in equilibrium.
4. It may give rise to the internal stresses in the body,on which it acts.

CHARACTERISTICS OF A FORCE
In order to determine the effect of a force,acting a on a body,we must know the following characteristics of a force:
  

VECTOR QUANTITIES

The vector quantities (or sometimes known as vectors) are those quantities which have both magnitude and direction such as force,displacement,velocity, acceleration,momentum etc.following are the important feature of vector quantities:

1. Representation of a vector.  A vector is  represented by a directed line.
2.Unit vector.  A vector, whose magnitude is unity, is known as unit vector.
3.Equal vector.  The vectors,which are parallel to each other and have same direction (i.e.,same sense) and equal magnitude are known as equal vectors.
4.Like vectors.  The vectors,which are parallel to each other and have same sense but unequal magnitude,are known as like vectors.
5. Addition of   vectors.
this method of adding the two vectors is called the triangle law of addition of vectors.similarly,if more than two vector are to be added,the same may be done first by adding the two vectors,and then by adding the third vector to the resultant of the first two and so on.This method of adding more than two vectors is called polygon Law of Addition of Vectors.
6.Subtraction of vectors. consider two vectors PQ and RS in which the vector RS is Required to be Subtracted .

ENGINEERING MACHANICS

The subject of Engineering Mechanics is that branch of applied science,which deals with the laws and principles of Mechanics,along with their applications to engineering problems.As a matter of fact,Knowledge of Engineering Mechanics is very essential for an engineer in planning,designing and construction of his various types of structure and mechanics in a most systematic and scientific manner.
BEGINNING AND DEVELOPMENT OF ENGINEERING MECHANICS
it will be  interesting to know, as to how the early man had been curious to know about the different processes going on the earth, In fact,he used to content himself,by holding gods  responsible for all the processes.  For a long time, the man had bee trying to improve his way of working. the first step, in this direction,was the discovery of a circular wheel,which led to the use of animal driven carts.The study of ancient civilization of Babylonians,Egyptian,Greeks and Roman reveal the use of water wheels and wind mills even during the pre-historic days.
It is believed that the  word 'Mechanics' was coined by a Greek philosopher Aristotle. He used this word for the problem of lever and the concept of centre of gravity.At that time,it included a few ideas,which were odd,unsystematic and based mostly on observations containing incomplete information.The first mathematical concept of this subject was developed by Archimedes.The story,for the discovery of First Law of Hydro statics,is very Popular even today in the history of the development  of  Engineering Mechanics.In the normal course,Hieron King of Syracuse got a golden crown made for his use.He suspected that the crown has been made with an adulterated gold. The king liked the design of the crown so much that he  did not want it to be melted,in order to check its purity.It is said that the king announced a huge reward for a person,who can check melting it. the legend goes that Archimedes, a pure mathematician, one day sitting in his bath room tub realised that if a  body is immersed in water,its apparent weight is reduced. He thought that the apparent loss of weight of the immersed body is equal to the weight of the liquid displaced.
It is believed that without further  thought,Archimedes jumped out of the bath tub and ran naked down the street shouting 'Eureka, eureka !"i.e.I have found it, I have found it !'
The subject did not receive any concrete contribution for nearly 1600 years In 1325,jean Buridan of paris University proposed an idea that a body in motion possessed a certain impetus i.e.motion in the period 1325-1350,a group of scientist led by the Thomas Bradwardene of Oxford University did not of work on plane motion of bodies.Leonarodo Da Vinci(1452-1519),
a great engineer and painter,gave many ideas in the study of machanism, friction and motion of bodies on inclined planes.Galileo (1564-1642) established the theory of projectiles and gave a rudimentary idea of inertia.Huyghens(1629-1695) developed the analysis of motion of a pendulum.  

CLASSIFICATION OF ICs

An integrated circuit (IC) consists of several interconnected transistors,resistors,capacitors etc.,all contained in one small package with external connecting terminals. The circuit may be entirely  self-contained,requiring only input and output connections and supply voltage to function. Alternatively,a few external components may have to be connected to make the circuits operative.
 on the basis of fabrication techniques used, the ICs can be divided into following three classes.
1. Monolithic ICs. The word 'monolithic' is derived from the Greek momos, meaning 'single' and lithos,meaning 'stone' and implies that the entire circuit is fabricated on a single chip of a semiconductor.In monolithic ICs,the components like transistors,diodes,resistors and capacitors are formed simultaneously by diffusion process steps.Then,the process of metallization is used in  interconnecting these components to from the required circuit. The dielectric or P-N junction is used to provide electrical isolation in monolithic identical ICs are by far the most common type of ICs used in practice,because of mass production,lower cost and higher reliabilty.
since their invention,manufacturers have been manufacturing monolithic ICs to carry  out all types of functions. commercially available ICs of this type can be used as amplifiers, voltage regulators,crowbars,AM receivers,TV circuits,and computer circuits.
However,the monolithic circuits have the following limitations or drawbacks:
(i) Low power rating.since monolithic ICs are of about the size of a discrete small-signal transistor,they typically have a maximum power rating of less than 1 watt.This limits their use to low-power applications.
(ii)poorer isolation between components.
(iii) No possibility of fabrication of inductors.
(iv)small range of values of passive components used in the ICs.
(v)Lack of flexibility in circuits design as for making any variation in the circuit, a new set of marks is required.
2. Thin and Thick Film ICs. These devices are larger than monolithic ICs but smaller than discrete circuits. These ICs can be used when power requirement is comparatively higher.with a thin-or  thick-film IC,the passive cmponents like resistors and capacitors are integrated, but the transistors and diodes are connected as discrete components to from a complete circuit.Therefore,commercially available  thin and thick-film circuits are combination of integrated and discrete components.

The essential difference between the thin- and thick-film ICs is not their relative thickness but method of deposition of film.Both have similar appearance,properties and general characteristics.

Thin-Film ICs are  fabricated by depositing films of conducting material on the surface of a glass or ceramic base. By controlling the width and thickness of the films,and by using different materials selected for their resistivity, resistors and conductors are fabricated.capacitors are produced by sandwiching a film of insulating oxide between  two conducting films,Inductors are made by depositing a spiral formation of film. Transistors and diodes can be produced by thin-film technology;but usually tiny discrete components are connected into the crcuit.

Integrated circuits

The integrated circuit was introduced in 1958.It has been called the most significant technological development of twentieth century.It has radically altered the world of electronics.The profound effect of these microelectronics 'giants' was first felt in the computer and digital field. First-generation electronic computers employed vacuum tubes.Vacuum tubes   were replaced by transistors, cheaper in cost, smaller in size,less power consuming and reliable,in second generation computers.Third generation computers used digital ICs, largely reducing computer size and increasing computer reliability and speed.Integrated circuits have further reduced product dimension and cost,while ensuring even greater reliability.
          As the state of the art advanced,specially designed ICs were used in linear circuits in communication,military,and industrial application. ICs and large scale ICs have changed the design of electronic devices from the use of only discrete components to hybrid solid-state devices which mix discrete components with ICs.


Discrete circuits consist of separately manufactured components,such as resistors,inductors,capacitors,diodes,transistors,etc.,joined by wires or plated conductors on printed boards.such circuits have two main drawbacks.Firstly,they occupy a larger space.This is because  of involvement of large number of components in large electronic circuit such as a TV circuit or a computer circuit. Secondly,there is problem of reliability,as hundreds of components are to be soldered.To overcome these drawbacks of space conservation and reliability,engineers started a drive for miniaturised circuits. This led to the development of integrated circuits in 1958.

Integrated circuit is not just a mere efficient transistor or several transistors inside a small case. It is a complete electronic circuit consisting of both the active and passive components(including their interconnections) fabricated on an extremely tiny single chip of silicon.The active components are those which are capable of producing gains,such as,transistors, FETs. Passive components are diodes,resistors etc. An etc IC is so small in size that we normally required  a microscope to see the connections between the components.The processes employed in fabrication of IC chips are basically the same as employed in the fabrication of discrete transistors,diodes etc.However,in IC technology,all the circuit elements(transistors,diodes,resistors,capacitors etc.)including their interconnections are fabricated at a time.Rather a batch of identical chips is fabricated at a time.This is the reason that such IC chips have identical characteristics.

Microwaves

Microwaves are electromagnetic waves whose frequencies range from 1GHz to 1000 GHz(1Ghz=1000000000 Hz).For comparison, the signal from an AM Radio station is 1 MHz (Mega Hertz=1000000 Hz)and the signal from FM radio station is 100 MHz.

Microwave( µ w's)   are so called since they are defined in terms of their wavelength in the sense that micro refer to tinyness-tinyness referring to the wavelength and the period of a cycle of a cm wave.In other words, the wavelength( λ) of cm waves at microwave frequencies are very shorts;typically  from a few tens of cm to a fraction of a mm.In short, a microwave is a signal that has a wavelength of 1 foot or less i.e,  λ<= 30.5 cms =~ 1 foot. This converts to a frequency of 984 MHz, approximetly= 1 Ghz.so,all frequencies above approximately 1000MHz (1GHz) to about 1000 GHz are microwave frequencies.

The higher frequency edge of microwaves borders on the infrared and visible-light regions or spectrum.This explains why microwaves behaves more like rays of light rays of light than ordinary radio waves. Due to this unique behaviours,microwave frequencies are classified separately from radio waves.

The visible light is above infrared region and falls between 430 THz and 1 PHz(peta Hz)This region includes the a fiber optics and laser region.This region above 1 PHz includes X-rays,Gamma Rays and cosmic Rays. 

ADVANTAGE OF MICROWAVES

1. Increased bandwidth availability 

Microwave have large band width(1GHz-103GHz) compared to the common bads namely MW,SW and UHF waves. The advantage of large bandwidths is that the frequency range of information channels will be  a small percentage of the carrier frequency   and more information can be transmitted in microwave region is very useful since the lower band of frequency is already crowded.

 Infact,Microwave region(1000 GHz)contain thousand sections of frequency band 0-100000000 Hz and hence any one of these thousand section may be used to transmit all the TV, ratio and other communication that is presently transmitted by the 0-10000000 Hz band.(Bandwidth of speech = 4 kHz;Music=10-15kHz. T.V=5-7 MHz; Telegraph channel=120-240Hz),i.e., greater bandwidth provides more room for stuff to be packed into the transmission.

 It is a current trend to use microwaves more and more in various long distance communication application such as Telephone networks, TV network,space communication ,Telemetry ,Defence, Railways, etc. FM and present day digital modulation schemes also require higher bandwidth.

PHOTOVOLTAIC OR SOLAR CELLS

These cells are semiconductor junction devices used for converting radiation energy into electrical energy.These cells generate a voltage proportional to electromagnetic radiation intensity a voltage proportional to electromagnetic radiation intensity and are called the photovoltaic cells because of their voltage generating capability.An example of such a cell is a silicon solar cell,which converts radiant energy of the sun into electrical energy.
Selenium and silicon are the most widely used materials for solar cells,though gallium arsenide,indium arsenide and cadmium sulphide are also used.

     The construction and cross section of a typical power solar cell for use as an energy converter are given in fig. the surface layer of P-type material is extremely thin so that light can penetrate to the juntion. The nickel-plated ring around the P-type material is the positive output terminal,and the plating at the bottom of the N-type material is the negative output terminal.power solar cells are also available in flat strip form for efficient coverage of available surface areas.The circuit symbol often used for a photovoltaic cell shown in fig.
  The photovoltaic cell can be operated satisfactorily over a wide range of temperature(say from -100 to 125 degree C). the temperature variations have little effect on short-circuit current but affect the open-circuit output voltage  considerably.These variation may be of the order of a few mV per degree C in output voltage. An individual solar cell generates an open-circuit voltage of about 500mV (depending on light intensity) when active. However, photocells can be connected in series to increase the available terminal voltage.
The advantage of such devices are their extremely fast response i.e., these devices can be used as energy   convertors directly.
Multiple-unit silicon photovoltaic devices may be used for sensing light in application such as reading punched cards in the data processing industry.
Gold-doped germinium cells with controlled spectral response characteristic act as photovoltaic device in the infrared region of the spectral and may be used as infrared detectors.
solar cells are extensively used as a source of power for many space satellites.The array of junctions can be distributed over the surface of the satellite or can be contained in solar cell "paddles" attached to the main body of the satellite. Application of solar cells are not restricted to outer space.It is possible to have useful power from the sun in terrestrial application using solar cells, even though the solar intensity is reduced by the atmosphere. About kW/m2 is available in a particularly sunny location but not all of this solar power can be converted into electrical power.

Full wave Rectifiers

In half-rectifiers only one half cycles of the input are utilized but in full-wave rectifiers both half cycles of the input are utilized. Alternate half cycles are inverted to give unidirectional load current.There are two types of full-wave rectifier circuits namely
1. center-tap rectifier and 2. bridge rectifier.
center-Tap rectifier:
in such a rectifier, the ac input is applied through a transformer, the anodes of the two diodes D1 and D2 (having similar characteristics) are connected to the opposite ends of the center tapped secondary winding and two cathodes are connected to each other and are connected also though the load resistance RL and back to the center of the transformer as shown in figure.
  when the top of the transformer secondary winding is positive,say during the first half cycle of the supply,the anode of Diode D1 is positive w.r.t. cathode, and anode of diode D2 is negative w.r.t cathode.Thus only diode D1 conducts,being forward biased and current flows from cathode to anode of ddiode D1, through load resistance RL and top half the transformer secondary making cathode end of load resistance RL positive.During the second  half cycle of the input voltage the polarity is reversed,marking the bottom of the secondary winding positive w.r.t  centre tap and thus diode D2 is forward biased and diode D1 is reverse biased. consequently during this half cycle of the input only the diode D2 conducts and current flows through the load  resistance RL and bottom of the transformer secondary making the cathode end of the load resistance RL positive.Thus the direction of flow of current through  the load resistance RL remains the same during both halves of the input supply voltage. Thus the circuit shown in figure acts as full-wave rectifier.
Bridge Rectifier: In the bridge circuit four diodes are connected in the form of a wheatstone bridge,two diametrically opposite junctuons of the bridge are connected to the secondary of a transformer and the other two are connected to the load, as shown in fig 2.

  when the upper end of the transformer secondary winding is positive ,say during first half cycles of the input supply,diodes D1 and D3 are forward biased and current flows thorugh arm AB, enters the load at positive terminal, leaves the load at negative terminal, and returns back flowing through arm DC.

Half-Wave Rectifier

When a single rectifier unit is placed in series with an ac supply,as illustrated in fig,it converts alternating voltage into unidirectional pulsing voltage,using one half cycles of the applied voltage,the other half cycles being suppressed because it conducts only in one direction.Unless there is an inductance or battery in the circuit,the current will be zero,therefore,for half the time. This is called half-wave rectification.
      Diode is an electronic device consisting of two elements known as cathode and anode.since in a diode electrons can flow in one direction only i.e., from cathode to anode so the diode provides the unilateral conduction necessary for rectification.This is true for diodes of all types-vacuum,gas--filled,crystal,semiconductor or metallic(copper oxide and selenium types) diodes. semiconductor diodes,because of their inherent advantages are usually used as a rectifying device.However, for very high voltage, vacuum diode may be employed.

circuit: The half wave rectifier circuit using a semiconductor diode with a load resistance RL but no smoothing filter is given in fig. The diode is connected in series with the secondary of the transformer and the load resistance RL, the primary of the transformer is being connected to the ac supply mains.

Working : The  ac voltage across the secondary winding changes polarity every half cycle. During the positive half cycles of the input ac voltage i.e., when upper end of the secondary winding is positive w.r.t its lower end,the diode is forward biased and, therefore,conducts current.if the forward resistance of the diode is assumed to be zero (in practice,however,a small resistance exist) the input voltage during the positive half cycles is directly applied to the load resistance RL, marking its upper end positive w.r.t its lower end. The wave forms of the output current and output voltage are of the same shape as that of the input ac voltage.
 During the negative half cycles of the input ac voltage i.e., when the lower end of the secondary winding is positive w.r.t. its upper end, the diode is reverse biased and so does not conduct.Thus during the negative half cycles of the input ac voltage the current through and voltage across the load remains zero if the reverse current, being very small in magnitude,is neglected.Thus for the negative half cycle  no power is delivered to the load.
       Thus the output voltage developed across load resistance RL(VL) is a series of positive half cycles of alternating voltage,with intervening very small constant negative voltage levels, as shown in fig.It is obvious from the figure that the output is not  a steady dc, but only a pulsating dc wave.since  only half cycle of the input wave are used,it is called a half wave rectifier.