ENGINEERING MECHANICS 😎...😎

      ENGINEERING              MECHANICS:-

Introduction-            Mechanics is the physical science concerned with the dynamical behavior (as

opposed to chemical and thermal behavior) of bodies that are acted on by 

mechanical disturbances. Since such behavior is involved in virtually all the 

situations that confront an engineer, mechanics lies at the core of much engi￾neering analysis. In fact, no physical science plays a greater role in engineer￾ing than does mechanics, and it is the oldest of all the physical sciences. The 

writings of Archimedes covering buoyancy and the lever were recorded 

before 200 B.C. Our modem knowledge of gravity and motion was established 

by Isaac Newton (1642-1727), whose laws founded Newtonian mechanics, 

the subject matter of this text. 

In 1905, Einstein placed limitations on Newton's formulations with his 

theory of relativity and thus set the stage for the development of relativistic 

mechanics. The newer theories, however, give results that depart from those 

of Newton's formulations only when the speed of a body approaches the 

speed of light (I 86,000 mileslsec). These speeds are encountered in the large￾scale phenomena of dynamical astronomy. Furthermore for small-scale 

phenomena involving subatomic particles, quantum mechanics must be used 

rather than Newtonian mechanics. Despite these limitations, it remains never￾theless true that, in the great bulk of engineering problems, Newtonian 

mechanics still applie d     

             ...# Basic's of units & dimensions of mechanics:-

To study mechanics, we must establish abstractions to describe those charac￾teristics of a body that interest us. These abstractions are called dimensions.

The dimensions that we pick, which are independent of all other dimensions,

are termed primary or basic dimensions, and the ones that are then developed

in terms of the basic dimensions we call secondary dimensions. Of the many

possible sets of basic dimensions that we could use, we will confine ourselves

at present to the set that includes the dimensions of length, time, and mass.

Another convenient set will he examined later.

Length-A Concept for Describing Size Quantitatively. In order to deter￾mine the size of an object, we must place a second object of known size next

to it. Thus, in pictures of machinery, a man often appears standing disinter￾estedly beside the apparatus. Without him, it would be difficult to gage the

size of the unfamiliar machine. Although the man has served as some sort of

standard measure, we can, of course, only get an approximate idea of the

machine's size. Men's heights vary, and, what is even worse, the shape of a

man is too complicated to be of much help in acquiring a precise measure￾ment of the machine's size. What we need, obviously, is an object that is

constant in shape and, moreover, simple in concept. Thus, instead of a three￾dimensional object, we choose a one-dimensional object.' Then, we can use

the known mathematical concepts of geometry to extend the measure of size

in one dimension to the three dimensions necessary to characterize a general

body. A straight line scratched on a metal bar that is kept at uniform thermal

and physical conditions (as, e.g., the meter bar kept at Skvres, France) serves

as this simple invariant standard in one dimension. We can now readily cal￾culate and communicate the distance along a cettain direction of an object by

counting the number of standards and fractions thereof that can be marked off

along this direction. We commonly refer to this distance as length, although

the term "length could also apply to the more general concept of size. Other

aspects of size, such as volume and area, can then be formulated in terms of

the standard by the methods of plane, spherical, and solid geometry.

A unit is the name we give an accepted measure of a dimension. Many

systems of units are actually employed around the world, but we shall only

use the two major systems, the American system and the SI system. The basic

unit of length in the American system is the foot, whereas the basic unit of

length in 

the SI system is the meter. 

wearing. But how do we determine this? We may say to ourselves: “During

the thirties, people wore the type of straw hat that the fellow in the picture is

wearing.” In other words, the “when” is tied to certain events that are experi￾enced by, or otherwise known to, the observer. For a more accurate descrip￾tion of “when,” we must find an action that appears to he completely

repeatable. Then, we can order the events under study by counting the num￾her of these repeatable actions and fractions thereof that occur while the

events transpire. The rotation of the earth gives rise to an event that serves as

a good measure of time-the day. But we need smaller units in most of our

work in engineering, and thus, generally, we tie events to the second, which is

an interval repeatable 86,400 times a day.

Mass-A Property of Matter. The student ordinarily has no trouble under￾standing the concepts of length and time because helshe is constantly aware

of the size of things through hisher senses of sight and touch, and is always

conscious of time by observing the flow of events in hisher daily life. The

concept of mass, however, is not as easily grasped since it does not impinge

as directly on our daily experience.

Mass is a property of matter that can be determined from two different

actions on bodies. To study the first action, suppose that we consider two

hard bodies of entirely different composition, size, shape, color, and so on. If

we attach the bodies to identical springs, as shown in Fig. 1.1, each spring

will extend some distance as a result of the attraction of gravity for the hod￾ies. By grinding off some of the material on the body that causes the greater

extension, we can make the deflections that are induced on both springs

equal. Even if we raise the springs to a new height above the earth’s surface,

thus lessening the deformation of the springs, the extensions induced by the

pull of gravity will he the same for both bodies. And since they are, we can

conclude that the bodies have an equivalent innate property. This property of

each body that manifests itself in the amount of gravitational attraction we

call man.

The equivalence of these bodies, after the aforementioned grinding oper￾ation, can be indicated in yet a second action. If we move both bodies an

equal distance downward, by stretching each spring, and then release them at

the same time, they will begin to move in an identical manner (except for

small variations due to differences in wind friction and local deformations of

the bodies). We have imposed, in effect, the same mechanical disturbance on

each body and we have elicited the same dynamical response. Hence, despite

many obvious differences, the two bo

dies again show an equivalence.

The pcoperry of mpcs, thn, Chomcrcrke8 a body both in the action of

na1 anrack and in tlu response IO a mekhnnicd

To communicate this property quantitatively, we may choose some 

mentioned actions. The two basic units commonly used in much American

engineering practice to measure mass are the pound mass, which is defined in

terms of the attraction of gravity for a standard body at a standard location,

and the slug, which is defined in terms of the dynamical response of a stan￾dard body to a standard mechanical disturbance. A similar duality of mass

units does not exist in the SI system. There only the kilugmm is used as the

basic measure of mass. The kilogram is measured in terms of response of a

body to a mechanical disturbance. Both systems of units will he discussed

further in a subsequent section.

We have now established three basic independent dimensions to

describe certain physical phenomena. It is convenient to identify these dimen￾sions in the following manner:

length [L]

time [tl

mass [MI

These formal expressions of identification for basic dimensions and the more

complicated groupings to he presented in Section 1.3 for secondary dimen￾sions are called “dimensional representations.”

Often, there are occasions when we want to change units during com￾putations. For instance, we may wish to change feet into inches or millime￾ters. In such a case, we must replace the unit in question by a physically

equivalent number of new units. Thus, a foot is replaced by 12 inches or 30.5

millimeters. A listing of common systems of units is given in Table 1.1, and

a table of equivalences hetween these and other units is given on the inside

covers. Such relations between units will he expressed in this way:

1 ft 12 in. = 305 mm

The three horizontal bars are not used to denote algebraic equivalence;

instead, they are used to indicate physical equivalence. Here is another way

of expressing the relations above:

Table 1.1 common systems of units

c!P

Mass Gram

Length Centimeter

Time Second

FOKC Dyne

English

Mass Pound mass

Length Foot

Time Second

Force Poundal

SI

Mass Kilogram

Length Meter

Time Second

Force Newton

American Practice

Mass Slug or pound mass

Length Foot

Time Second

Force Puund force 

Secondary dimensions units:-

When physical characteristics are described in terms of basic dimensions by

the use of suitable definitions (e.g., velocity is defined2 as a distance divided

by a time interval), such quantities are called secondary dimensional quanti￾ties. In Section 1.4, we will see that these quantities may also be established as

a consequence of natural laws. The dimensional representation of secondary

quantities is given in terms of the basic dimensions that enter into the formula￾tion of the concept. For example, the dimensional representation of velocity is

[velocity] = - [Ll

[/I

That is, the dimensional representation of velocity is the dimension length

divided by the dimension time. The units for a secondary quantity are then

given in terms of the units of the constituent basic dimensions. Thus,

[velocity units] = - [ftl

[secl

A chunge of units from one system into another usually involves a

change in the scale of measure of the secondary quantities involved in the

problem. Thus, one scale unit of velocity in the American system is 1 foot per

second, while in the SI system it is I meter per second. How may these scale

units he correctly related for complicated secondary quantities? That is, for

our simple case, how many meters per second are equivalent to 1 foot per

second? The formal expressions of dimensional representation may he put to

good use for such an evaluation. The procedure is as follows. Express the

dependent quantity dimensionally; substitute existing units for the basic

dimensions; and finally, change these units to the equivalent numbers of units

in the new system. The result gives the number of scale units of the quantity

in the new system of units that is equivalent to 1 scale unit of the quantity in

the old system. Performing these operations for velocity, we would thus have ....

which means that ,305 scale unit of velocity in the SI system is equivalent to

I scale unit in the American system.

Another way of changing units when secondary dimensions are present

is to make use of the formalism illustrated in relations 1.1. To change a unit

in an expression, multiply this unit by a ratio physically equivalent to unity,

as we discussed earlier, so that the old unit is canceled out, leaving the

desired unit with the proper numerical coefficient. In the example of velocity

used above, we may replace ft/sec by mlsec in the following manner:

It should he clear that, when we multiply by such ratios to accomplish a

change of units as shown above, we do not alter the magnitude of the actual

physical quantity represented by the expression. Students are strongly urged

to employ the above technique in their work, for the use of less formal meth￾ods is generally an invitation to error. 

DIMENSIONS RELATION BETWEEN FORCE &MASS:-We shall now employ the law of dimensional homogeneity to establish a new

secondary dimension-namely force. A superficial use of Newton’s law will

be employed for this purpose. In a later section, this law will be presented in

greater detail, but it will suffice at this time to state that the acceleration of a

particle3 is inversely proportional to its mass for a given disturbance. Mathe￾matically, this becomes

(1.2) 1 a=-

m

where - is the proportionality symbol. Inserting the constant of proportional￾ity, F, we have, on rearranging the equation,

F=ma (1.3)

The mechanical disturbance, represented by F and calledforce, must have the

following dimensional representation, according to the law of dimensional

homogeneity:

[F] = [MI- [Ll

[fIZ (1.4)

The type of disturbance for which relation 1.2 is valid is usually the action of

one body on another by direct contact. However, other actions, such as mag￾netic, electrostatic, and gravitational actions of one body on another involving

no contact, also create mechanical effects that are valid in Newton’s equation...

We could have initiated the study of mechanics by consideringfiirce as

a basic dimension, the manifestation of which can he measured by the elon￾gation of a standard spring at a prescribed temperature. Experiment would

then indicate that for a given body the acceleration is directly proportional to

the applied force. Mathematically,

F m a; therefore, F = mu

from which we see that the proportionality constant now represents the prop￾erty of mass. Here, mass is now a secondary quantity whose dimensional rep￾resentation is determined from Newton's law:

As was mentioned earlier, we now have a choice between two systems

of basic dimensions-the MLt or the FLr system of basic dimensions. Physi￾cists prefer the former, whereas engineers usually prefer the latter. 

UNITS OF MASS:-As we have already seen, the concept of mass arose from two types of actions

-those of motion and gravitational attraction. In American engineering prac￾tice, units of mass are based on hoth actions, and this sometimes leads to con￾fusion. Let us consider the FLt system of basic dimensions tor the following

discussion. The unit of force may he taken to be the pound-force (Ihf), which

is defined as a force that extends a standard spring a certain distance at

a given temperature. Using Newton's law, we then define the slug as the

amount of mass that a I-pound force will cause to accelerate at the rate of

I foot per second per second.

On the other hand, another unit of mass can he stipulated if we use the

gravitational effect as a criterion. Herc. the pound muxs (Ihm) is defined as

the amount of matter that is drawn by gravity toward the earth by a force of

I pound-force (Ihf) at a specified position on the earth's surface.

We have formulated two units of mass by two different actions, and to

relate these units we must subject them to the sumt. action. Thus, we can take

1 pound mass and see what fraction or multiplc of it will be accelerated

1 ft/sec2 under the action of I pound afforce. This fraction or multiple will then

represent the number of units of pound mass that are equivalent to I slug.

It turns out that this coefficient is go, where g, has the value corresponding to

the acceleration of gravity at a position on the earth's surface where the

pound mass was standardized. To three significant figures, the value of R~ is

32.2. We may then make the statement of equivalence that

I slug = 32.2 pounds mass To use the pound-mass unit in Newton’s law, it is necessary to divide by

go to form units of mass, that have been derived from Newton’s law. Thus,

where m has the units of pound mass and &go has units of slugs. Having

properly introduced into Newton’s law the pound-mass unit from the view￾point of physical equivalence, let us now consider the dimensional homo￾geneity of the resulting equation. The right side of &. 1.6 must have the

dimensional representation of F and, since the unit here for F is the pound

force, the right side must then have this unit. Examination of the units on the

right side of the equation then indicates that the units of go must be

(1.7)

How does weight tit into this picture? Weight is defined as the force of

gravity on a body. Its value will depend on the position of the body relative to

the earth‘s surface. At a location on the earth’s surface where the pound mass is

standardized, a mass of 1 pound (Ibm) has the weight of 1 pound (Ibf), but with

increasing altitude the weight will become smaller than 1 pound (Ibf). The

mass, however, remains at all times a I-pound mass (Ibm). If the altitude is not

exceedingly large, the measure of weight, in Ibf, will practically equal the mea￾sure of mass, in Ibm. Therefore, it is unfortunately the practice in engineering to

think erroneously of weight at positions other than on the earth‘s surface as the

measure of mass, and consequently to use the symbol W to represent either Ibm

or Ibf. In this age of rockets and missiles, it behooves us to be careful about the

proper usage of units of mass and weight throughout the entire text.

If we know the weight of a body at some point, we can determine its

mass in slugs very easily, provided that we know the acceleration of gravity,

g, at that point. Thus, according to Newton’s law,

W(lbf) = m(s1ugs) x g(ft/sec*)

Therefore,

(1 3)

Up to this point, we have only considered the American system of

units. In the SI system of units, a kilogram is the amount of mass that will

accelerate 1 m/sec2 under the action of a force of 1 newton. Here we do not

have the problem of 2 units of mass; the kilogram is the basic unit of mass. 9.81 m/sec2. A newton, on the other hand, is the force that causes I kilogram

of mass to have an acceleration of 1 m/sec2. Hence, Y.8 1 newtons are equiva￾lent to I kilogram of force. That is,

9.81 newtons 1 kilogram(force) = 2.205 Ibf

Note from the above that the newton is a comparatively small force, equaling

approximately one-fifth of a pound. A kilonewton (1000 newtons), which

will be used often, is about 200 Ib. In this text, we shall nor use the kilogram

as a unit of force. However, you should he aware that many people do."

Note that at the earth's surface the weight W o1a mass M is:

W(newtons) = [M(kilograms)](Y.81)(m/s2) (1.9)

Hence:

W(newtons) M(kilograms) = ____~~~~

9.81 (rnls') (1.10)

Away from the earth's surfxe, use the acceleration of gravity x rather than

9.81 in the above equations...

However, we do have another k

ind of problem-that the kilogram is unfortu￾nately also used as a measure of force, as is the newton. One kilogram of

force is the weight of 1 kilogram of mass at the earth‘s surface, where the

acceleration of gravity (Le., the acceleration due to the force of gravity) is......

    To.be continue:-

     

STEVE WAUGH .......(the spirit of Indian cricket 🏏).. 🥰🏏🔥

This is a book created by Steve Waugh AO, former Australian

Cricket Captain – about his passion for India, photography and

of course cricket. It’s been a labour of love which has taken him

eighteen months. The first edition, a large format photo book,

The Spirit of Cricket – India will be released on November 1.

Steve’s first visit to India was in 1986, as a member of the touring

Australian Cricket Team. He recalled being overwhelmed by the

absolute and complete bombardment of his senses. From the

secluded comfort of the team bus he witnessed through the

window the constant stream of unfolding scenarios, as if he was

in a movie back lot full of different plots, actors and colour filled

backdrops.

He craved to get out on the streets and laneways, meet the locals

and see how they interacted with each other and photograph

their fascinating daily activities.

However with fame and adulation it wasn’t realistic to stop the

team bus, alight and endeavour to capture all the unfolding

scenarios that were in front of him.

That’s where the concept of The Spirit of Cricket originated

from. It was a passionate desire to get out amongst the people

of India, to finally capture all the emotion and splendour through

the lens of his trusty CANON camera....In January 2020, Steve travelled through India again, over 18

days, meeting many new and old friends. He spent time in

the Maidans in Mumbai, and the backstreets of Kolkata and

Jodhpur, and stopped regularly to enjoy the local roadside

matches along the way. He also trekked out in the desert in

Rajasthan to discover a game of cricket, and into the foothills of

the Himalayas to meet a team of cricketing monks.

Steve toured a bat and ball Factory, played cricket with kids

by the river, and was clean bowled on the beach at Juhu. He

met blind and physically challenged cricketers who totally

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Dharamshala. He found the opportunity to meet the oldest and

the very youngest of players, and play cricket with a Maharajah

in his classical Palace ballroom.

On this book, Steve said “I have chosen 220 photographs from

the tens of thousands I captured, and now, with this new book,

proudly share and celebrate my collection with you. I hope I have

done the people of India justice with the showcased images,

and my quest to capture the very essence and “spirit” of the

game and the passion of the people who love it.             ”“Attitude, energy, enthusiasm and imagination,

that’s all you need besides a bat an ball.”.          “Imagination can

inspire the champions

       

of tomorrow.”