Lecture 1 Engg Mech

8/2/2019 Lecture 1 Engg Mech

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Engineering Mechanics

Instructor: Dr. M. Nasir Amin

(C) 2005 Pearson Education South Asia Pte Ltd 1

Introduction to Engineering Mechanics


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Chapter Outline

Engineering & Mechanics Learning Mechanics

Fundamental Concepts

Newtonian Gravitation Units


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Introduction

Mechanics is the physical science whichdeals with the effects of forces on objects

Main branches of mechanics are as following

Mechanics of rigid bodies

Mechanics of deformable bodies

Mechanics of rigid bodies


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Introduction

Designing & constructing devices:

Understand the physics underlying thedesigns.

Use mathematical models to predict theirbehaviour.

Learn how to analyze & predict the behaviors

of physical systems by studying mechanics.


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1.1 Engineering & Mechanics

Knowledge of previous designs,experiments, ingenuity & creativity todevelop new designs.

Develop mathematical equations based onthe physical characteristics of the devicedesigns:

Predict the behaviorModify the design

Test the design prior to actual construction


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Elementary Mechanics the study offorces & their effects

Statics the study of objects in equilibrium

Dynamics the study of objects in motion

Retrace historical development of ideas.


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Applications in many fields of engineering:

Statics: equilibrium equations

Designing structures (mechanical & civil)

Dynamics: motion equations

Analyze responses of buildings toearthquakes (civil)

Determine trajectories of satellites(aerospace)



1.2 Learning Mechanics

Problem solving procedures: Identify information given & information to be

determined. Restate the problem in your ownwords. Understand the physical system/modelinvolved.

Develop a strategy, i.e. identify the principles& equations that apply & decide how to use

them. Draw diagrams to help visualization.




Problem solving procedures:Try to predict the answer to develop intuition help to recognize an incorrect answer.

Solve the equations, interpret the results &compare with your prediction reality check

Is your answer reasonable?




Calculators & Computers:To solve algebraic expression in terms of

given quantities.

A calculator with trigonometric & logarithmicfunctions is sufficient.

Programmable calculator/computer withproblem-solving software such as Mathcad orMATHLAB is convenient.




Engineering Applications:Describes how mechanics is applied in

various fields of engineering.

Emphasis on 2 essential aspects ofengineering:

Design to choose parameters values tosatisfy stated design criteria

Safety to evaluate the safety of devicesand choose parameter values to satisfystated safety requirements



1.3 Fundamental Concepts

Numbers:Engineering measurements, calculations &

results

Significant Digits the number of meaningful(i.e. accurate) digits in a number, counting tothe right starting with the first nonzero digit:

E.g. 7.630 & 0.007630 (4 significant digits)

7630, 000 = 7.630 x 106

digits)tsignifican(63.14159





Numbers:Rounding off:

E.g.




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Space & Time:Space:

3-dimensional space & locations/positions

of points in space.Distance between 2 points in space =

length of the straight line joining them

SI unit of length: meter (m)U.S. Customary unit: foot (ft)


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Space & Time:Time:

Measured by the intervals between

repeatable events.SI unit & U.S. Customary unit of time:

second (s)


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Position of a point in space relative tosome reference point changes with time:

Rate of change of position = velocity

SI unit: meters per second (m/s)

U.S. Customary unit: feet per second (ft/s)

Rate of change of velocity = acceleration

SI unit: meters per second squared (m/s2)

U.S. Customary unit: feet per secondsquared (ft/s2)


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Six elementary fundamental principles

Parallelogram Law

Principle of Transmissibility

Newtons 1st Law of Motion

Newtons 2nd Law of Motion

Newtons 3rd Law of Motion

Newtons Law of Gravitation


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Parallelogram Law

Two forces acting on a particle can be replaced

by a single force, called their resultant

F1

F2F +F1 F2=


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Principle of Transmissibility

Motion of a rigid body will remain unchanged if

a force acting at a given point of the rigid bodyis replaced by a force of the same magnitude

and same direction, but acting at a different

point, provided that the two forces have the

same line of action


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Newtons 1st Law of Motion

When the sum of the forces acting on a

particle = 0, its velocity is constant. In particular, if the particle is initially

stationary, it will remain stationary.


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Newtons 2nd Law of Motion When the sum of the forces acting on a

particle is 0, the sum of forces is equal to

the rate of change of the linear momentum ofthe particle.

If the mass is constant, the sum of forces isequal to the product of the mass of the

particle & its acceleration.

F = m . a


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Newtons 3rd Law of Motion The mutual forces exerted by 2 particles on

each other are equal in magnitude & opposite

in direction. The particles remains in state ofequilibrium only if exerted forces on them arecollinear


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Force & mass are defined by the 2nd lawChoose an arbitrary object to have a unit mass

& define a unit force to be the force that gives

the unit mass an acceleration of unit magnitudeApply a unit force to the mass, measure the

resulting acceleration mass

SI unit: kilogram (kg)

U.S. Customary unit: slug


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Force & mass are defined by the 2nd law:Apply a force to the unit mass, measure the

resulting acceleration force

SI unit: newton (N)U.S. Customary unit: pound (lb)


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Limitations to the validity of Newtons Laws:Problems involving velocities that are not small

compared to the velocity of light (3 x 108 m/s)

Einsteins special theory of relativityPhenomena on the atomic scale Quantum

mechanics


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1.4 Newtonian Gravitation

Gravitational force between2 particles of mass m1 & m2that are separated by adistance r (Fig. 1.4) is:

1.12

21

r

mGmF

where G= universal gravitational constant


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Gravitational force between a particle of massm1 & a homogenous sphere of mass m2 is alsogiven by Eq. (1.1)


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Weight of an object of mass mdue to thegravitational attraction of the earth is approximatedby:

where mE= mass of earth,

r= distance from the center of earth to

the object

2.12r

GmmW E


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Weight of object at sea level (r = RE):

The value of gvaries from location to location onthe surface of the earth.

g= 9.81 m/s2 (SI units)

6.1mgW


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1.5 Units

International System of Units:

Base units:

Length: meters (m)

Mass: kilograms (kg)Time: second (s)

Derived Unit:

Expressed in terms of base unitsE.g. Force is measured in newtons (N)

22 m/skg1m/s1kg1N1


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1.5 Units

Prefixes:

E.g. 1 kg = 1000 g, 1 Mg = 106 g = 1000 kg


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1.5 Units

U.S. Customary Units:

Base units:

Length: feet (ft)

Force: pounds (lb)Time: second (s)

Derived Unit:

Mass: slug (the mass of materialaccelerated at 1 ft/s2 by a force of 1 lb)

Newtons 2nd law:

/ftslb1slug1

ft/s1slug1lb1

2

2


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1.5 Units

Angular Units:Angles are normally

expressed in radians (rad)

Defined to be the ratio of thepart of the circumferencesubtended by to the radiusof the circle

Angles are also expressed indegrees:

rad2360


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1.5 Units

Conversion of Units:Values must be expressed in terms of one

system of units before they are substitutedinto the equation


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1.5 Units

E.g. to express 1 mi/h in terms of ft/s:

ft/s1.47

s3600

h1

mi1

ft5280mi/h1mi/h1


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1.5 Units

Convert

(a) 60 miles/h to ft/sec

(b) 100 lb.ft/s2 to kg.m/s2(c) 20 slug/ft

3to kg/m

3

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Lecture 1 Engg Mech