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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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1.1 Engineering & Mechanics
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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1.1 Engineering & Mechanics
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)
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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.
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1.2 Learning Mechanics
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?
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1.2 Learning Mechanics
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.
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1.2 Learning Mechanics
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
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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
digits)tsignifican(33.14
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1.3 Fundamental Concepts
Numbers:Rounding off:
E.g.
digits)tsignifican(63.14159
digits)tsignifican(33.14
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1.3 Fundamental Concepts
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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1.3 Fundamental Concepts
Space & Time:Time:
Measured by the intervals between
repeatable events.SI unit & U.S. Customary unit of time:
second (s)
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1.3 Fundamental Concepts
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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1.3 Fundamental Concepts
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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1.3 Fundamental Concepts
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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1.3 Fundamental Concepts
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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1.3 Fundamental Concepts
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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1.3 Fundamental Concepts
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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1.3 Fundamental Concepts
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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1.3 Fundamental Concepts
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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1.3 Fundamental Concepts
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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1.3 Fundamental Concepts
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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1.4 Newtonian Gravitation
Gravitational force between a particle of massm1 & a homogenous sphere of mass m2 is alsogiven by Eq. (1.1)
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1.4 Newtonian Gravitation
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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1.4 Newtonian Gravitation
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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