introduction to engineering mechanics

Introduction to

APPLIED MECHANIC

Sby

RAMESH CH. PANDA

APME101: APPLIED MECHANICS

L: 4 T: 0 P: 2

Course Objective:•To make the awareness to the

students about the basic concepts of mechanics

•To understand examines the response of bodies or systems of bodies to external forces

To bridges the gap between physical theory and its application to technology.

Introduction: Concept and Definition of Engineering Mechanics, Types of Mechanics, Application of engineering mechanics in practical fields. Definition of Applied Mechanics. Definition, basic quantities and derived quantities of basic units and derived units. Different systems of units (FPS, CGS, MKS and SI) and their conversion from one system to another system. Concept of rigid body, scalar and vector quantities.

Laws of Forces: Definition, measurement, representation, types of forces, effects and characteristics of a force. Different force systems (coplanar and non-coplanar), principle of transmissibility of forces, law of super-position. Composition and resolution of coplanar concurrent forces, resultant force, laws of forces-Triangle law of forces, Polygon law of forces, Parallelogram law of forces. Free body diagrams, concept of Lami’s Theorem.

Friction: Definition and concept of friction, types of friction, force of friction. Laws of static friction, coefficient of friction, angle of friction, angle of repose, cone of friction. Equilibrium of a body lying on a horizontal plane and rough inclined plane. Calculation of least force required to maintain equilibrium of a body on a rough inclined plane subjected to a force: a) Acting along the inclined plane horizontally b) At some angle with the inclined plane.

Moment: Concept of moment, Varignon’s theorem. Principle of moments - application of moments to simple mechanisms, parallel forces-like and unlike parallel forces, calculation of their resultant, concept of couple, properties and effect, general cases of coplanar force system, general conditions of equilibrium of bodies under coplanar forces.

Center of Gravity: Concept of gravity, gravitational force, centroid and centre of gravity. Centroid for regular lamina and centre of gravity for regular solids. Position of centre of gravity of compound bodies and centroid of composite area. CG of bodies with portions removed.

Moment of Inertia: Concept of moment of inertia and second moment of area and radius of gyration, theorems of parallel and perpendicular axis, second moment of area of common geometrical sections: rectangle, triangle, circle. Second moment of area for L, T and I sections, section modulus.

Simple Machine: Concept of machine, mechanical advantage, velocity ratio and efficiency of a machine, their relationship, law of machine, simple machines (lever, wheel and axle, pulleys, jack winch crab inclined plane, worm and worm wheel only) ideal machine and effect of friction in machines.

Science ?

sciencemay be defined as the growth

of ideas through observation and experimentation

Applied Science?

The branch of science, which co ordinates the research work, for practical utility and services of the mankind, is known as Applied Science.

Engineering?

Engineering is the application of mathematics, empirical evidence and scientific, economic, social, and practical knowledge in order to invent, innovate, design, build, maintain, research, and improve structures, machines, tools, systems, components, materials, processes and organizations.

Mechanics?

The branch of applied physics dealing with motion and forces

producing motion.OR

Mechanics is the science which describes and predicts the

conditions of rest or motion of bodies under the action of forces

mechanicsMechanics is an area of science

concerned with the behavior of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment.

Applied mechanics ?

Applied mechanics is a branch of the physical sciences and the practical application of mechanics. Applied mechanics describes the response of bodies (solids and fluids) or systems of bodies to external forces.

STATICS

It is that branch of Engineering Mechanics, which deals with the forces and their effects, while acting upon the bodies at rest.

DYNAMICS

It is that branch of Engineering Mechanics, which deals with the forces and their effects, whileacting upon the bodies in motion.

The subject of Dynamics may be further sub-divided into the

following two branches :1. Kinetics, and 2. Kinematics.

KINETICS

It is the branch of Dynamics, which deals with the bodies in motion due to the applicationof forces.

KINEMATICS It is that branch of Dynamics,

which deals with the bodies in motion, without any reference to the forces which are responsible for the motion.

Eng. Malek AbuwardaLecture 1 Engineering Mechanics – Statics23

Basic Terms Essential basic terms to be understood

Rigid body: the relative movement between its parts are negligibleDynamics: dealing with a rigid-body in motionLength: applied to the linear dimension of a strait line or curved lineArea: the two dimensional size of shape or surfaceVolume: the three dimensional size of the space occupied by substance

Force: the action of one body on another whether it’s a push or a pull force

Mass: the amount of matter in a body

Weight: the force with which a body is attracted toward the centre of the Earth

Particle: a body of negligible dimension

© 2007 The McGraw-Hill Companies, Inc. All rights reserved.

Vector Mechanics for Engineers: Statics

EighthEdition

Triangle Law of Vectors

• Triangle Law of Vectors states that if two vectors are represented as adjacent sides of a triangle then the third side taken in opposite order is the resultant of the two. This law is used to find the resultant of two vector which gives both magnitude and direction

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Vector Mechanics for Engineers: Statics

EighthEdition

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Vector Mechanics for Engineers: Statics

EighthEdition

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Vector Mechanics for Engineers: Statics

EighthEdition

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Vector Mechanics for Engineers: Statics

EighthEdition

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Vector Mechanics for Engineers: Statics

EighthEdition

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Vector Mechanics for Engineers: Statics

EighthEdition

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Vector Mechanics for Engineers: Statics

EighthEdition

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Vector Mechanics for Engineers: Statics

EighthEdition

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Vector Mechanics for Engineers: Statics

EighthEdition

newton's second law of motion

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Vector Mechanics for Engineers: Statics

EighthEdition

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Vector Mechanics for Engineers: Statics

EighthEdition

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Vector Mechanics for Engineers: Statics

EighthEdition

newton's third law of motion

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Vector Mechanics for Engineers: Statics

EighthEdition

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Vector Mechanics for Engineers: Statics

EighthEdition

newton's third law of gravity

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Vector Mechanics for Engineers: Statics

EighthEdition

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Free-Body Diagrams:• Free-Body Diagrams:

Create separate diagrams for each of the bodies involved with a clear indication of all forces acting on each body.

•

Major topics of applied mechanics

Archimedes of Syracuse

Omar Khayyám

Galileo Galilei

Johannes Kepler

Isaac Newton

Classification of mechanics

1. Classical mechanics2. Quantum mechanics

Classical mechanicsNewtonian mechanics- theory of motion

Analytical mechanics- system energyHamiltonian- mechanics-conservation of energy

Lagrangian mechanics- principle of the least action.

Classical statistical mechanics-thermodynamic

Celestial mechanics- galaxies

Astrodynamics-spacecraft 

Solid mechanics elasticity

Classical mechanics Acoustics Statics Fluid mechanics, Soil mechanics Continuum mechanics Hydraulics Fluid statics, Applied mechanics or Engineering

mechanics Biomechanics

Classical mechanicsBiophysicsRelativistic/ Einsteinian mechanics

Quantum mechanics Schrödinger wave mechanics-wavefunction of a

single particle

Matrix mechanics-finite-dimensional state space

Quantum statistical mechanics-Particle physics-Nuclear physicsCondensed matter physics

UNITS1. FUNDAMENTAL UNITS2. DERIVED UNITS

FUNDAMENTAL UNITS

DERIVED UNITS

SYSTEMS OF UNITS1. C.G.S. units -Centimetre–gram–second

system of units 2. F.P.S. units -Foot–pound–second system 

3. M.K.S. units- metre, kilogram, and/or second

4. S.I. units (INTERNATIONAL SYSTEM OF UNITS)

S.I. units (INTERNATIONAL SYSTEM OF UNITS)

a system of physical units ( SI units ) based on the metre, kilogram, second, ampere, kelvin, candela, and mole, together with a set of prefixes to indicate multiplication or division by a power of ten.

S.I. UNITS (INTERNATIONAL SYSTEM

OF UNITS)

Dimensions500.101 SI Primitives

DIMENSION UNIT SYMBOL for UNIT

Length meter m

Mass kilogram kg

Time second s

Elec. Current ampere A

luminous intensity candela cd

amount of substance mole mol

Dimensions500.101 SI Derived units

DESCRIPTION DERIVED UNIT SYMBOL DIMENSION

Force newton N mkg/s2

Energy joule J m2kg/s2

Pressure pascal Pa kg/(ms2)

Power watt W m2kg/s3

SI Unit Prefixes - Part IName Symbol Factor

tera- T 1012

giga- G 109

mega- M 106

kilo- k 103

hecto- h 102

deka- da 101

SI Unit Prefixes- Part II

Name Symbol Factordeci- d 10-1

centi- c 10-2

milli- m 10-3

micro- μ 10-6

nano- n 10-9

pico- p 10-12

femto- f 10-15

The Seven Base SI UnitsQuantity Unit SymbolLength meter mMass kilogram kgTemperature kelvin KTime second sAmount of Substance

mole mol

Luminous Intensity candela cdElectric Current ampere a

Derived SI Units (examples)Quantity unit Symbol

Volume cubic meter m3

Density kilograms per cubic meter

kg/m3

Speed meter per second m/s

Newton kg m/ s2 N

Energy Joule (kg m2/s2) J

Pressure Pascal (kg/(ms2) Pa

Scientific Notation

M x 10n

• M is the coefficient • 10 is the base• n is the exponent or power of 10

Factor-Label Method of Unit Conversion

• Example: Convert 5km to m:• Multiply the original measurement by a

conversion factor.

NEW UNIT85km x 1,000m = 85,000m

1km OLD UNIT

Factor-Label Method of Unit Conversion: Example

• Example: Convert 789m to km:

789m x 1km =0.789km= 7.89x10-1km

1000m

Convert 75.00 km/h to m/s 75.00 km x 1000 m x 1 h___ = 20.83m/s h 1 km 3600 s

Standard prefixes for the SI units of measure

USEFUL DATA

TRIGONOMETRY

RULES FOR S.I. UNITS

standard abberviations

TRIGONOMETRY

INTEGRAL CALCULUS

SCALAR QUANTITIESThe scalar quantities (or

sometimes known as scalars) are those quantities which have magnitude

only such as length, mass, time, distance, volume, density, temperature, speed etc.

VECTOR QUANTITIES

1. Unit vector. A vector, whose magnitude is unity,is known as unit vector.

2. Equal vectors. The vectors, which are parallel to each other and have same direction (i.e.,

same sense) and equal magnitude are known as equal vectors. 3. Like vectors. The vectors, which are parallel to each other and have

same sense but unequal magnitude, are known as like vectors.

Example 1Two forces of 100 N and 150 N are

acting simultaneously at a point. What is the resultant of these two forces, if the angle between them is 45°?

Example 2.

Two forces act at an angle of 120°. The bigger force is of 40 N and theresultant is perpendicular to the smaller one. Find the smaller force.