Introduction
to
APPLIED
MECHANIC
S
by
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
mechanics
 Mechanics
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.
Basic Terms
 Essential basic terms to be understood
Rigid body: the relative movement between its parts are negligible
Dynamics: dealing with a rigid-body in motion
Length: applied to the linear dimension of a strait line or curved line
Area: the two dimensional size of shape or surface
Volume: 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
23
Lecture 1
Engineering Mechanics – Statics
Eng. Malek Abuwarda
Eighth
Edition
Vector Mechanics for Engineers: Statics
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
© 2007 The McGraw-Hill Companies, Inc. All rights reserved.
1 - 24
Eighth
Edition
Vector Mechanics for Engineers: Statics
© 2007 The McGraw-Hill Companies, Inc. All rights reserved.
1 - 25
Eighth
Edition
Vector Mechanics for Engineers: Statics
© 2007 The McGraw-Hill Companies, Inc. All rights reserved.
1 - 26
Eighth
Edition
Vector Mechanics for Engineers: Statics
© 2007 The McGraw-Hill Companies, Inc. All rights reserved.
1 - 27
Eighth
Edition
Vector Mechanics for Engineers: Statics
© 2007 The McGraw-Hill Companies, Inc. All rights reserved.
1 - 28
Eighth
Edition
Vector Mechanics for Engineers: Statics
© 2007 The McGraw-Hill Companies, Inc. All rights reserved.
1 - 29
Eighth
Edition
Vector Mechanics for Engineers: Statics
© 2007 The McGraw-Hill Companies, Inc. All rights reserved.
1 - 30
Eighth
Edition
Vector Mechanics for Engineers: Statics
© 2007 The McGraw-Hill Companies, Inc. All rights reserved.
1 - 31
Eighth
Edition
Vector Mechanics for Engineers: Statics
© 2007 The McGraw-Hill Companies, Inc. All rights reserved.
1 - 32
Eighth
Edition
Vector Mechanics for Engineers: Statics
newton's second law of motion
© 2007 The McGraw-Hill Companies, Inc. All rights reserved.
1 - 33
Eighth
Edition
Vector Mechanics for Engineers: Statics
© 2007 The McGraw-Hill Companies, Inc. All rights reserved.
1 - 34
Eighth
Edition
Vector Mechanics for Engineers: Statics
© 2007 The McGraw-Hill Companies, Inc. All rights reserved.
1 - 35
Eighth
Edition
Vector Mechanics for Engineers: Statics
newton's third law of motion
© 2007 The McGraw-Hill Companies, Inc. All rights reserved.
1 - 36
Eighth
Edition
Vector Mechanics for Engineers: Statics
© 2007 The McGraw-Hill Companies, Inc. All rights reserved.
1 - 37
Eighth
Edition
Vector Mechanics for Engineers: Statics
newton's third law of gravity
© 2007 The McGraw-Hill Companies, Inc. All rights reserved.
1 - 38
Eighth
Edition
Vector Mechanics for Engineers: Statics
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.
•
© 2007 The McGraw-Hill Companies, Inc. All rights reserved.
1 - 39
Major topics of applied mechanics
Archimedes of Syracuse
Omar Khayyám
Galileo Galilei
Johannes Kepler
Isaac Newton
Classification of mechanics
 1.
Classical mechanics
 2. Quantum mechanics
Classical mechanics
 Newtonian
mechanics- theory of motion
 Analytical mechanics- system energy
 Hamiltonian- mechanics-conservation of energy
 Lagrangian mechanics- principle of the least action.
 Classical statistical mechanicsthermodynamic
 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 mechanics
 Biophysics
 Relativistic/
Einsteinian mechanics
Quantum mechanics
 Schrödinger
 Matrix
wave mechanics-
wavefunction of a single particle
mechanics-finite-dimensional state space
 Quantum statistical mechanics Particle physics Nuclear physics
 Condensed matter physics
UNITS
 1.
FUNDAMENTAL UNITS
 2. DERIVED UNITS
FUNDAMENTAL UNITS
DERIVED UNITS
SYSTEMS OF UNITS
 1.
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)
Dimensions
500.101
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
Dimensions
500.101
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 I
Name
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
Factor
deci-
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 Units
Quantity
Unit
Symbol
Length
meter
m
Mass
kilogram
kg
Temperature
kelvin
K
Time
second
s
Amount of
mole
Substance
Luminous Intensity candela
mol
Electric Current
a
ampere
cd
Derived SI Units (examples)
Quantity
unit
Symbol
Volume
cubic meter
m3
Density
Speed
kilograms per
kg/m3
cubic meter
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 10
n
• 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 UNIT
85km x 1,000m
1km
OLD UNIT
=
85,000m
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 QUANTITIES
 The
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 1
 Two
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 the
resultant is perpendicular to the smaller
one. Find the smaller force.