APPLIED MECHANICS (1).ppt

Newton’s first law of motion
 Newton’s first law of motion states that ” A body
continues its state of rest or of uniform motion in a
straight line provided no net force acts on it.
Newton’s 1st law of motion deals with the inertial
property of matter, therefore, newton’s 1st law of
motion is known as the law of inertia.

Newton’s first law of motion

Newton’s second law of
motion
 The acceleration of an object as produced by a
net force is directly proportional to the
magnitude of the net force, in the same
direction as the net force, and inversely
proportional to the mass of the object.

Newton’s second law of
motion

Newton’s third law of motion
 Newton's third law: If an object A exerts a force on
object B, then object B must exert a force of equal
magnitude and opposite direction back on object A.
This law represents a certain symmetry in nature:
forces always occur in pairs, and one body cannot
exert a force on another without experiencing a force
itself. States that for every action (force) in nature
there is an equal and opposite reaction.

Newton’s third law of motion

Newton’s law of Gravity
 Newton's law of gravitation, statement that any
particle of matter in the universe attracts any other
with a force varying directly as the product of the
masses and inversely as the square of the distance
between them.

SYLLABUS
 Section I
 Unit 1: Fundamentals of Statics
 Basic Concepts and Fundamental Laws, Force, Moment and Couple, System of Forces,
Resultant, Resolution and Composition of Forces, Varignon’s Theorem, Law of Moments.
 Unit 2: Equilibrium
 Lami s’ Theorem, Free Body Diagram, Equilibrium of Forces, Equilibrium conditions,
Surface friction for bodies on horizontal and inclined planes. Beams: Types of Loads,
Types of supports, Analysis of Simple beams, Virtual work method for support reactions.
 Unit 3: Centroid and Moment of Inertia
 Centroid and Center of Gravity, Moment of Inertia of Standard shapes from first
principle, Parallel and perpendicular axis theorem, Moment of Inertia of plain and
composite figures, Radius of Gyration

SYLLABUS
 Section II
 Unit 4: Kinetics of Linear
 Introduction to Kinematics of Linear motion (no numerical on
kinematics), Kinetics of linear motion, Newton’s Laws, De’Alembert’s
Principle, Work- Energy Principle, Impulse Momentum Principle
 Unit 5: Kinetics of Circular Motion
 Introduction to Kinematics of Circular motion (no numerical on
kinematics), Rotation with constant and variable angular acceleration,
centripetal and centrifugal force, condition of skidding and overturning.
 Unit 6: Impact and Collision
 Impact, Types of Impact, Law of conservation of Momentum,
Coefficient of Restitution, Numerical on Direct central Impact.

 Reference Books
 1.Engineering Mechanics by S. S. Bhavikattis, New Age International Pvt. Ltd.
 2.Engineering Mechanics by R. K. Bansal and Sanjay Bansal.
 3.Vector Mechanics for Engineers Vol.I and II by F. P. Beer and E. R. Johnston, Tata Mc-Graw Hill
Publication.
 4.Engineering Mechanics by Manoj K Harbola, Cengage Learning
 5.Engineering Mechanics by K. I. Kumar, Tata Mc-Graw Hill Publication
 6.Engineering Mechanics by S. B. Junnerkar.
 7.Engineering Mechanics by Irving H. Shames, Prentice Hall of India, New Delhi.
 8.Applied Mechanics by S. N. Saluja, Satya Prakashan, New Delhi.
 9.Engineering Mechanics by Statics and Dynamics by Ferdinand Singer, Harper and Row Publications
 10.Engineering Mechanics by R. S. Khurmi, S. Chand Publications
 11.Fundamentals of Engineering Mechanics by S. Rajasekaran, G.Sankarasubramanian,Vikas
Publishing House
 12) “Applied Mechanics- Dynamics &Statics ” by I. B. Prasad, Khanna Publisher, Delhi

Reference Books
 1.Engineering Mechanics by S. S. Bhavikattis, New Age International Pvt. Ltd.
 2.Engineering Mechanics by R. K. Bansal and Sanjay Bansal.
 3.Vector Mechanics for Engineers Vol.I and II by F. P. Beer and E. R. Johnston,
Tata Mc-Graw Hill Publication.
 4.Engineering Mechanics by Manoj K Harbola, Cengage Learning
 5.Engineering Mechanics by K. I. Kumar, Tata Mc-Graw Hill Publication
 6.Engineering Mechanics by S. B. Junnerkar.
 7.Engineering Mechanics by Irving H. Shames, Prentice Hall of India, New
Delhi.
 8.Applied Mechanics by S. N. Saluja, Satya Prakashan, New Delhi.
 9.Engineering Mechanics by Statics and Dynamics by Ferdinand Singer, Harper
and Row Publications
 10.Engineering Mechanics by R. S. Khurmi, S. Chand Publications
 11.Fundamentals of Engineering Mechanics by S. Rajasekaran,
G.Sankarasubramanian,Vikas Publishing House
 12) “Applied Mechanics- Dynamics &Statics ” by I. B. Prasad, Khanna
Publisher, Delhi

Engineering
mechanics
Mechanics
of Solids
Mechanics
of rigid
bodies
Mechanics
of Deformed
bodies
Mechanics
of Fluids
Ideal fluid

Define
 Engineering : is science which is brought into practise by research
for development of mankind.
 Applied Mechanics: is branch of engineering which deals with
Force & their effects while acting upon the body at rest & in
motion.
 Statics : is branch of Applied Mechanics which deals with Force &
their effects while acting upon the body at rest.
 Dynamics : is branch of Applied Mechanics which deals with Force
& their effects while acting upon the body in motion.

Define
 Kinematics : is branch of Dynamics which deals with Force
& their effects while acting upon the body in motion without
referring Force causing motion .
 Kinetics : is branch of Dynamics which deals with Force &
their effects while acting upon the body in motion referring
Force causing motion .
 Mass : The quantity of matter possessed by a body is called
mass.
 Space : The geometric region in which study of body is done
is called space.
 Particle : A particle may be defined as an object which has
only mass & no size.
 Rigid bodies : A body is said to be rigid if the relative
position of particle in it do not change under the action of
Forces.

Laws of Mechanics
 Newton’s first law
 Newton’s second law
 Newton’s third law
 Newton’s law of gravitational
 Law of Transmissibility of Force
 Parallelogram law of Forces

Newton’s first law
 It states that every body continues in its state of rest or
of uniform motion in a straight line unless it is
compelled by an external agency acting on it.
 Force: as the external agency which changes or tends to
change the state of rest or uniform motion of the body.

Newton’s second law
 It states that the rate of change of momentum of a body
is directly proportional to the impressed Force & it takes
place in the direction of the Force acting on it.

Characteristics of a Force
 Magnitude
 Point of Application
 Line of action
 Direction

 Sign Convention For Force

Newton’s third law
 It states that for every action there is an equal &
opposite reaction

Newton’s law of gravitational
 The Force of attraction between any two bodies is
directly proportional to their masses & inversely
proportional to the square of the distance between them.

Law of Transmissibility of Force
 The state of rest or motion of the rigid body is
unaltered if a Force acting on the body is replaced
by another Force of the same magnitude &
direction but acting anywhere on the body along
the line of action of the replaced Force.

Parallelogram law of Forces
 If two Forces acting simultaneously on a body at a point
are represented in magnitude & direction by the two
adjacent sides of a parallelogram, their resultant is
represented in magnitude & direction by the diagonal of
the parallelogram which passes through the point of
intersection of the two sides representing the Forces.

System of Forces
 When in a problem more than one Force acting, it
is known as Force system or system of Forces

System of Forces
System of
Forces
Coplanar
Collinear
Parallel
Concurrent
Non
concurrent
Non
coplanar
Parallel
Concurrent
Non
concurrent

System of Forces
 Coplanar Forces
 When the lines of action of a set of forces lie in a single plane is
called coplanar force system.

System of Forces
 Non Coplanar Forces
 When the line of action of all the forces do not lie in one
plane, is called Non-coplanar force system

System of Forces
 Collinear Forces
 When the lines of action of all the forces of a system act along the
same line, this force system is called collinear force system.

System of Forces
 Coplanar Parallel Force System
 When the lines of action of a set of forces lie in a single plane
& parallel.
 All forces lie in same plane, parallel & in same direction.

System of Forces
 Coplanar Concurrent Force System
 A force system in which all the forces lie in a single plane and
meet at one point

System of Forces
 Coplanar Non Concurrent Force System
 The forces do not meet at a common point however, they lie
in a single plane.

System of Forces
 Non Coplanar Parallel Force System
 In this system, the forces lie in a different planes but parallel.

System of Forces
 Non Coplanar Concurrent Force System
 In this system, the forces lie in a different planes but pass
through a single point.

System of Forces
 Non Coplanar Non Concurrent Force System
 The forces which do not lie in a single plane and do not pass
through a single point are known as non-coplanar and non-
concurrent forces.

Resultant Forces
 A single Force which will have the same effect as that of
number of Forces acting such single Force is called
Resultant.
 The process of finding Resultant is called composition of
Forces.

Composition Of Forces
 Consider two Forces F1 & F2 are acting on a particle as shown
in figure. Let angle between two Forces is ϴ .
 If parallelogram is drawn AB will represent Force F2 & AD
will represent Force F1 than according to law of parallelogram
of Forces AC represent Resultant

Resolution of Forces
 The Resolution of Forces is exactly opposite process
of composition of Forces. It is the process of finding
number of component Forces which will have same
effect as that of single Force.

General Method of Composition of
Forces
 The method explain to find Resultant of number of Forces acting
on a body.

Step 1 Resolution of Forces in
Mutual perpendicular direction

Step 2 Add sum of Forces in
Mutual perpendicular direction

Step 3 We get two
component Forces

Graphically method to find
Resultant

TO FIND RESULTANT FOR
COPLANAR CONCURRENT
FORCE SYSTEM

To Find Resultant of given Force
System

Problem
 A system of four Forces acting on a body as shown in figure, find
the resultant

Two Forces acting on a body are 500N & 1000N as shown in
figure. Determine the third Force F such that the Resultant of all
the three Forces is 1000N directed at 45 degree to x axis

The resultant of two forces, one of which is double the other is 260
N. If the direction of the larger Force is reversed & the other
remains unaltered, the resultant reduces to 180N. Determine the
magnitude of the Forces & the angle between the Forces

Two forces 100KN & 200KN act on a particle & their lines of
action are inclined to each other at an angle of 40o . Find their
resultant in magnitude & direction

A system of Forces acting on a body resting on an inclined plane is as shown in
figure. Determine the resultant Force if ϴ =60, W = 1000N, vertically downward,
N=500N acting normal to the plane, F=100N, acting down the plane & T=1200N, acting
parallel to plane?

RESULTANT OF SYSTEM OF COPLANAR NON CONCURRENT FORCES

MOMENT
 Moment is the rotation effect of Force
 Moment of a Force about a point is defined as the
product of the magnitude of the Force & the
perpendicular distance of the point from the line of action
of the Force.
 The point about which the moment is considered is
called moment centre.
 The perpendicular distance of the point from the line of
action of the Force is called moment arm.

Couple
 Two parallel Forces equal in magnitude & opposite in
direction & separated by a definite distance are said to
form a couple.

Properties of a couple
 A couple consists of a pair of equal & opposite parallel Forces which are
separated by a definite distance.
 The translatory effect of a couple on the body is zero.
 The rotational effect of a couple about any point is a constant & it is equal to
the product of the magnitude of the Forces & the perpendicular distance
between the two Forces.

Varignon’s Theorem
 The algebraic sum of moments of a system of coplanar Forces about
a moment centre is equal to the moment of their resultant forces
about the same moment centre.

For the Force system acting on body OABC as shown in fig calculate the
magnitude & direction of Resultant Forces also determine i)Distance of resultant
from point ‘o’ ii) Point where resultant meets x axis & y axis

Find the Resultant of the Force system shown in fig acting
on a lamina of equilateral triangular shape

Determine the Resultant of the system of Forces acting
on a beam as shown in figure

Find resultant for the force system shown in figure &
locate it with respect to ‘A’

The Law of Polygon of Forces
 if any number of coplanar concurrent forces can be represented in
magnitude and direction by the sides of a polygon taken in order; then their
resultant will be represented by the closing side of the polygon taken in
opposite order”.

TRIANGLE LAW OF FORCES:
 It states that if two concurrent forces are acting simultaneously on a
body and are represented in magnitude and direction by the sides of a
triangle taken in order, then the third side of the triangle represents their
resultant of the forces in magnitude and direction taken in opposite
order.

Equilibrium of Forces
 A body is said to be in equilibrium if its state of rest or of
uniform motion in a straight line is not altered.
 It means no resultant Force acts on the body.
 Equation of Equilibrium
 Graphical Condition of Equilibrium. The "graphical
condition of equilibrium" for a system of concurrent
forces is that the polygon for the forces must close. For if
the polygon closes, then the resultant equals zero .

Free Body Diagram
 The diagram of a body in which the body under consideration
is freed from all contact surfaces & is shown with all the
Forces on it is called Free Body Diagram

Lami’s Theorem
 Lami's Theorem states, “When three forces acting at a point
are in equilibrium, then each force is proportional to the sine
of the angle between the other two forces”.

Determine the horizontal Force F to be applied to the block
weighing 1500N to hold it in position on a smooth inclined plane
AB which makes an angle of 30 degree with the horizontal?

A 200N sphere is resting as shown in figure. Determine the
reaction developed at contact surfaces. Assume all contact
surfaces are smooth

A system of connected flexible cables shown in fig is supporting two
vertical forces 200N & 250N at points B & D. Determine the Forces in
various segments of the cable?

Friction Force
 Friction is the force that resists motion when the surface of one object
comes in contact with the surface of another
 Limiting friction occurs when the moving force and the force opposing
motion are equal, any addition to the moving force will cause slipping.
 When the force acting on the body is less than the limiting friction, then
the body remains at rest. The friction now acting between the
surfaces of contact is statics friction
 When the force acting on the body is greater than the limiting friction,
then the body comes into motion. The friction now acting between the
surfaces of contact is dynamic friction. The dynamic friction is always
less than the limiting friction.

Laws of Friction
• The friction force acts in a direction opposite to that in which body
tends to move.
• The friction experienced by the object is dependent on the nature of
the surface it is in contact with.
• Friction is independent of the area of contact as long as there is an
area of contact
• Till the limiting value is reached the magnitude of friction is exactly
equal to the force which tends to move the body.
• After the body starts moving the dynamic friction comes into play
the magnitude of which is less than that of limiting friction.

Friction Force
 Coefficient of Friction: The magnitude of limiting Friction bears a
constant ratio to the normal reaction between the two surface & this
ratio is called Coefficient of Friction.

Angle of Friction
 The angle between the resultant reaction & the normal to the plane
on which the motion of the body is impending.

Angle of Repose
 The maximum angle at which an object can rest on an inclined
plane without sliding down.

Cone of Friction
 The inverted cone with semi central angle equal to limiting frictional
angle is called cone of Friction

A block weighing 500N just starts moving down a rough inclined plane
when supported by a force of 200N acting parallel to the plane in upward
direction. The same block is on the verge of moving up the plane when
pulled by a Force of 300N acting parallel to the plane. Find the inclination
of the plane & coefficient of friction between the inclined plane & block

Determine the reaction at A & B for the given loading shown in fig

Find the reaction for the Cantilever Beam shown in fig

Find the reaction for the given beam at A & B

Virtual Work Method
 Work done by a Body

Virtual Work Method
 A small displacement given to the body is in equilibrium then the
total work done by the system should be zero. This approach is
called Virtual work method
 Sign convention

Determine the reaction developed in the simply supported beam
as shown in fig by virtual work method

Determine the reaction developed in the simply supported
beam as shown in fig by virtual work method

Centroid & Moment of Inertia
 Centroid:- The point at which the total area of a plane figure is
assumed to be concentrated is known as centroid.
 Centre of Gravity:- Centre of gravity of a body is the point through
which the whole weight of the body is assumed to be concentrated is
known as Centre of Gravity

Centroid axis or Axis of symmetry

Determination of centroid of simple figure from First Principle

Centroid of some common figure
Shape Figure x y Area
Square
Rectangle
Circle
Half circle
Quarter circle
Traingle

Find the Centroid of the given Figure

Moment of Inertia
 The product of the area & the square of the distance of the centroid
of the area from an axis is known as Moment of Inertia of the area
about that axis.

Radius of Gyration
 Radius of Gyration of a area about an axis is a distance such that its
square multiplied by the area gives moment of Inertia of the area about
the given axis.

Moment of Inertia of Rectangle from First Principle

Moment of Inertia of standard figures

Parallel axis theorem
 The moment of inertia of a body about an axis parallel to the body
passing through its centre is equal to the sum of moment of inertia of
the body about the axis passing through the centre and product of the
area of the body times the square of the distance between the two
axes.

Perpendicular axis theorem
 For any plane body the moment of inertia about any of its axes which
are perpendicular to the plane is equal to the sum of the moment of
inertia about any two perpendicular axes in the plane of the body
which intersect the first axis in the plane.

Find Moment of Inertia of I section having flange width
160mm, depth of flange 10mm, width of web 10mm & depth
of web 220mm about Horizontal centroidal axis?

Find Moment of Inertia of given figure about Horizontal
Centroidal axis

Find moment of inertia about the base for the following composite
section

Find moment of inertia about horizontal & vertical centroidal
axis for the given figure

Collision of Elastic Bodies
 Elastic Bodies : A body which regains its original state completely on
removal of the deforming force is called perfectly elastic.
 Plastic Bodies : A body which does not regains its original state
completely on removal of the deforming force is called perfectly
plastic.
 Line of Impact : It is the common normal to the surface of contact
between the colliding bodies is called line of Impact.

Collision Bodies
 Elastic Collision
An elastic collision is one where there is no net loss in kinetic energy in the system due to the
collision.
 Inelastic Collision
An inelastic collision is a type of collision where this is a loss of kinetic energy. The lost kinetic
energy is transformed into thermal energy, sound energy, and material deformation.

Types of Impact
 Direct Impact
 Oblique Impact
 Central Impact
 Eccentric Impact

Direct Impact
 If the velocities of colliding bodies are directed along the line of
Impact than it is called Direct Impact.

Oblique Impact
 If the velocities of colliding bodies are not directed along the line of
Impact than it is called Oblique Impact.

Central Impact
 If the mass centres of the colliding bodies are directed
along the line of Impact than it is called Central Impact

Eccentric Impact
 If the mass centres of the colliding bodies are not directed along the
line of Impact than it is called Eccentric Impact

Law of Conservation Of Momentum

Loss of Energy
 Loss of Kinetic Energy

Two balls of masses 2kg & 3kg are moving with velocities 2m/s
& 3m/s towards each other. If the coefficient of restitution is 0.5,
find the velocity of the two balls after impact

Two balls of masses 2kg & 3kg are moving with velocities
2m/s & 3m/s moving in same direction. If the coefficient of
restitution is 0.5, find the velocity of the two balls after
impact

A ball is dropped from a height of 10m on a fixed horizontal
floor to what height it will rebound on its first second & third
bounce given e=0.75?

A ball dropped from a height of 1.6m is observed to rebound
to a height of 1.10m from the horizontal floor. Determine
coefficient of restitution & the % of energy loss during impact

A heavy elastic ball drops from the ceiling of a room & after
rebounding twice from the floor reaches a height of equal to
one half of the ceiling. Find the coefficient of restitution?

A vehicle of mass 800Kg & moving with a velocity of 12m/s
strikes another vehicle of mass 500Kg moving with 9m/s in
the same direction. Both the vehicle get coupled together due
to impact. Find the common velocity with which the two
vehicles will move?

Newton's Laws Of Rotational
Motion
 Newton's First Law for Rotation an object at rest tends to remain
at rest, and an object that is spinning tends to spin with a
constant angular velocity, unless it is acted on by a nonzero net
torque.
 Newton’s Second Law for Rotation The rate of change of angular
momentum of a body is directly proportional to the impressed
torque & takes place in the same direction in which torque acts.
 Newton’s Third Law for Rotation To every torque there is always
& equal & opposite torque.
 A third law of rotational motion states that for every (centripetal)
force pulling inward toward the center of rotation, there is and
equal and opposite (centrifugal) force pushing outward toward
from the center of rotation.

Centripetal & Centrifugal Force
 Centripetal force is the component of force acting on an object in
curvilinear motion which is directed toward the axis of rotation or
center of curvature.

Centripetal & Centrifugal Force
 Centrifugal force is a force that arises from the body’s inertia and
appears to act on a body that is moving in a circular path which is
directed away from the centre around which the body is moving.

Centripetal & Centrifugal acceleration

Motion on a level circular road

CONDITION OF SKIDDING ON LEVEL ROAD

CONDITION OF OVERTURNING ON BANKED ROAD

CONDITION OF SKIDDING ON BANKED ROAD

An Automobile weighing 15KN moving at a speed of 54Km/hr traverse a
sag in the road the sag being part of a circle of radius 20m. Find the
reaction between the car & the road while travelling at the lowest point of
the sag?

A motor cycle is moving in a spherical cage of 3.6m radius in a
circus show. The mass of the motor cycle & the rider together is
240kg. What shall be the minimum speed with which the motor
cyclist can pass through the highest point without losing contact
inside the cage?

APPLIED MECHANICS (1).ppt

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