Learn Online Courses of Subject Engineering Mechanics of First Year Engineering. Clear the Concepts of Engineering Mechanics Through Video Lectures and PDF Notes. Visit us: https://ekeeda.com/streamdetails/subject/Engineering-Mechanics
Learn Online Courses of Subject Engineering Mechanics of First Year Engineering. Clear the Concepts of Engineering Mechanics Through Video Lectures and PDF Notes. Visit us: https://ekeeda.com/streamdetails/subject/Engineering-Mechanics
Learn Online Courses of Subject Engineering Mechanics of First Year Engineering. Clear the Concepts of Engineering Mechanics Through Video Lectures and PDF Notes. Visit us: https://ekeeda.com/streamdetails/subject/Engineering-Mechanics
6-1 FRICTION
After reading this module, you should be able to . . .
6.01 Distinguish between friction in a static situation and a
kinetic situation.
6.03 For objects on horizontal, vertical, or inclined planes in
situations involving friction, draw free-body diagrams and
apply Newton’s second law.
6-2 THE DRAG FORCE AND TERMINAL SPEED
After reading this module, you should be able to . . .
6.04 Apply the relationship between the drag force on an
object moving through air and the speed of the object.
6.02 Determine direction and magnitude of a frictional force.
6.05 Determine the terminal speed of an object falling
through air.
6-3 UNIFORM CIRCULAR MOTION
After reading this module, you should be able to. . .
6.06 Sketch the path taken in uniform circular motion and
explain the velocity, acceleration, and force vectors
(magnitudes and directions) during the motion.
6.07 ldentify that unless there is a radially inward net force
(a centripetal force), an object cannot move in circular motion.
6.08 For a particle in uniform circular motion, apply the relationship between the radius of the path, the particle’s
speed and mass, and the net force acting on the particle. etc...
12-1 EQUILIBRIUM\
After reading this module, you should be able to . . .
12.01 Distinguish between equilibrium and static equilibrium.
12.02 Specify the four conditions for static equilibrium.
12.03 Explain center of gravity and how it relates to center of
mass.
12.04 For a given distribution of particles, calculate the coordinates of the center of gravity and the center of mass.
12-2 SOME EXAMPLES OF STATIC EQUILIBRIUM
After reading this module, you should be able to . . .
12.05 Apply the force and torque conditions for static
equilibrium.
12.06 Identify that a wise choice about the placement of the origin (about which to calculate torques) can simplify the
calculations by eliminating one or more unknown forces
from the torque equation.
12-3 ELASTICITY
After reading this module, you should be able to . . .
12.07 Explain what an indeterminate situation is.
12.08 For tension and compression, apply the equation that
relates stress to strain and Young’s modulus.
12.09 Distinguish between yield strength and ultimate strength.
12.10 For shearing, apply the equation that relates stress to
strain and the shear modulus.
12.11 For hydraulic stress, apply the equation that relates
fluid pressure to strain and the bulk modulus. etc...
Introduction to statics and its Applications in Real Life
countents
Introduction to statics
Force and Equilibrium
Structural Analysis
Friction
Centroid
Moments of Inertia
Learn Online Courses of Subject Engineering Mechanics of First Year Engineering. Clear the Concepts of Engineering Mechanics Through Video Lectures and PDF Notes. Visit us: https://ekeeda.com/streamdetails/subject/Engineering-Mechanics
Have a data in the form of required information in descriptive form.And learn to know how newtons's laws of motion are applicable in different phenomena-----------------------------'--'---'---'''''''-----------------------------------
6-1 FRICTION
After reading this module, you should be able to . . .
6.01 Distinguish between friction in a static situation and a
kinetic situation.
6.03 For objects on horizontal, vertical, or inclined planes in
situations involving friction, draw free-body diagrams and
apply Newton’s second law.
6-2 THE DRAG FORCE AND TERMINAL SPEED
After reading this module, you should be able to . . .
6.04 Apply the relationship between the drag force on an
object moving through air and the speed of the object.
6.02 Determine direction and magnitude of a frictional force.
6.05 Determine the terminal speed of an object falling
through air.
6-3 UNIFORM CIRCULAR MOTION
After reading this module, you should be able to. . .
6.06 Sketch the path taken in uniform circular motion and
explain the velocity, acceleration, and force vectors
(magnitudes and directions) during the motion.
6.07 ldentify that unless there is a radially inward net force
(a centripetal force), an object cannot move in circular motion.
6.08 For a particle in uniform circular motion, apply the relationship between the radius of the path, the particle’s
speed and mass, and the net force acting on the particle. etc...
12-1 EQUILIBRIUM\
After reading this module, you should be able to . . .
12.01 Distinguish between equilibrium and static equilibrium.
12.02 Specify the four conditions for static equilibrium.
12.03 Explain center of gravity and how it relates to center of
mass.
12.04 For a given distribution of particles, calculate the coordinates of the center of gravity and the center of mass.
12-2 SOME EXAMPLES OF STATIC EQUILIBRIUM
After reading this module, you should be able to . . .
12.05 Apply the force and torque conditions for static
equilibrium.
12.06 Identify that a wise choice about the placement of the origin (about which to calculate torques) can simplify the
calculations by eliminating one or more unknown forces
from the torque equation.
12-3 ELASTICITY
After reading this module, you should be able to . . .
12.07 Explain what an indeterminate situation is.
12.08 For tension and compression, apply the equation that
relates stress to strain and Young’s modulus.
12.09 Distinguish between yield strength and ultimate strength.
12.10 For shearing, apply the equation that relates stress to
strain and the shear modulus.
12.11 For hydraulic stress, apply the equation that relates
fluid pressure to strain and the bulk modulus. etc...
Introduction to statics and its Applications in Real Life
countents
Introduction to statics
Force and Equilibrium
Structural Analysis
Friction
Centroid
Moments of Inertia
Learn Online Courses of Subject Engineering Mechanics of First Year Engineering. Clear the Concepts of Engineering Mechanics Through Video Lectures and PDF Notes. Visit us: https://ekeeda.com/streamdetails/subject/Engineering-Mechanics
Have a data in the form of required information in descriptive form.And learn to know how newtons's laws of motion are applicable in different phenomena-----------------------------'--'---'---'''''''-----------------------------------
Ekeeda Provides Online Civil Engineering Degree Subjects Courses, Video Lectures for All Engineering Universities. Video Tutorials Covers Subjects of Mechanical Engineering Degree. Visit us: https://ekeeda.com/
5-1 NEWTON’S FIRST AND SECOND LAWS
After reading this module, you should be able to . . .
5.01 Identify that a force is a vector quantity and thus has
both magnitude and direction and also components.
5.02 Given two or more forces acting on the same particle,
add the forces as vectors to get the net force.
5.03 Identify Newton’s first and second laws of motion.
5.04 Identify inertial reference frames.
5.05 Sketch a free-body diagram for an object, showing the
object as a particle and drawing the forces acting on it as
vectors with their tails anchored on the particle.
5.06 Apply the relationship (Newton’s second law) between
the net force on an object, the mass of the object, and the
acceleration produced by the net force.
5.07 Identify that only external forces on an object can cause
the object to accelerate.
5-2 SOME PARTICULAR FORCES
After reading this module, you should be able to . . .
5.08 Determine the magnitude and direction of the gravitational force acting on a body with a given mass, at a location
with a given free-fall acceleration.
5.09 Identify that the weight of a body is the magnitude of the
net force required to prevent the body from falling freely, as
measured from the reference frame of the ground.
5.10 Identify that a scale gives an object’s weight when the
measurement is done in an inertial frame but not in an accelerating frame, where it gives an apparent weight.
5.11 Determine the magnitude and direction of the normal
force on an object when the object is pressed or pulled
onto a surface.
5.12 Identify that the force parallel to the surface is a frictional
the force that appears when the object slides or attempts to
slide along the surface.
5.13 Identify that a tension force is said to pull at both ends of
a cord (or a cord-like object) when the cord is taut. etc...
Introduction to Classical Mechanics:
UNIT-I : Elementary survey of Classical Mechanics: Newtonian mechanics for single particle and system of particles, Types of the forces and the single particle system examples, Limitation of Newton’s program, conservation laws viz Linear momentum, Angular Momentum & Total Energy, work-energy theorem; open systems (with variable mass). Principle of Virtual work, D’Alembert’s principle’ applications.
UNIT-II : Constraints; Definition, Types, cause & effects, Need, Justification for realizing constraints on the system
LECTURE 1 PHY5521 Classical Mechanics Honour to Masters LevelDavidTinarwo1
Classical mechanics, a well-organized introductory lecture. This is easy to follow, and a must-go-through lecture. UNIT-I : Elementary survey of Classical Mechanics: Newtonian mechanics for single particle and system of particles, Types of the forces and the single particle system examples, Limitation of Newton’s program, conservation laws viz Linear momentum, Angular Momentum & Total Energy, work-energy theorem; open systems (with variable mass). Principle of Virtual work, D’Alembert’s principle’ applications.
UNIT-II : Constraints; Definition, Types, cause & effects, Need, Justification for realizing constraints on the system, Difficulties introduced by imposing constraints on the system, Examples of constraints, Introduction of generalized coordinates justification. Lagrange’s equations; Linear generalized potentials, Generalized coordinates and momenta & energy; Gauge function for Lagrangian and its gauge invariance, Applications to constrained systems and generalized forces.
Theory of Vibrations: Introduction to the theory of vibrations in multi-degree-of-freedom systems, Normal modes and modal analysis, Nonlinear oscillations and chaos theory.
Canonical Transformations: Properties and classification of canonical transformations, Action-angle variables and their applications in integrable systems, Canonical perturbation theory and perturbation methods.
Poisson's and Lagrange's Brackets: Definitions and properties of Poisson's brackets, Relationship between Poisson's brackets and Hamilton's equations, Lagrange's brackets and their applications in dynamics. UNIT-III : Cyclic coordinates, Integrals of the motion, Concepts of symmetry, homogeneity and isotropy, Invariance under Galilean transformations Hamilton’s equation of motion: Legendre’s dual transformation, Principle of least action; derivation of equations of motion; variation and end points; Hamilton’s principle and characteristic functions; Hamilton-Jacobi equation.
UNIT-IV : Central force fields: Definition and properties, Two-body central force problem, gravitational and electrostatic potentials in central force fields, closure and stability of circular orbits; general analysis of orbits; Kepler’s laws and equation, Classification of orbits, orbital dynamics and celestial mechanics, differential equation of orbit, Virial Theorem.
UNIT-V : Canonical transformation; generating functions; Properties; group property; examples; infinitesimal generators; Poisson bracket; Poisson theorems; angular momentum PBs; Transition from discrete to continuous system, small oscillations (longitudinal oscillations in elastic rod); normal modes and coordinates.
Dynamic force analysis – Inertia force and Inertia torque– D Alembert’s principle –Dynamic Analysis in reciprocating engines – Gas forces – Inertia effect of connecting rod– Bearing loads – Crank shaft torque
Physics Project On Physical World, Units and MeasurementSamiran Ghosh
This PowerPoint is Physical World, Units and Measurement. This is basically the first chapter of 11th class/grade. This power point explains the basic or fundamental physics with some information about SI units and fundamental forces.
In physics, a force is any interaction which tends to change the motion of an object.
In other words, a force can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e., to accelerate.
Force can also be described by intuitive concepts such as a push or a pull.
A force has both magnitude and direction, making it a vector quantity. It is measured in the SI unit of newtons and represented by the symbol F.
The original form of Newton's second law states that the net force acting upon an object is equal to the rate at which its momentum changes with time.
If the mass of the object is constant, this law implies that the acceleration of an object is directly proportional to the net force acting on the object, is in the direction of the net force, and is inversely proportional to the mass of the object.
As a formula, this is expressed as:
Related concepts to force include: thrust, which increases the velocity of an object; drag, which decreases the velocity of an object; and torque which produces changes in rotational speed of an object. In an extended body, each part usually applies forces on the adjacent parts; the distribution of such forces through the body is the so-called mechanical stress.
Pressure is a simple type of stress. Stress usually causes deformation of solid materials, or flow in fluids.
Aristotle famously described a force
Mechanical Engineering is the Branch of Engineering.The mechanical engineering field requires an understanding of core areas including mechanics, dynamics, thermodynamics, materials science and structural analysis,Fluid Mechanics, Metrology and Instrumentation, Dynamics of Machinery- II, Manufacturing Processes II, Industrial Drafting and Machine Design, Engineering Graphics, Power Plant Engineering. Ekeeda offers Online Mechanical Engineering Courses for all the Subjects as per the Syllabus. Visit us: https://ekeeda.com/streamdetails/stream/mechanical-engineering
Ekeeda Provides Online Video Lectures for Mechanical Engineering Degree Subject Courses for All Engineering Universities. Visit us: https://ekeeda.com/streamdetails/stream/mechanical-engineering
Ekeeda Provides Online Video Lectures for Mechanical Engineering Degree Subject Courses for All Engineering Universities. Visit us: https://ekeeda.com/streamdetails/stream/mechanical-engineering
Civil Engineering is the Branch of Engineering.The Civil engineering field requires an understanding of core areas including Mechanics of Solids, Structural Mechanics - I, Building Construction Materials, Surveying - I, Geology and Geotechnical Engineering, Structural Mechanics, Building Construction, Water Resources and Irrigation, Environmental Engineering, Transportation Engineering, Construction and Project Management. Ekeeda offers Online Mechanical Engineering Courses for all the Subjects as per the Syllabus Visit us: https://ekeeda.com/streamdetails/stream/civil-engineering
Civil Engineering is the Branch of Engineering.The Civil engineering field requires an understanding of core areas including Mechanics of Solids, Structural Mechanics - I, Building Construction Materials, Surveying - I, Geology and Geotechnical Engineering, Structural Mechanics, Building Construction, Water Resources and Irrigation, Environmental Engineering, Transportation Engineering, Construction and Project Management. Ekeeda offers Online Mechanical Engineering Courses for all the Subjects as per the Syllabus Visit us: https://ekeeda.com/streamdetails/stream/civil-engineering
Ekeeda Provides Online Video Lectures for Civil Engineering Degree Subject Courses for All Engineering Universities. Visit us: https://ekeeda.com/streamdetails/stream/civil-engineering
Ekeeda Provides Online Video Lectures for Civil Engineering Degree Subject Courses for All Engineering Universities. Visit us: https://ekeeda.com/streamdetails/stream/civil-engineering
Kinetics of particles impulse momentum methodEkeeda
Ekeeda Provides Online Video Lectures for Civil Engineering Degree Subject Courses for All Engineering Universities. Visit us: https://ekeeda.com/streamdetails/stream/civil-engineering
Learn Online Courses of Subject Introduction to Civil Engineering and Engineering Mechanics. Clear the Concepts of Introduction to Civil Engineering and Engineering Mechanics Through Video Lectures and PDF Notes. Visit us: https://ekeeda.com/streamdetails/subject/introduction-to-civil-engineering-and-engineering-mechanics
Learn Online Courses of Subject Introduction to Civil Engineering and Engineering Mechanics. Clear the Concepts of Introduction to Civil Engineering and Engineering Mechanics Through Video Lectures and PDF Notes. Visit us: https://ekeeda.com/streamdetails/subject/introduction-to-civil-engineering-and-engineering-mechanics
Ekeeda Provides Online Video Lectures for Civil Engineering Degree Subject Courses for All Engineering Universities. Visit us: https://ekeeda.com/streamdetails/stream/civil-engineering
Coplanar forces res & comp of forces - for mergeEkeeda
Ekeeda Provides Online Video Lectures for Civil Engineering Degree Subject Courses for All Engineering Universities. Visit us: https://ekeeda.com/streamdetails/stream/civil-engineering
Ekeeda Provides Online Video Lectures for Civil Engineering Degree Subject Courses for All Engineering Universities. Visit us: https://ekeeda.com/streamdetails/stream/civil-engineering
Ekeeda Provides Online Video Lectures for Civil Engineering Degree Subject Courses for All Engineering Universities. Visit us: https://ekeeda.com/streamdetails/stream/civil-engineering
Infomatica, as it stands today, is a manifestation of our values, toil, and dedication towards imparting knowledge to the pupils of the society. Visit us: http://www.infomaticaacademy.com/
Infomatica, as it stands today, is a manifestation of our values, toil, and dedication towards imparting knowledge to the pupils of the society. Visit us: http://www.infomaticaacademy.com/
Infomatica, as it stands today, is a manifestation of our values, toil, and dedication towards imparting knowledge to the pupils of the society. Visit us/l http://www.infomaticaacademy.com/
Infomatica, as it stands today, is a manifestation of our values, toil, and dedication towards imparting knowledge to the pupils of the society. Visit us: http://www.infomaticaacademy.com/
Infomatica, as it stands today, is a manifestation of our values, toil, and dedication towards imparting knowledge to the pupils of the society. Visit us: http://www.infomaticaacademy.com/
Ekeeda Provides Online Engineering Subjects Video Lectures and Tutorials of Mumbai University (MU) Courses. Visit us: https://ekeeda.com/streamdetails/University/Mumbai-University
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
Vaccine management system project report documentation..pdfKamal Acharya
The Division of Vaccine and Immunization is facing increasing difficulty monitoring vaccines and other commodities distribution once they have been distributed from the national stores. With the introduction of new vaccines, more challenges have been anticipated with this additions posing serious threat to the already over strained vaccine supply chain system in Kenya.
TECHNICAL TRAINING MANUAL GENERAL FAMILIARIZATION COURSEDuvanRamosGarzon1
AIRCRAFT GENERAL
The Single Aisle is the most advanced family aircraft in service today, with fly-by-wire flight controls.
The A318, A319, A320 and A321 are twin-engine subsonic medium range aircraft.
The family offers a choice of engines
Event Management System Vb Net Project Report.pdfKamal Acharya
In present era, the scopes of information technology growing with a very fast .We do not see any are untouched from this industry. The scope of information technology has become wider includes: Business and industry. Household Business, Communication, Education, Entertainment, Science, Medicine, Engineering, Distance Learning, Weather Forecasting. Carrier Searching and so on.
My project named “Event Management System” is software that store and maintained all events coordinated in college. It also helpful to print related reports. My project will help to record the events coordinated by faculties with their Name, Event subject, date & details in an efficient & effective ways.
In my system we have to make a system by which a user can record all events coordinated by a particular faculty. In our proposed system some more featured are added which differs it from the existing system such as security.
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Automobile Management System Project Report.pdfKamal Acharya
The proposed project is developed to manage the automobile in the automobile dealer company. The main module in this project is login, automobile management, customer management, sales, complaints and reports. The first module is the login. The automobile showroom owner should login to the project for usage. The username and password are verified and if it is correct, next form opens. If the username and password are not correct, it shows the error message.
When a customer search for a automobile, if the automobile is available, they will be taken to a page that shows the details of the automobile including automobile name, automobile ID, quantity, price etc. “Automobile Management System” is useful for maintaining automobiles, customers effectively and hence helps for establishing good relation between customer and automobile organization. It contains various customized modules for effectively maintaining automobiles and stock information accurately and safely.
When the automobile is sold to the customer, stock will be reduced automatically. When a new purchase is made, stock will be increased automatically. While selecting automobiles for sale, the proposed software will automatically check for total number of available stock of that particular item, if the total stock of that particular item is less than 5, software will notify the user to purchase the particular item.
Also when the user tries to sale items which are not in stock, the system will prompt the user that the stock is not enough. Customers of this system can search for a automobile; can purchase a automobile easily by selecting fast. On the other hand the stock of automobiles can be maintained perfectly by the automobile shop manager overcoming the drawbacks of existing system.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
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P
WHAT IS MECHANICS?
Mechanics may be defined as that branch of physical science which is
concerned with the study of resultant effect of action of forces on bodies,
both in the state of rest and in motion.
Mechanics is subdivided into three branches, Mechanics of Rigid Bodies,
Mechanics of Deformable Bodies and Mechanics of Fluids.
In this book we shall study Mechanics of Rigid Bodies. In Rigid Body
Mechanics bodies are assumed to be perfectly rigid i.e. there is no
deformation of bodies under the action of loads to which they are subjected.
Though the engineering structures and machines do deform under the
action of loads, their deformation is so little that it does not affect the
conditions of equilibrium or equations of motion which are applied in their
study'.
Study of mechanics of Rigid bodies forms a basis for the study of other two
branches i.e. Mechanics of Deformable Bodies and Mechanics of Fluids. It
is therefore a basic subject in engineering study.
HISTORICAL BACKGROUND
The study of mechanics was developed very early in history. Early
contributions were made by Aristotle (384 -322B.c) and Archimedes (2g7 -
2t2 B.C). In his writings, Aristotle dealt with the principle of lever which
enables one to lift heavy object with comparatively lesser force. At that age
the requirements of engineering were mainly confined to construction work.
It is therefore surprising that the study of motion of bodies on inclined
plane, lifting of loads by use of lever and pulleys have been recorded in
ancient writings. On the other hand Archimedes established the
phenomenon of Buoyancy.
It was Galileo Galilie (1564 - 1642) who introduced time factor in the study
of the effect of forces on bodies. His experiments with motion of pendulum
and falling bodies contributed to the wider and deeper study of the subject
late on.
Introduction
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The major and most significant contribution to mechanics came from Sir
Issac Newton (1642 - L727) who propounded the theories of Fundamental
laws of motion and the Lows of universal gravitational acceleration. During
the same period Varignon (1654 - 17221a French mathematician
introduced what is now referred as Varignon's theorem. All this happened
much before the introduction of vector algebra.
In 1687 Varignon and Newton presented the Lau of parallelogram of forces.
Further application and derivation of theorems based on these laws were
made by D’Alembert 17 L7 - 1783), Euler (1736 - 1813), Lagrange and
others.
Plank (1858 - 1943) and Bhor (1885- 19621made contributions in the area
of Quantum Mechanics. In 1.905, Einstein formulated his theory of
relativity, referred to as Relativistic Mechanics, which challenged the
Newton's law of motion. However it was found that Einstein's theory had
certain limitations and therefore could not be applied under normal
conditions. Newton's laws therefore form the base of study of mechanics
and are therefore at times referred to as Newtonian Mechanics.
FUNDAMENTAL CONCEPTS
The study of mechanics has to start with knowing of fundamental. Concepts
involving length, time, mass and force. In Newtonian Mechanics length, time
and mass are the absolute concepts independent of each other.
Length
The concept of length means the position occupied by a point in space with
respect to a certain reference point like the origin. The three lengths in three
different directions define the position of the point. It therefore describes the
size of the system formed by number of points in space.
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Time
Whenever an event takes place, the time involved should also be known along
with the position. Though time of an event is not necessary in statics, it is
required in dynamics which deals with bodies in motion.
Mass
It is the quantity of matter contained in a body. This quantity does not change
on account of the position occupied by the body. This property is used to
compare bodies e.g. two bodies having different mass would have different
attractions to the earth or they would offer different resistance to the change
in their velocities during motion.
Force
A force is the action of one body on another body. The action could be a push'
or a 'pull'. A force is exerted when there is an actual contact between the two
bodies for e.g. a boy hitting a nail with a hammer. A force can also act even if
there is no contact between the two bodies, such as the magnetic or
gravitational force. Force is a vector quantity and is completely defined by its
magnitude, its direction and point of application fundamental.
FUNDAMENTAL PRINCIPLES
The study of Mechanics of Rigid Bodies is based on the six fundamental
principles presented below. These principles have their origin in experimental
evidences. Various theorems used in mechanics have been derived from
them.
1. Newton's First Law of Motion
Everybody continues in its state of rest or of uniform motion in a straight
line unless it is acted upon by an unbalanced force.
2. Newton's Second Law of Motion
The rate of change of momentum of a body is directly proportional to the
impressed force and takes place in the direction of the force. It is
mathematically written as
.F ma
where 'F' is the resultant force acting on a body of mass 'm' moving with
acceleration 'a'.
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3. Newton's Third Law of Motion
For every action there is an equal and opposite reaction.
4. Newton's Law of Gravitational Attraction
After formulating the three laws of motion, Newton put forth his iaw of
gravitational attraction which states "The force of attraction between any
two bodies in the universe is directly proportional to the product of their
masses and inversely proportional to the square of the distance between
them”.
If M and n are the masses of two bodies separated by a distance r
between them, they mutually attract each other with a force F, given by
2 2
. .
F or F G.
r r
M n M n
Where, G is the Universal constant of gravitational attraction.
An important case of attraction is between a particle of mass m located at
or near the surface of earth and the earth itself of mass M. If R is the
radius of earth then the force of attraction defined as the weight of the
particle would be
W = 2
. .
r
G M n
Or W = m.g if g = 2
.
r
G M
The value of g varies with the altitude above the surface of earth and also
with the latitude i.e. location on earth, since the earth is not exactly
spherical. For all practical computations g = 9.81 m/s2 can be used.
5. The principle of transmissibility of Force-
It states "A force being a sliding vector, continues to act along its line of
action and therefore makes no charge if it acts from a different point on its
line of action on a rigid body". This principle has been illustrated in detail
with figures in article 2.5
6. Law of parallelogram of forces.
It states "If two forces acting simultaneously on a body at a point Are
represented in magnitude and direction by the two adjacent sides of a
parallelogram then their resultant is represented in magnitude and
direction by the diagonal of the parallelogram which passes through the
point of intersection of the two sides representing the forces". This law has
been further discussed in article 2.9
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IDEALIZATIONS IN MECHANICS
In order to simplify the applications of theories in mechanics some
assumptions or idealizations are made which result in simplified solutions.
These are discussed below.
Particle
A particle is a body whose shape and size is neglected because those being
negligible and insignificant as compared to other dimensions and lengths
involved in the analysis of the body. For example, in the motion analysis of
a vehicle on a highway between two stations kilometers apart, the shape
and size of the vehicle become insignificant and therefore the vehicle can be
idealized as a particle
Rigid Body
A rigid body is a body whose shape and size is taken into consideration
during its analysis. Such a body is said to be made up of number of
particles which remain at fixed distances from each other. On application of
the loads or during motion the shape and size of the body does not change.
For example, the pillar supports of a building structure do deform under
the action of the loads they carry, but the deformations are very small as
compared to the lengths of the pillars and therefore the pillars can be
idealized as a rigid body.
Point Load (Concentrated Force)
Point load or concentrated force is an idealization that a force acts at a
point on the body though in fact it must be acting over a certain area. This
idealization could be satisfactorily used when the area on which the force
acts is small, for example, the normal reaction force which the types of the
wheels receive from the ground can be idealized to act at a point though
actually it acts over a certain area. This idealization would hold true since
the area of contact is very small as compared to the size of the wheel.
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THE INTERNATIONAL SYSTEM OF UNITS
Of the four fundamental concepts i.e. length, time, mass and force, three of
them length, time and mass have fundamental units. The fourth concept i.e.
force has a derived unit which is based on the three fundamental units.
Fundamental units also known as the basic units are arbitrarily defined and
are independent of each other. In this book SI units have been extensively
used. The SI unit of length is meter (m), of mass is kilogram (kg), of time is
seconds (s) Derived units depend on the fundamental units. The SI unit of
force is Newton (N). 1N= 1kg m/s2.
The SI units used in mechanics are listed below.
Quantity SI Unit Formula Symbol
Length Metre Basic Unit M
Mass Kilogram Basic Unit Kg
Time Second Basic Unit S
Acceleration Metre per second square m/s2 -
Angle Radian - Rad
Angular
Acceleration
Radian per second
square
Rad/s2 -
Angular
Velocity
Radian per second rad / s -
Area Square metre M2 -
Couple Newton-metre N.m -
Density Kilogram per cubic metre Kg/m3 -
Energy Joule N.m J
Force Newton Kg.m/s2 N
Frequency Hertz 1
s
Hz
Impulse Newton-second Kg.m/s -
Moment of
force
Newton-metre N.m -
Power Watt J/s W
Pressure Pascal N/m2 Pa
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Stress Pascal N/m2 Pa
Velocity Meter per second m/s -
Volume of
solids
Cubic metre M3 -
Volume of
liquids
Litre 10-3 m3 L
Work Joule N.m J
PROCEDURE OF PROBLEM ANALYSIS
Solving problems is the best way of learning the subject of mechanics.
While solving the problems follow the guidelines listed below. This should
help in successful solution of the problem.
1. After reading the problem carefully, the student should try to relate the
data of the problem to an actual physical engineering situation.
2. Even if the problem figure is given, draw your own necessary figure and
superimpose the problem data on it. The figure should be neat and clear. It
should show the various forces acting on the body. Such figures Are known
as free body diagrams and these play a very vital role in problem solution.
3. Apply the relevant fundamental principles and express the requirement in
mathematical equations. Break the working in suitable steps and record
them in an orderly manner. Check the equations dimensionally and use a
consistent set of units throughout. There may be more than one equation
which would require proper mathematical solution.
4. Try to reason the answer, or cross check the same by solving the same
problem by any other alternate method if possible, to check the correctness
of solution. Record the answers at the end of the solution.
Exercise 1
1) What is Mechanics?
2) State in brief the historical background of the development of the study of
mechanics.
3) Explain the fundamental concepts of Length, Time and Mass.
4) State and explain Newton's Law of Gravitational Attraction.
5) Explain "Idealization in Mechanics”.