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MAE 241 - Statics
Summer 2011
Dr. Konstantinos A. Sierros
Office Hours: M and W 10:30 11:30 (263 ESB new add)
Teaching Blog: http://wvumechanicsonline.blogspot.com
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Textbook
R. C. Hibbeler, STATICS, 12th Edition, Pearson Prentice Hall, NewJersey USA, 2004, ISBN 0-13-607790-0
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Tentative Schedule
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Chapter 1: General principles
Objectives
Intro to the basic quantities and
idealizations of mechanicsNewtons laws
SI unit system
Numerical calculations procedure
General guide for problem solving
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1.1 Mechanics
Mechanics is a branch of physics that is concerned with the state of
rest or motion of bodies that are subjected to the action of forces
Mechanics
Rigid-body
Deformable-body
Fluid
Rigid-body mechanics
Statics Dynamics
Statics deals with the equilibrium of bodies that are either at rest
or move with constant velocity. Dynamics is dealing with bodies
in accelerated motion
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History
Archimedes
(287-212 B.C.)
Lever principle
Galileo Galilei
(1564-1642.)Pendulums, falling
bodies
Newton
(1642-1727)
3 Fundamental laws
Euler
DAlembert
Langrange
and others
The subjects of statics developed very early in history because its
principles can be formulated simply from measurements of geometryand force
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1.2 Fundamental concepts
Basic quantities Length is used to locate the position of a point in
space and describe the size of a physical system
Time is conceived as a succession of events
Mass is a measure of a quantity of matter that is
used to compare the action of one body with that
of another
Force is considered as push or pull exerted by
one body or another.
- Direct contact (eg. A person pushing a wall)- Distant action (gravitational, electrical, magnetic
forces)
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1.2 Fundamental concepts
Idealizations
We use some idealizations in order to simplify the
application of theory
Particle: It has a mass, but its size can be neglected
(eg size of earth is insignificant as compared to the size
of its orbit)
When a body is modelled as a particle, mechanics
become simpler since the geometry of the body is not
involved in the analysis of the problem
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1.2 Fundamental concepts
Idealizations
A Rigid body can be considered as a combination of a large number of
particles in which all the particles remain at a fixed distance from one
another, both before and after applying a load
A Concentratedforce represents the effect of a loading which is assumed
to act at a point on a body. (eg. Contact force between wheel and ground)
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Newtons three laws of motion
The basis of engineering mechanics is formed by Newtons three laws
of motion. These laws, based on experimental observation, apply to
the motion of a particle as measured from a nonacceleratingreference
frame.
1st LawA particle originally at rest, or moving in
a straight line with constant velocity, tends to
remain in this state provided the particle is notSubjected to an unbalanced force
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Newtons three laws of motion
2nd LawA particle acted upon by an unbalancedforce F experiences an
acceleration a that has the same direction as the force and a magnitude
directly proportional to the force
F = ma
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Newtons three laws of motion
3rd LawThe mutual forces of action and reaction between two particles
are equal, opposite, and collinear
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Newtons law of gravitational attraction
F is force of gravitation between two particles
G is constant of gravitation measured
experimentally, G=66.73*10-12 m3/(kg s2)
m1,m2 represent the mass of each particle
r is the distance between the two particles
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Newtons law of gravitational attraction
Weight
According to the equation described, any two particleshave a mutual attractive (gravitational) force acting between them
For a particle located at the surface of the earth (or close enough) the
only gravitational force, of significant magnitude, is that between the
earth and the particle. This force is termed weight.
If we put m1 = m and m2 =Me (mass of earth) and r is distance between
the particle and the earths center
Letting g=GMe/r2, then W = mg
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Units of measurement
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Conversion of units
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The International System of units
SI is used throughout
Rules for use
(please read carefully page 10)
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Numerical calculations
Dimensional homogeneity: Each term in an equation must be expressed
in the same unitsSignificant figures:Number of significant figures determines accuracy of
the number. Use engineering notation.
Rounding off numbers: Any numerical figure ending in five or greater is
rounded up and a number less less than five is rounded downCalculations: Do not round off calculations until expressing the final
result. Round off the answer to three significant figures
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General procedure for analysis
Read the problem carefully and correlate physical situation with
theory
Tabulate the problem data and draw diagrams
Apply the relevant principles, generally
with equations
Solve the equations and report the answer
Judge the answer in technical terms and
common sense to determine whether the
answer seems reasonable
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Chapter 2:Force vectors
Objectives
To show how to add forces and
resolve them into components
using the Parallelogram Law
Cartesian vectors
Introduce dot product
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2.1 Scalars and vectors
Ascalaris any positive or negative physical quantity that can becompletely specified by its magnitude (eg. length, mass, time)
A vectoris any physical quantity that requires both a magnitude
and a direction for its complete description (eg. force, moment)