Lecture 1- 1page

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Vector Mechanics for Engineers: StaticsE i gh t h

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Contents

What is Mechanics?

Fundamental Concepts

Fundamental Principles

Systems of Units

Method of Problem Solution

Numerical Accuracy





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What is Mechanics?

• Mechanics is the science which describes and predicts

the conditions of rest or motion of bodies under the

action of forces.

• Categories of Mechanics:

- Rigid bodies

- Statics

- Dynamics

- Deformable bodies

- Fluids

• Mechanics is an applied science - it is not an abstract

or pure science but does not have the empiricismfound in other engineering sciences.

• Mechanics is the foundation of most engineering sciences

and is an indispensable prerequisite to their study.





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BRANCHES OF MECHANICS

Statics Dynamics

Rigid Bodies

(Things that do not change shape)

Deformable Bodies

(Things that do change shape)

Incompressible Compressible

Fluids

Mechanics

Type title here





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Fundamental Concepts

• Space - associated with the notion of the position of a point P given in

terms of three coordinates measured from a reference point or origin.

• Time - definition of an event requires specification of the time and

position at which it occurred.

• Mass - used to characterize and compare bodies, e.g., response to

earth’s gravitational attraction and resistance to changes in translational

motion.

• Force - represents the action of one body on another. A force is

characterized by its point of application, magnitude, and direction, i.e.,

a force is a vector quantity.

In Newtonian Mechanics, space, time, and mass are absolute concepts,

independent of each other. Force, however, is not independent of the

other three. The force acting on a body is related to the mass of the body

and the variation of its velocity with time.





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Fundamental Principles

• Parallelogram Law

• Principle of Transmissibility

• Newton’s First Law: If the resultant force on a

particle is zero, the particle will remain at rest

or continue to move in a straight line.

• Newton’s Third Law: The forces of action and

reaction between two particles have the same

magnitude and line of action with opposite

sense.

• Newton’s Second Law: A particle will havean acceleration proportional to a nonzero

resultant applied force.

amF r

r

=

• Newton’s Law of Gravitation: Two particles

are attracted with equal and opposite forces,





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Systems of Units

• Kinetic Units: length, time, mass,

and force.

• Three of the kinetic units, referred to

as basic units, may be defined

arbitrarily. The fourth unit, referredto as a derived unit , must have a

definition compatible with Newton’s

2nd Law,

amF rv

=

• International System of Units (SI):

The basic units are length, time, and

mass which are arbitrarily defined as the

meter (m), second (s), and kilogram

(kg). Force is the derived unit,

( ) ⎟ ⎠

⎞⎜⎝

⎛ =

=

2s

m1kg1 N1

maF

• U.S. Customary Units:

The basic units are length, time, and

force which are arbitrarily defined as the

foot (ft), second (s), and pound (lb).

Mass is the derived unit,

sft1

lb1

slug1 =

=a

F m





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Table 1-1 in the textbook summarizes these unit systems.





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COMMON CONVERSION FACTORS

• 1 ft = 0.3048 m

• 1 lb = 4.4482 N

• 1 slug = 14.5938 kg

• Example: Convert a torque value of47 in • lb into SI units.

• Answer is 5.31026116 N • m??

• Work problems in the units given

unless otherwise instructed!!





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RULES FOR USING SI SYMBOLS

• No Plurals (e.g., m = 5 kg not kgs )

• Separate Units with a • (e.g., meter second = m • s )

• Most symbols are in lowercase ( some exception are N,

Pa, M and G)

• Exponential powers apply to units , e.g., cm2 = cm • cm

• Other rules are given in your textbook





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NUMERICAL CALCULATIONS

• Must have dimensional “homogeneity.” Dimensions have to be the same on both sides of the equal sign, (e.g. distance =

speed × time.)

• Be consistent when rounding off.

- greater than 5, round up (3528 3530)

- smaller than 5, round down (0.03521 0.0352)

- equal to 5, see your textbook.

• Use an appropriate number of significant figures (3 for

answer, at least 4 for intermediate calculations).





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Method of Problem Solution

• Problem Statement :

Includes given data, specification of

what is to be determined, and a figure

showing all quantities involved.

• Free-Body Diagrams:

Create separate diagrams for each of

the bodies involved with a clear

indication of all forces acting oneach body.

• Fundamental Principles:

The fundamental principles are

applied to express the conditions ofrest or motion of each body. The

rules of algebra are applied to solve

the equations for the unknown

quantities.

• Solution Check :

- Test for errors in reasoning by

verifying that the units of the

computed results are correct,

- test for errors in computation by

substituting given data and computed

results into previously unused

equations based on the six principles,

- always apply experience and physicalintuition to assess whether results seem

“reasonable”





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Numerical Accuracy

• The accuracy of a solution depends on 1) accuracy of the given

data, and 2) accuracy of the computations performed. The solution

cannot be more accurate than the less accurate of these two.

• As a general rule for engineering problems, the data are seldom

known with an accuracy greater than 0.2%. Therefore, it is usually

appropriate to record parameters beginning with “1” with four digits

and with three digits in all other cases, i.e., 40.2 lb and 15.58 lb.

• The use of hand calculators and computers generally makes the

accuracy of the computations much greater than the accuracy of the

data. Hence, the solution accuracy is usually limited by the data

accuracy.

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