Ch01 Statics-Pearson 1 Hr

8/12/2019 Ch01 Statics-Pearson 1 Hr

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Engineering Mechanics: Statics

Chapter 1General Principles


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Chapter Outline

MechanicsFundamental Concepts

Units of MeasurementThe International System of UnitsNumerical CalculationsGeneral Procedure for Analysis


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1.1 Mechanics

Mechanics can be divided into 3branches:

- Rigid-body Mechanics- Deformable-body Mechanics- Fluid Mechanics

Rigid-body Mechanics deals with- Statics- Dynamics


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1.1 Mechanics

Statics Equilibrium of bodies At rest

Move with constant velocityDynamics Accelerated motion of

bodies


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1.2 Fundamentals Concepts

Basic QuantitiesLength

Locate position and describe size of physicalsystem

Define distance and geometric properties of abodyMass

Comparison of action of one body againstanother

Measure of resistance of matter to a change invelocity


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Basic QuantitiesTime

Conceive as succession of eventsForce push or pull exerted by one body onanother

Occur due to direct contact between bodiesEg: Person pushing against the wall

Occur through a distance without directcontact Eg: Gravitational, electrical and magneticforces


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IdealizationsParticles

Consider mass but neglect sizeEg: Size of Earth insignificant compared to itssize of orbitRigid Body

Combination of large number of particles Neglect material propertiesEg: Deformations in structures, machines andmechanism


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IdealizationsConcentrated Force

Effect of loading, assumed to act at apoint on a body

Represented by a concentrated force,

provided loading area is small compared tooverall sizeEg: Contact force between wheel and ground


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Newtons Three Laws of Motion First Law

A particle originally at rest, or moving in astraight line with constant velocity, willremain in this state provided that the particleis not subjected to an unbalanced

force


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Newtons Three Laws of Motion Second Law

A particle acted upon by an unbalancedforce F experiences an acceleration a thathas the same direction as the force and amagnitude that is directly proportional to the

force

ma F


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Newtons Three Laws of Motion Third Law

The mutual forces of action and reactionbetween two particles are equal and,opposite and collinear


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Newtons Law of Gravitational Attraction

F = force of gravitation between two particlesG = universal constant of gravitationm1,m 2 = mass of each of the two particlesr = distance between the two particles

221

r mmG F


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Weight,

Letting yields

2

r

mM GW e

2/ r GM g e

mg W


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Comparing F = mg with F = mag is the acceleration due to gravity

Since g is dependent on r, weight of a body isnot an absolute quantityMagnitude is determined from where themeasurement is takenFor most engineering calculations, g isdetermined at sea level and at a latitude of 45


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1.3 Units of Measurement

SI UnitsSyst me International d Unit sF = ma is maintained only if

Three of the units, called base units , arearbitrarily defined

Fourth unit is derived from the equationSI system specifies length in meters (m), time inseconds (s) and mass in kilograms (kg)Unit of force, called Newton (N) is derived from F= ma


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2

.

s

mkg

Name Length Time Mass Force

International Systems ofUnits (SI)

Meter(m) Second(s) Kilogram(kg) Newton(N)


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At the standard location,g = 9.806 65 m/s 2

For calculations, we useg = 9.81 m/s 2

Thus,

W = mg (g = 9.81m/s 2)Hence, a body of mass 1 kg has a weightof 9.81 N, a 2 kg body weighs 19.62 N


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1.4 The International System ofUnits

PrefixesFor a very large or very small numerical

quantity, the units can be modified byusing a prefixEach represent a multiple or sub-multipleof a unitEg: 4,000,000 N = 4000 kN (kilo-newton)

= 4 MN (mega- newton)0.005m = 5 mm (milli-meter)


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ExponentialForm

Prefix SI Symbol

Multiple1 000 000 000 10 9 Giga G

1 000 000 10 6 Mega M

1 000 10 3 Kilo k

Sub-Multiple0.001 10 -3 Milli m

0.000 001 10 -6 Micro

0.000 000 001 10 -9 nano n


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Rules for UseNever write a symbol with a plural s.

Easily confused with second (s)Symbols are always written inlowercase letters, except the 2 largestprefixes, mega (M) and giga (G)Symbols named after an individual arecapitalized Eg: newton (N)


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Rules for UseQuantities defined by several units

which are multiples, are separated by adotEg: N = kg.m/s 2 = kg.m.s -2

The exponential power represented fora unit having a prefix refer to both theunit and its prefixEg: N2 = ( N) 2 = N. N


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Rules for UsePhysical constants with several digits on

either side should be written with a spacebetween 3 digits rather than a commaEg: 73 569.213 427In calculations, represent numbers interms of their base or derived units byconverting all prefixes to powers of 10


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Rules for UseEg: (50kN)(60nm) = [50(10 3)N][60(10 -9)m]

= 3000(10 -6)N.m= 3(10 -3)N.m= 3 mN.m

The final result should be expressed usinga single prefix


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Rules for UseCompound prefix should not be used

Eg: k s (kilo-micro-second) should be expressed asms (milli-second) since1 k s = 1 (10 3)(10 -6) s = 1 (10 -3) s = 1msWith exception of base unit kilogram, avoid useof prefix in the denominator of composite unitsEg: Do not write N/mm but rather kN/m

Also, m/mg should be expressed as Mm/kg


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Rules for Use Although not expressed in terms of

multiples of 10, the minute, hour etc areretained for practical purposes as multiplesof second.

Plane angular measurements are madeusing radians. In this class, degrees wouldbe often used where 180 = rad


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1.5 Numerical Calculations

Dimensional Homogeneity- Each term must be expressed in thesame unitsEg: s = vt + at 2 where s is positionin meters (m), t is time in seconds (s),v is velocity in m/s and a is accelerationin m/s 2

- Regardless of how the equation isevaluated, it maintains its dimensionalhomogeneity


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Dimensional Homogeneity- All the terms of an equation can be

replaced by a consistent set of units,that can be used as a partial check foralgebraic manipulations of an equation


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Significant Figures- The accuracy of a number is specified bythe number of significant figures it contains

- A significant figure is any digit includingzero, provided it is not used to specify thelocation of the decimal point for the numberEg: 5604 and 34.52 have four significantnumbers


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Significant Figures- When numbers begin or end with zero, we make

use of prefixes to clarify the number of significantfiguresEg: 400 as one significant figure would be 0.4(10 3)

2500 as three significant figures would be2.50(10 3)


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Computers are often used in engineering foradvanced design and analysis


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Rounding Off Numbers- Calculated results should always be

rounded off to an appropriate number of

significant figures


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Rules for Rounding to n significantfigures- If the n+1 digit is less than 5, the n+1 digit and

others following it are droppedEg: 2.326 and 0.451 rounded off to n = 2significance figures would be 2.3 and 0.45

- If the n+1 digit is equal to 5 with zero following it,then round nth digit to an even numberEg: 1.245(10 3) and 0.8655 rounded off to n = 3significant figures become 1.24(10 3) and 0.866


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Rules for Rounding to n significantfigures- If the n+1 digit is greater than 5 or equalto 5 with non-zero digits following it,increase the nth digit by 1 and drop then+1digit and the others following itEg: 0.723 87 and 565.5003 rounded off ton = 3 significance figures become 0.724and 566


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Calculations- To ensure the accuracy of the final

results, always retain a greater number ofdigits than the problem data- If possible, try work out computations sothat numbers that are approximately equalare not subtracted-In engineering, we generally round offfinal answers to three significant figures


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Example 1.1Evaluate each of the following and express withSI units having an approximate prefix: (a) (50

mN)(6 GN), (b) (400 mm)(0.6 MN) 2, (c) 45MN3 /900 Gg

SolutionFirst convert to base units, perform indicatedoperations and choose an appropriate prefix


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(a)

2

33

26

26

93

300

10

1

10

110300

10300

1061050

650

kN

N kN

N kN

N

N

N N

GN mN


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(b)

2

29

2123

263

2

.144

.101441036.010400

106.010400

6.0400

kN Gm

N m N m

N m

MN mm


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kg kN

kg kN kg N

kN N

kg N kg

N

Gg MN

/50

/1005.0

1

10

11005.0

/1005.0

10900

1045

900/45

3

33

3

312

312

6

36

3

(c)


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1.6 General Procedure for Analysis

Most efficient way of learning is to solveproblems

To be successful at this, it is important topresent work in a logical and orderly way assuggested:1) Read problem carefully and try correlateactual physical situation with theory2) Draw any necessary diagrams andtabulate the problem data


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3) Apply relevant principles, generally inmathematics forms4) Solve the necessary equationsalgebraically as far as practical, making surethat they are dimensionally homogenous,using a consistent set of units and completethe solution numerically5) Report the answer with no moresignificance figures than accuracy of thegiven data


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6) Study the answer with technical judgment andcommon sense to determine whether or not itseems reasonable


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When solving the problems, do the work asneatly as possible. Being neat generallystimulates clear and orderly thinking and vice

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Ch01 Statics-Pearson 1 Hr