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# 6161103 1 general principles

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### 6161103 1 general principles

1. 1. Chapter 1 General PrinciplesEngineering Mechanics: Statics
2. 2. Chapter ObjectivesTo provide an introduction to the basic quantities andidealizations of mechanics.To give a statement of Newton’s Laws of Motion andGravitation.To review the principles for applying the SI system ofunits.To examine the standard procedures for performingnumerical calculations.To present a general guide for solving problems.
3. 3. Chapter OutlineMechanicsFundamental ConceptsUnits of MeasurementThe International System of UnitsNumerical CalculationsGeneral Procedure for Analysis
4. 4. 1.1 MechanicsMechanics can be divided into 3branches:- Rigid-body Mechanics- Deformable-body Mechanics- Fluid MechanicsRigid-body Mechanics deals with- Statics- Dynamics
5. 5. 1.1 Mechanics Statics – Equilibrium of bodies At rest Move with constant velocityDynamics – Accelerated motion of bodies
6. 6. 1.2 Fundamentals ConceptsBasic Quantities Length – Locate position and describe size of physical system – Define distance and geometric properties of a body Mass – Comparison of action of one body against another – Measure of resistance of matter to a change in velocity
7. 7. 1.2 Fundamentals ConceptsBasic Quantities Time – Conceive as succession of events Force – “push” or “pull” exerted by one body on another – Occur due to direct contact between bodies Eg: Person pushing against the wall – Occur through a distance without direct contact Eg: Gravitational, electrical and magnetic forces
8. 8. 1.2 Fundamentals ConceptsIdealizations Particles – Consider mass but neglect size Eg: Size of Earth insignificant compared to its size of orbit Rigid Body – Combination of large number of particles – Neglect material properties Eg: Deformations in structures, machines and mechanism
9. 9. 1.2 Fundamentals ConceptsIdealizations Concentrated Force – Effect of loading, assumed to act at a point on a body – Represented by a concentrated force, provided loading area is small compared to overall size Eg: Contact force between wheel and ground
10. 10. 1.2 Fundamentals ConceptsNewton’s Three Laws of Motion First Law “A particle originally at rest, or moving in a straight line with constant velocity, will remain in this state provided that the particle is not subjected to an unbalanced force”
11. 11. 1.2 Fundamentals ConceptsNewton’s Three Laws of Motion Second Law “A particle acted upon by an unbalanced force F experiences an acceleration a that has the same direction as the force and a magnitude that is directly proportional to the force” F = ma
12. 12. 1.2 Fundamentals ConceptsNewton’s Three Laws of Motion Third Law “The mutual forces of action and reaction between two particles are equal and, opposite and collinear”
13. 13. 1.2 Fundamentals ConceptsNewton’s Law of Gravitational Attraction m1 m 2 F =G 2 rF = force of gravitation between two particlesG = universal constant of gravitationm1,m2 = mass of each of the two particlesr = distance between the two particles
14. 14. 1.2 Fundamentals Concepts mM e Weight, W =G 2 rLetting g = GM e / r 2 yields W = mg
15. 15. 1.2 Fundamentals ConceptsComparing F = mg with F = ma g is the acceleration due to gravity Since g is dependent on r, weight of a body is not an absolute quantity Magnitude is determined from where the measurement is taken For most engineering calculations, g is determined at sea level and at a latitude of 45°
16. 16. 1.3 Units of MeasurementSI Units Système International d’Unités F = ma is maintained only if – Three of the units, called base units, are arbitrarily defined – Fourth unit is derived from the equation SI system specifies length in meters (m), time in seconds (s) and mass in kilograms (kg) Unit of force, called Newton (N) is derived from F = ma
17. 17. 1.3 Units of MeasurementName Length Time Mass ForceInternationa Meter Second Kilogram Newtonl Systems of (m) (s) (kg) (N)Units (SI)  kg .m   2   s 
18. 18. 1.3 Units of MeasurementAt the standard location,g = 9.806 65 m/s2For calculations, we useg = 9.81 m/s2Thus,W = mg (g = 9.81m/s2)Hence, a body of mass 1 kg has a weightof 9.81 N, a 2 kg body weighs 19.62 N
19. 19. 1.4 The International System of UnitsPrefixes For a very large or very small numerical quantity, the units can be modified by using a prefix Each represent a multiple or sub-multiple of a unit Eg: 4,000,000 N = 4000 kN (kilo-newton) = 4 MN (mega- newton) 0.005m = 5 mm (milli-meter)
20. 20. 1.4 The International System of Units Exponential Prefix SI Symbol FormMultiple1 000 000 000 109 Giga G1 000 000 106 Mega M1 000 103 Kilo kSub-Multiple0.001 10-3 Milli m0.000 001 10-6 Micro µ0.000 000 001 10-9 nano n
21. 21. 1.4 The International System of UnitsRules for Use Never write a symbol with a plural “s”. Easily confused with second (s) Symbols are always written in lowercase letters, except the 2 largest prefixes, mega (M) and giga (G) Symbols named after an individual are capitalized Eg: newton (N)
22. 22. 1.4 The International System of UnitsRules for Use Quantities defined by several units which are multiples, are separated by a dot Eg: N = kg.m/s2 = kg.m.s-2 The exponential power represented for a unit having a prefix refer to both the unit and its prefix Eg: µN2 = (µN)2 = µN. µN
23. 23. 1.4 The International System of UnitsRules for Use Physical constants with several digits on either side should be written with a space between 3 digits rather than a comma Eg: 73 569.213 427 In calculations, represent numbers in terms of their base or derived units by converting all prefixes to powers of 10
24. 24. 1.4 The International System of UnitsRules for UseEg: (50kN)(60nm) = [50(103)N][60(10-9)m] = 3000(10-6)N.m = 3(10-3)N.m = 3 mN.m The final result should be expressed using a single prefix
25. 25. 1.4 The International System of UnitsRules for Use Compound prefix should not be used Eg: kµs (kilo-micro-second) should be expressed as ms (milli-second) since 1 kµs = 1 (103)(10-6) s = 1 (10-3) s = 1ms With exception of base unit kilogram, avoid use of prefix in the denominator of composite units Eg: Do not write N/mm but rather kN/m Also, m/mg should be expressed as Mm/kg
26. 26. 1.4 The International System of UnitsRules for Use Although not expressed in terms of multiples of 10, the minute, hour etc are retained for practical purposes as multiples of second. Plane angular measurements are made using radians. In this class, degrees would be often used where 180° = π rad
27. 27. 1.5 Numerical CalculationsDimensional Homogeneity- Each term must be expressed in thesame unitsEg: s = vt + ½ at2 where s is positionin meters (m), t is time in seconds (s),v is velocity in m/s and a is accelerationin m/s2- Regardless of how the equation isevaluated, it maintains its dimensionalhomogeneity
28. 28. 1.5 Numerical CalculationsDimensional Homogeneity- All the terms of an equation can bereplaced by a consistent set of units,that can be used as a partial check foralgebraic manipulations of an equation
29. 29. 1.5 Numerical CalculationsSignificant 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
30. 30. 1.5 Numerical Calculations Significant Figures - When numbers begin or end with zero, we make use of prefixes to clarify the number of significant figuresEg: 400 as one significant figure would be 0.4(103) 2500 as three significant figures would be 2.50(103)
31. 31. 1.5 Numerical CalculationsComputers are often used in engineering foradvanced design and analysis
32. 32. 1.5 Numerical CalculationsRounding Off Numbers- For numerical calculations, the accuracyobtained from the solution of a problemwould never be better than the accuracy ofthe problem data- Often handheld calculators or computersinvolve more figures in the answer than thenumber of significant figures in the data
33. 33. 1.5 Numerical CalculationsRounding Off Numbers- Calculated results should always be“rounded off” to an appropriate number ofsignificant figures
34. 34. 1.5 Numerical CalculationsRules for Rounding to n significantfigures- If the n+1 digit is less than 5, the n+1 digit andothers 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(103) and 0.8655 rounded off to n = 3significant figures become 1.24(103) and 0.866
35. 35. 1.5 Numerical CalculationsRules 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
36. 36. 1.5 Numerical CalculationsCalculations- To ensure the accuracy of the finalresults, 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
37. 37. 1.5 Numerical CalculationsExample 1.1Evaluate each of the following and express withSI units having an approximate prefix: (a) (50mN)(6 GN), (b) (400 mm)(0.6 MN)2, (c) 45MN3/900 GgSolutionFirst convert to base units, perform indicatedoperations and choose an appropriate prefix
38. 38. 1.5 Numerical Calculations(a) (50mN )(6GN ) [ ( ) ][ ( ) ] = 50 10 −3 N 6 109 N = 300(10 )N 6 2 = 300(10 )N  6  1kN  1kN  2 3  3  10 N 10 N   = 300kN 2
39. 39. 1.5 Numerical Calculations(b) (400mm )(0.6MN )2 [ ( )m][0.6(10 )N ] = 400 10 −3 6 2 = [400(10 )m][0.36(10 )N ] −3 12 2 = 144(10 )m.N 9 2 = 144Gm.kN 2
40. 40. 1.5 Numerical Calculations(c) 3 45MN / 900Gg = ( 45 10 N 6 ) 3 ( ) 900 106 kg = 0.05(10 )N / kg12 3 = 0.05(10 )N   1kN  1 12 3  3  10 N  kg = 0.05(10 )kN / kg 3 3 = 50kN 3 / kg
41. 41. 1.6 General Procedure for AnalysisMost efficient way of learning is to solveproblemsTo 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
42. 42. 1.6 General Procedure for Analysis3) 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
43. 43. 1.6 General Procedure for Analysis6) Study the answer with technical judgment andcommon sense to determine whether or not itseems reasonable
44. 44. 1.6 General Procedure for AnalysisWhen solving the problems, do the work asneatly as possible. Being neat generallystimulates clear and orderly thinking and viceversa.