mekanik engineering chapter 1
Transcript of mekanik engineering chapter 1
Engineering Mechanics: Statics
Engineering Mechanics: Statics
Chapter 1General Principles
Chapter 1General Principles
Chapter ObjectivesChapter Objectives
To provide an introduction to the basic quantities and idealizations of mechanics.
To give a statement of Newton’s Laws of Motion and Gravitation.
To review the principles for applying the SI system of units.
To examine the standard procedures for performing numerical calculations.
To present a general guide for solving problems.
Chapter OutlineChapter Outline
MechanicsFundamental ConceptsUnits of MeasurementThe International System of UnitsNumerical CalculationsGeneral Procedure for Analysis
1.1 Mechanics1.1 Mechanics
Mechanics can be divided into 3 branches:- Rigid-body Mechanics- Deformable-body Mechanics- Fluid Mechanics
Rigid-body Mechanics deals with - Statics - Dynamics
1.1 Mechanics1.1 Mechanics
Statics – Equilibrium of bodies At rest Move with constant velocity. (Bidang statik adalah berkenaan dengan keseimbangan badan-badan yang
berada dalam keadaan rehat atau bergerak dengan halaju malar apabila ditindak oleh daya-daya)
Dynamics – Accelerated motion of bodies
(berkenaan dengan badan yang bergerak dengan pecutan)
1.2 Fundamentals Concepts 1.2 Fundamentals Concepts
Basic Quantities Length
– Locate position and describe size of physical system– Define distance and geometric properties of a body(ialah ukuran kedudukan satu titik dalam ruang untuk menerangkan saiz fizikal sistem berkenaan.)
Mass – Comparison of action of one body against another– Measure of resistance of matter to a change in velocity(Jisim ialah sifat sesuatu jasad/objek yang menentukan berapa banyak penentangan objek itu terhadap perubahan dalam halajunya.)
1.2 Fundamentals Concepts 1.2 Fundamentals Concepts
Basic Quantities Time
– Conceive as succession of events(pengukuran terhadap kejadian-kejadian yang berlaku secara berturutan)
Force(tindakan satu badan (samada menolak atau menarik) keatas badan lain).
– “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
1.2 Fundamentals Concepts1.2 Fundamentals Concepts
Idealizations Particles
– Consider mass but neglect sizeEg: Size of Earth insignificant compared to its size of orbit(zarah-satu badan yang sangat kecil apabila jisim atau dimensinya tidak diambil kira dalam analisis sessuatu masalah)
Rigid Body– Combination of large number of particles – Neglect material properties(cantuman rangkaian zarah-zarah yang banyak, apabila semua zarah ini berada pada satu jarak yang tetap antara satu sama lain samada sebelum atau selepas badan itu ditindakan daya)
1.2 Fundamentals Concepts1.2 Fundamentals Concepts
Newton’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”
APLIKASI HUKUM KEDUA NEWTONAPLIKASI HUKUM KEDUA NEWTON
APLIKASI HUKUM 1 NEWTONAPLIKASI HUKUM 1 NEWTON
MENGAPA ORANG ITU BISA TERPENTAL ????
1.2 Fundamentals Concepts1.2 Fundamentals Concepts
Newton’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” maF
APLIKASI HUKUM KEDUA NEWTONAPLIKASI HUKUM KEDUA NEWTON
APLIKASI HUKUM KEDUA NEWTONAPLIKASI HUKUM KEDUA NEWTON
1.2 Fundamentals Concepts1.2 Fundamentals Concepts
Newton’s Three Laws of Motion Third Law
“The mutual forces of action and reaction between two particles are equal and, opposite and collinear”
1.2 Fundamentals Concepts1.2 Fundamentals Concepts
Comparing 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°
1.3 Units of Measurement1.3 Units of Measurement
SI Units Système International d’UnitésF = 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
1.3 Units of Measurement1.3 Units of Measurement
2.
s
mkg
Name Length Time Mass Force
International Systems of Units (SI)
Meter (m)
Second (s)
Kilogram (kg)
Newton (N)
1.3 Units of Measurement1.3 Units of Measurement
At the standard location, g = 9.806 65 m/s2
For calculations, we use g = 9.81 m/s2
Thus,
W = mg (g = 9.81m/s2)Hence, a body of mass 1 kg has a
weight of 9.81 N, a 2 kg body weighs 19.62 N
1.4 The International System of Units
1.4 The International System of Units
PrefixesFor 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 unitEg: 4,000,000 N = 4000 kN (kilo-newton)
= 4 MN (mega- newton) 0.005m = 5 mm (milli-meter)
1.4 The International System of Units
1.4 The International System of Units
Exponential Form
Prefix SI Symbol
Multiple1 000 000 000 109 Giga G
1 000 000 106 Mega M
1 000 103 Kilo k
Sub-Multiple0.001 10-3 Milli m
0.000 001 10-6 Micro μ
0.000 000 001 10-9 nano n
1.4 The International System of Units
1.4 The International System of Units
Rules for UseNever 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)
1.4 The International System of Units
1.4 The International System of Units
Rules for UseQuantities defined by several units
which are multiples, are separated by a dotEg: 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 prefixEg: μN2 = (μN)2 = μN. μN
1.4 The International System of Units
1.4 The International System of Units
Rules for UsePhysical constants with several digits
on either side should be written with a space between 3 digits rather than a commaEg: 73 569.213 427
In calculations, represent numbers in terms of their base or derived units by converting all prefixes to powers of 10
1.4 The International System of Units
1.4 The International System of Units
Rules 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
1.4 The International System of Units
1.4 The International System of Units
Rules 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 unitsEg: Do not write N/mm but rather kN/mAlso, m/mg should be expressed as Mm/kg
1.4 The International System of Units
1.4 The International System of Units
Rules for UseAlthough 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
1.5 Numerical Calculations1.5 Numerical Calculations
Dimensional Homogeneity- Each term must be expressed in the same unitsEg: s = vt + ½ at2 where s is position in meters (m), t is time in seconds (s), v is velocity in m/s and a is acceleration in m/s2
- Regardless of how the equation is evaluated, it maintains its dimensional homogeneity
1.5 Numerical Calculations1.5 Numerical Calculations
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 for algebraic manipulations of an equation
1.5 Numerical Calculations1.5 Numerical Calculations
Significant Figures- The accuracy of a number is specified by the number of significant figures it contains
- A significant figure is any digit including zero, provided it is not used to specify the location of the decimal point for the numberEg: 5604 and 34.52 have four significant numbers
1.5 Numerical Calculations1.5 Numerical Calculations
Significant Figures- When numbers begin or end with zero, we make use of prefixes to clarify the number of significant figures
Eg: 400 as one significant figure would be 0.4(103) 2500 as three significant figures would be 2.50(103)
1.5 Numerical Calculations1.5 Numerical Calculations
Computers are often used in engineering foradvanced design and analysis
1.5 Numerical Calculations1.5 Numerical Calculations
Rounding Off Numbers- For numerical calculations, the accuracy obtained from the solution of a problem would never be better than the accuracy of the problem data
- Often handheld calculators or computers involve more figures in the answer than the number of significant figures in the data
1.5 Numerical Calculations1.5 Numerical Calculations
Rounding Off Numbers- Calculated results should always be “rounded off” to an appropriate number of significant figures
1.5 Numerical Calculations1.5 Numerical Calculations
Rules for Rounding to n significant figures- 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 = 2 significance 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 = 3 significant figures become 1.24(103) and 0.866
1.5 Numerical Calculations1.5 Numerical Calculations
Rules for Rounding to n significant figures- If the n+1 digit is greater than 5 or equal to 5 with non-zero digits following it, increase the nth digit by 1 and drop the n+1digit and the others following itEg: 0.723 87 and 565.5003 rounded off to n = 3 significance figures become 0.724 and 566
1.5 Numerical Calculations1.5 Numerical Calculations
Calculations- To ensure the accuracy of the final results, always retain a greater number of digits than the problem data- If possible, try work out computations so that numbers that are approximately equal are not subtracted-In engineering, we generally round off final answers to three significant figures
1.5 Numerical Calculations1.5 Numerical Calculations
Example 1.1 Evaluate each of the following and express
with SI units having an approximate prefix: (a) (50 mN)(6 GN), (b) (400 mm)(0.6 MN)2, (c) 45 MN3/900 Gg
Solution First convert to base units, perform indicated operations and choose an appropriate prefix
1.5 Numerical Calculations1.5 Numerical Calculations
(a)
2
3326
26
93
300
10
1
10
110300
10300
1061050
650
kN
N
kN
N
kNN
N
NN
GNmN
1.5 Numerical Calculations1.5 Numerical Calculations
(b)
2
29
2123
263
2
.144
.10144
1036.010400
106.010400
6.0400
kNGm
Nm
Nm
Nm
MNmm
1.5 Numerical Calculations1.5 Numerical Calculations
kgkN
kgkN
kgN
kNN
kgN
kg
N
GgMN
/50
/1005.0
1
10
11005.0
/1005.0
10900
1045
900/45
3
33
3312
312
6
36
3
(c)
1.6 General Procedure for Analysis
1.6 General Procedure for Analysis
Most efficient way of learning is to solve problems
To be successful at this, it is important to present work in a logical and orderly way as suggested:1) Read problem carefully and try correlate actual physical situation with theory2) Draw any necessary diagrams and tabulate the problem data
1.6 General Procedure for Analysis
1.6 General Procedure for Analysis
3) Apply relevant principles, generally in mathematics forms4) Solve the necessary equations algebraically as far as practical, making sure that they are dimensionally homogenous, using a consistent set of units and complete the solution numerically5) Report the answer with no more significance figures than accuracy of the given data
1.6 General Procedure for Analysis
1.6 General Procedure for Analysis
6) Study the answer with technical judgment and common sense to determine whether or not it seems reasonable
1.6 General Procedure for Analysis
1.6 General Procedure for Analysis
When solving the problems, do the work as neatly as possible. Being neat generally stimulates clear and orderly thinking and vice versa.