Q.1 to Q.25: Will carry one mark each (sub-total 25 marks).
1/3 mark will be deducted for each wrong answer.
Q.26 to Q.55: Will carry two marks each (sub-total 60 marks)
2/3 mark will be deducted for each wrong answer.
Q.48 through Q.51 (2 pairs) will be common data questions.
Each question will carry two marks
2/3 mark will be deducted for each wrong answer.
Question pairs (Q.52, Q.53) and (Q.54, Q.55) will be linked answer questions.
The answer to the second question of the last two pairs will depend on the answer to the first question of the pair.
If the first question in the linked pair is wrongly answered or is un-attempted, then the answer to the second question in the pair will not be evaluated. Each question will carry two marks
There will be negative marks only for wrong answer to the first question of the linked answer question pair i.e. for
Q.52 and Q.54, 2/3 mark will be deducted for each wrong answer.
There is no negative marking for Q.53 and Q.55.
Q.56 to Q.60 : From General Aptitude (GA) will carry one mark each (sub-total 5 marks).
1/3 mark will be deducted for each wrong answer.
Q.61 to Q.65 : From GA will carry two marks each (sub-total 10 marks)
2/3 mark will be deducted for each wrong answer.
All the papers will contain few questions on Engineering Mathematics carrying 15 marks.
Monday, December 20, 2010
GATE SYLLABUS FOR MECHANICAL
APPLIED MECHANICS AND DESIGN
(1) Engineering Mechanics:
Equivalent force systems, free-body concepts, equations of equilibrium, trusses and frames, virtual work and minimum potential energy. Kinematics and dynamics of particles and rigid bodies, impulse and momentum , energy methods, central force motion.
(2) Strength of Materials:
Stress and strain, Elastic constants, stress-strain relationship, Mohr's circle, deflection of beams, bending and shear stress, shear force and bending moment diagrams, torsion of circular shafts, thin thick cylinders, Euler's theory of columns, strain energy methods, thermal stress.
(3) Theory of machines:
Analysis of plane mechanisms, dynamic analysis of slider-crank mechanism, planer cams and followers, gear tooth profiles, kinematics and design of gears, governors and flywheels, balancing of reciprocating and rotating masses.
(4) Vibrations:
Free and forced vibrations of single degree freedom systems, effect of damping, vibration isolation, resonance, critical speed shafts.
(5) Design of Machine Elements:
Designing for statics and dynamic loading, fatigue strength, failure theories, design of bolted, riveted and welded joints, design of shafts and keys, design of spur gears, brakes and clutches, rolling and sliding contact bearings , belt, ropes and chain drives.
THERMAL SCIENCE AND ENGINEERING
(1) Fluid Mechanics:
Fluid properties, fluid statics, manometer, buoyancy, control-volume analysis of mass, momentum and energy, fluid acceleration, differential equation of continuity and momentum. Bernouli's equation. Viscous flow of incompressible fluids; boundary layer, flow through pipes, head losses in pipes, bends etc.
(2) Turbo machines:
velocity triangles Euler's equation, specific speed, Pelton wheel, centrifugal pump, Francis and Kaplan turbines.
(3) Heat-Transfer:
Modes of heat transfer, one dimensional heat conduction, resistance concept, electrical analogy, unsteady heat conduction, fins, dimensionless parameters in free and forced convective heat layer, effect of turbulence, radiative heat transfer, black and Grey surfaces shape factors, network analysis, heat exchanger performance, LMTD and NTU methods.
(4) Thermodynamics:
Zeroth, fact and second laws of thermodynamics, thermodynamic system and processes, irreversibility and availability, behavior of ideal and real gases, properties of pure substances, calculation of work and heat in ideal processes. Analysis of thermodynamics cycles related to energy conversion. Carnot, Rankine, Otto, Diesel, Brayton and Vapour compression cycle.
(5) Steam engineering:
Steam generators, Steam engines, steam turbines-impulse and reaction, velocity diagrams, compounding, reheat factor.
(6) I.C. Engines:
Requirements and suitability of fuels in IC engines, fuel ratings, fuel- air mixture requirements, normal combustion in SI and CI engines, engine performance calculations, components of gas turbine.
(7) Reciprocating Air Compressor:
Isothermal, adiabatic and polytropic compression, staging the compression process, inter cooling and after cooling, minimum work requirement, volumetric efficiency. Centrifugal and axial flow compressors.
(8) Refrigeration and air-conditioning:
Refrigerant compressors, expansion devices, condensers and evaporators, properties of moist air, psychometric chart, basic psychometric processes.
MANUFACTURING AND INDUSTRIAL ENGINEERING
(1) Engineering materials:
Structure and properties of engineering materials and their applications, heat treatment.
(2) Metal casting:
Casting processes- pattern making, moulds and cores, solidification, design of casting, casting defects.
(3) Metal working:
Stress-strain diagrams for ductile and brittle material, plastic deformation, mechanisms, fundamentals of hot and cold working processes-forging, extrusion, wire drawing, sheet metal working, punching, blanking, bending, deep drawing, coining and spinning.
(4) Machining Processes and Machine Tool Operation:
Mechanics of metal cutting, single and multipoint cutting tools, geometry and machining aspects, tool life, machinability, economics of machining, non- traditional machining processes.
(5) Metrology and Inspection:
Limits, fits and tolerances, linear and angular measurements, comparators, gauge design interferometry,form and finish measurement, measurement of screw threads, alignment and testing methods.
(6) Tool Engineering:
Principles of work holding, design of jigs and fixtures, design of press working tools.
(7) Manufacturing Analysis:
Part-print analysis, tolerance analysis in manufactureing and assembly, time and cost analysis.
(8) Computer Integrated Manufacturing:
Basic concepts of CAD, CAM , Group technology.
(9) Work Study:
Method study, work measurement time study, work sampling, job evaluation, merit rating.
(10) Production planning and control:
Forecasting models, aggregate production planning, master scheduling, materials requirements planning.
(11) Inventory control:
Deterministic and probabilistic models, safety stock inventory control systems.
(12) Operations Research:
Linear programming, simplex and duplex method, transportation, assignment, network flow models, simple queuing models, PERT and CPM.
ENGINEERING MATHEMATICS
(1) Linear Algebra:
Algebra of matrices, system of linear equations, eigen values and eigen vectors
(2) Calculus:
Taylor series, fourier series, partial derivatives, total derivatives, definite and improper integrals, multiple integrals
(3) Vector Calculus:
Gradient, divergence and curl, line and surface integrals, Green, Gauss, and Stokes theorem
(4) Differential Equations:
Linear ODE's, First order non-linear ODE's, initial and boundary value problems, Laplace Transform, PDE's-laplace, wave and diffusion equations.
(5) Numerical methods:
Solution of system of linear equations, interpolation, numerical integration, newton-raphson method, runge-kutta method.
(6) Probability and statics:
Gaussian, Weibul distribution and their properties, method of least squares , regrassion analysis, analysis of variance.
General Aptitude (GA)
Verbal Ability: English grammar, sentence completion, verbal analogies, word groups, instructions, critical reasoning and verbal deduction.
Numerical Ability: Numerical computation, numerical estimation, numerical reasoning and data interpretation.
(1) Engineering Mechanics:
Equivalent force systems, free-body concepts, equations of equilibrium, trusses and frames, virtual work and minimum potential energy. Kinematics and dynamics of particles and rigid bodies, impulse and momentum , energy methods, central force motion.
(2) Strength of Materials:
Stress and strain, Elastic constants, stress-strain relationship, Mohr's circle, deflection of beams, bending and shear stress, shear force and bending moment diagrams, torsion of circular shafts, thin thick cylinders, Euler's theory of columns, strain energy methods, thermal stress.
(3) Theory of machines:
Analysis of plane mechanisms, dynamic analysis of slider-crank mechanism, planer cams and followers, gear tooth profiles, kinematics and design of gears, governors and flywheels, balancing of reciprocating and rotating masses.
(4) Vibrations:
Free and forced vibrations of single degree freedom systems, effect of damping, vibration isolation, resonance, critical speed shafts.
(5) Design of Machine Elements:
Designing for statics and dynamic loading, fatigue strength, failure theories, design of bolted, riveted and welded joints, design of shafts and keys, design of spur gears, brakes and clutches, rolling and sliding contact bearings , belt, ropes and chain drives.
THERMAL SCIENCE AND ENGINEERING
(1) Fluid Mechanics:
Fluid properties, fluid statics, manometer, buoyancy, control-volume analysis of mass, momentum and energy, fluid acceleration, differential equation of continuity and momentum. Bernouli's equation. Viscous flow of incompressible fluids; boundary layer, flow through pipes, head losses in pipes, bends etc.
(2) Turbo machines:
velocity triangles Euler's equation, specific speed, Pelton wheel, centrifugal pump, Francis and Kaplan turbines.
(3) Heat-Transfer:
Modes of heat transfer, one dimensional heat conduction, resistance concept, electrical analogy, unsteady heat conduction, fins, dimensionless parameters in free and forced convective heat layer, effect of turbulence, radiative heat transfer, black and Grey surfaces shape factors, network analysis, heat exchanger performance, LMTD and NTU methods.
(4) Thermodynamics:
Zeroth, fact and second laws of thermodynamics, thermodynamic system and processes, irreversibility and availability, behavior of ideal and real gases, properties of pure substances, calculation of work and heat in ideal processes. Analysis of thermodynamics cycles related to energy conversion. Carnot, Rankine, Otto, Diesel, Brayton and Vapour compression cycle.
(5) Steam engineering:
Steam generators, Steam engines, steam turbines-impulse and reaction, velocity diagrams, compounding, reheat factor.
(6) I.C. Engines:
Requirements and suitability of fuels in IC engines, fuel ratings, fuel- air mixture requirements, normal combustion in SI and CI engines, engine performance calculations, components of gas turbine.
(7) Reciprocating Air Compressor:
Isothermal, adiabatic and polytropic compression, staging the compression process, inter cooling and after cooling, minimum work requirement, volumetric efficiency. Centrifugal and axial flow compressors.
(8) Refrigeration and air-conditioning:
Refrigerant compressors, expansion devices, condensers and evaporators, properties of moist air, psychometric chart, basic psychometric processes.
MANUFACTURING AND INDUSTRIAL ENGINEERING
(1) Engineering materials:
Structure and properties of engineering materials and their applications, heat treatment.
(2) Metal casting:
Casting processes- pattern making, moulds and cores, solidification, design of casting, casting defects.
(3) Metal working:
Stress-strain diagrams for ductile and brittle material, plastic deformation, mechanisms, fundamentals of hot and cold working processes-forging, extrusion, wire drawing, sheet metal working, punching, blanking, bending, deep drawing, coining and spinning.
(4) Machining Processes and Machine Tool Operation:
Mechanics of metal cutting, single and multipoint cutting tools, geometry and machining aspects, tool life, machinability, economics of machining, non- traditional machining processes.
(5) Metrology and Inspection:
Limits, fits and tolerances, linear and angular measurements, comparators, gauge design interferometry,form and finish measurement, measurement of screw threads, alignment and testing methods.
(6) Tool Engineering:
Principles of work holding, design of jigs and fixtures, design of press working tools.
(7) Manufacturing Analysis:
Part-print analysis, tolerance analysis in manufactureing and assembly, time and cost analysis.
(8) Computer Integrated Manufacturing:
Basic concepts of CAD, CAM , Group technology.
(9) Work Study:
Method study, work measurement time study, work sampling, job evaluation, merit rating.
(10) Production planning and control:
Forecasting models, aggregate production planning, master scheduling, materials requirements planning.
(11) Inventory control:
Deterministic and probabilistic models, safety stock inventory control systems.
(12) Operations Research:
Linear programming, simplex and duplex method, transportation, assignment, network flow models, simple queuing models, PERT and CPM.
ENGINEERING MATHEMATICS
(1) Linear Algebra:
Algebra of matrices, system of linear equations, eigen values and eigen vectors
(2) Calculus:
Taylor series, fourier series, partial derivatives, total derivatives, definite and improper integrals, multiple integrals
(3) Vector Calculus:
Gradient, divergence and curl, line and surface integrals, Green, Gauss, and Stokes theorem
(4) Differential Equations:
Linear ODE's, First order non-linear ODE's, initial and boundary value problems, Laplace Transform, PDE's-laplace, wave and diffusion equations.
(5) Numerical methods:
Solution of system of linear equations, interpolation, numerical integration, newton-raphson method, runge-kutta method.
(6) Probability and statics:
Gaussian, Weibul distribution and their properties, method of least squares , regrassion analysis, analysis of variance.
General Aptitude (GA)
Verbal Ability: English grammar, sentence completion, verbal analogies, word groups, instructions, critical reasoning and verbal deduction.
Numerical Ability: Numerical computation, numerical estimation, numerical reasoning and data interpretation.
Monday, December 13, 2010
Engineering Mechanics Objective Links
Mechanics Objective With Answers
Engineering Mechanics 2008 Objective Paper
Engineering Mechanics 2008 Objective Paper - key
Applied Mechanics 2008 Objective Paper
Applied Mechanics 2008 Objective Paper - key
Classical Mechanics 2008 Objective Paper
Classical Mechanics 2008 Objective Paper - key
1.Mechanics Objective Model Papers
Engineering Mechanics 2008 Objective Paper
Engineering Mechanics 2008 Objective Paper - key
Applied Mechanics 2008 Objective Paper
Applied Mechanics 2008 Objective Paper - key
Classical Mechanics 2008 Objective Paper
Classical Mechanics 2008 Objective Paper - key
1.Mechanics Objective Model Papers
Saturday, October 9, 2010
R09 - ENGINEERING MECHANICS
I Year B.Tech.
UNIT – I
Introduction to Engineering. Mechanics – Basic Concepts.
Systems of Forces : Coplanar Concurrent Forces – Components in Space – Resultant – Moment of Force
and its Application – Couples and Resultant of Force Systems.
UNIT – II
Equilibrium of Systems of Forces : Free Body Diagrams, Equations of Equilibrium of Coplanar Systems,
Spatial Systems for concurrent forces. Lamis Theorem, Graphical method for the equilibrium of coplanar
forces, Converse of the law of Triangle of forces, converse of the law of polygon of forces condition of
equilibrium.
UNIT – III
Centroid : Centroids of simple figures (from basic principles ) – Centroids of Composite Figures
Centre of Gravity : Centre of gravity of simple body (from basis principles), centre of gravity of composite
bodies, pappus theorem.
UNIT – IV
Area moment of Inertia : Definition – Polar Moment of Inertia, Transfer Theorem, Moments of Inertia of
Composite Figures, Products of Inertia, Transfer Formula for Product of Inertia.
Mass Moment of Inertia : Moment of Inertia of Masses, Transfer Formula for Mass Moments of Inertia,
mass moment of inertia of composite bodies.
UNIT – V
Analysis of perfect frames ( Analytical Method) – Types of Frames – Assumptions for forces in members of a
perfect frame, Method of joints, Method of sections, Force table, Cantilever Trusses, Structures with one end
hinged and the other freely supported on rollers carrying horizontal or inclined loads.
UNIT – VI
Kinematics : Rectilinear and Curvilinear motions – Velocity and Acceleration – Motion of Rigid Body –
Types and their Analysis in Planar Motion.
Kinetics : Analysis as a Particle and Analysis as a Rigid Body in Translation – Central Force Motion –
Equations of Plane Motion – Fixed Axis Rotation – Rolling Bodies.
UNIT – VII
Work – Energy Method : Equations for Translation, Work-Energy Applications to Particle Motion,
Connected System-Fixed Axis Rotation and Plane Motion. Impulse momentum method.
UNIT – VIII
Principle of virtual work: Equilibrium of ideal systems, efficiency of simple machines, stable and unstable
Equilibriums
TEXT BOOKS :
1. Engineering. Mechanics / Timoshenko & Young.
2. Engineering. Mechanics / S.S. Bhavikatti & J.G. Rajasekharappa
REFERENCES :
1. Engineering Mechanics / Fedinand . L. Singer / Harper – Collins.
2. Engineering. Mechanics / Irving. H. Shames Prentice – Hall.
3. Engineering. Mechanics Umesh Regl / Tayal.
4. Engineering. Mechanics / R.V. Kulkarni & R.D. Askhevkar
5. Engineering. Mechanics/Khurmi/S.Chand.
6. Engineering. Mechanics / KL Kumar / Tata McGraw Hill.
UNIT – I
Introduction to Engineering. Mechanics – Basic Concepts.
Systems of Forces : Coplanar Concurrent Forces – Components in Space – Resultant – Moment of Force
and its Application – Couples and Resultant of Force Systems.
UNIT – II
Equilibrium of Systems of Forces : Free Body Diagrams, Equations of Equilibrium of Coplanar Systems,
Spatial Systems for concurrent forces. Lamis Theorem, Graphical method for the equilibrium of coplanar
forces, Converse of the law of Triangle of forces, converse of the law of polygon of forces condition of
equilibrium.
UNIT – III
Centroid : Centroids of simple figures (from basic principles ) – Centroids of Composite Figures
Centre of Gravity : Centre of gravity of simple body (from basis principles), centre of gravity of composite
bodies, pappus theorem.
UNIT – IV
Area moment of Inertia : Definition – Polar Moment of Inertia, Transfer Theorem, Moments of Inertia of
Composite Figures, Products of Inertia, Transfer Formula for Product of Inertia.
Mass Moment of Inertia : Moment of Inertia of Masses, Transfer Formula for Mass Moments of Inertia,
mass moment of inertia of composite bodies.
UNIT – V
Analysis of perfect frames ( Analytical Method) – Types of Frames – Assumptions for forces in members of a
perfect frame, Method of joints, Method of sections, Force table, Cantilever Trusses, Structures with one end
hinged and the other freely supported on rollers carrying horizontal or inclined loads.
UNIT – VI
Kinematics : Rectilinear and Curvilinear motions – Velocity and Acceleration – Motion of Rigid Body –
Types and their Analysis in Planar Motion.
Kinetics : Analysis as a Particle and Analysis as a Rigid Body in Translation – Central Force Motion –
Equations of Plane Motion – Fixed Axis Rotation – Rolling Bodies.
UNIT – VII
Work – Energy Method : Equations for Translation, Work-Energy Applications to Particle Motion,
Connected System-Fixed Axis Rotation and Plane Motion. Impulse momentum method.
UNIT – VIII
Principle of virtual work: Equilibrium of ideal systems, efficiency of simple machines, stable and unstable
Equilibriums
TEXT BOOKS :
1. Engineering. Mechanics / Timoshenko & Young.
2. Engineering. Mechanics / S.S. Bhavikatti & J.G. Rajasekharappa
REFERENCES :
1. Engineering Mechanics / Fedinand . L. Singer / Harper – Collins.
2. Engineering. Mechanics / Irving. H. Shames Prentice – Hall.
3. Engineering. Mechanics Umesh Regl / Tayal.
4. Engineering. Mechanics / R.V. Kulkarni & R.D. Askhevkar
5. Engineering. Mechanics/Khurmi/S.Chand.
6. Engineering. Mechanics / KL Kumar / Tata McGraw Hill.
R09 - ENGINEERING DRAWING
I Year B.Tech.
UNIT – I
INTRODUCTION TO ENGINEERING DRAWING : Principles of Engineering Graphics and their Significance
– Drawing Instruments and their Use – Conventions in Drawing – Lettering – BIS Conventions. Curves used
in Engineering Practice & their Constructions :
a) Conic Sections including the Rectangular Hyperbola – General method only.
{Ellipse,Parabola,Hyperbola,Rectangular Hyperbola}
b) Cycloid, Epicycloid and Hypocycloid
c) Involute.
d) Scales: Different types of Scales, Plain scales,Diagonal scales,vernier scales, comparative scales, scales of chords.
UNIT – II
DRAWING OF PROJECTIONS OR VIEWS ORTHOGRAPHIC PROJECTION IN FIRST ANGLE
PROJECTION: Principles of Orthographic Projections – Conventions – First and Third Angle, Projections of
Points and Lines inclined to both planes, True lengths, traces.
UNIT – III
PROJECTIONS OF PLANES & SOLIDS: Projections of regular Planes, auxiliary planes and Auxiliary
projection inclined to both planes. Projections of Regular Solids inclined to both planes – Auxiliary Views.
UNIT – IV
SECTIONS AND SECTIONAL VIEWS:- Right Regular Solids – Prism, Cylinder, Pyramid, Cone – Auxiliary views.
DEVELOPMENT AND INTERPENETRATION OF SOLIDS: Development of Surfaces of Right, Regular
Solids – Prisms, Cylinder, Pyramid Cone and their parts. Interpenetration of Right Regular Solids
UNIT – V
INTERSECTION OF SOLIDS:- Intersection of Cylinder Vs Cylinder, Cylinder Vs Prism, Cylinder Vs Cone.
UNIT - VI
ISOMETRIC PROJECTIONS : Principles of Isometric Projection – Isometric Scale – Isometric Views–
Conventions – Isometric Views of Lines, Plane Figures, Simple and Compound Solids – Isometric Projection
of objects having non- isometric lines. Isometric Projection of Spherical Parts.
UNIT –VII
TRANSFORMATION OF PROJECTIONS : Conversion of Isometric Views to Orthographic Views –Conventions.
UNIT – VIII
PERSPECTIVE PROJECTIONS : Perspective View : Points, Lines, Plane Figures and Simple Solids,
Vanishing Point Methods (General Method only).
TEXT BOOKS :
1. Engineering Drawing, N.D. Bhat / Charotar
2. Engineering Drawing and Graphics, Venugopal / New age.
3. Engineering Drawing – Basant Agrawal, TMH
REFERENCES :
1. Engineering drawing – P.J. Shah.S.Chand.
2. Engineering Drawing, Narayana and Kannaiah / Scitech publishers.
3. Engineering Drawing- Johle/Tata Macgraw Hill.
4. Computer Aided Engineering Drawing- Trymbaka Murthy- I.K. International.
5. Engineering Drawing – Grower.
6. Engineering Graphics for Degree – K.C. John.
UNIT – I
INTRODUCTION TO ENGINEERING DRAWING : Principles of Engineering Graphics and their Significance
– Drawing Instruments and their Use – Conventions in Drawing – Lettering – BIS Conventions. Curves used
in Engineering Practice & their Constructions :
a) Conic Sections including the Rectangular Hyperbola – General method only.
{Ellipse,Parabola,Hyperbola,Rectangular Hyperbola}
b) Cycloid, Epicycloid and Hypocycloid
c) Involute.
d) Scales: Different types of Scales, Plain scales,Diagonal scales,vernier scales, comparative scales, scales of chords.
UNIT – II
DRAWING OF PROJECTIONS OR VIEWS ORTHOGRAPHIC PROJECTION IN FIRST ANGLE
PROJECTION: Principles of Orthographic Projections – Conventions – First and Third Angle, Projections of
Points and Lines inclined to both planes, True lengths, traces.
UNIT – III
PROJECTIONS OF PLANES & SOLIDS: Projections of regular Planes, auxiliary planes and Auxiliary
projection inclined to both planes. Projections of Regular Solids inclined to both planes – Auxiliary Views.
UNIT – IV
SECTIONS AND SECTIONAL VIEWS:- Right Regular Solids – Prism, Cylinder, Pyramid, Cone – Auxiliary views.
DEVELOPMENT AND INTERPENETRATION OF SOLIDS: Development of Surfaces of Right, Regular
Solids – Prisms, Cylinder, Pyramid Cone and their parts. Interpenetration of Right Regular Solids
UNIT – V
INTERSECTION OF SOLIDS:- Intersection of Cylinder Vs Cylinder, Cylinder Vs Prism, Cylinder Vs Cone.
UNIT - VI
ISOMETRIC PROJECTIONS : Principles of Isometric Projection – Isometric Scale – Isometric Views–
Conventions – Isometric Views of Lines, Plane Figures, Simple and Compound Solids – Isometric Projection
of objects having non- isometric lines. Isometric Projection of Spherical Parts.
UNIT –VII
TRANSFORMATION OF PROJECTIONS : Conversion of Isometric Views to Orthographic Views –Conventions.
UNIT – VIII
PERSPECTIVE PROJECTIONS : Perspective View : Points, Lines, Plane Figures and Simple Solids,
Vanishing Point Methods (General Method only).
TEXT BOOKS :
1. Engineering Drawing, N.D. Bhat / Charotar
2. Engineering Drawing and Graphics, Venugopal / New age.
3. Engineering Drawing – Basant Agrawal, TMH
REFERENCES :
1. Engineering drawing – P.J. Shah.S.Chand.
2. Engineering Drawing, Narayana and Kannaiah / Scitech publishers.
3. Engineering Drawing- Johle/Tata Macgraw Hill.
4. Computer Aided Engineering Drawing- Trymbaka Murthy- I.K. International.
5. Engineering Drawing – Grower.
6. Engineering Graphics for Degree – K.C. John.
Friday, October 8, 2010
Rules of Resolution of a Force
Very Important Rules to follow for Mechanics
Nallimilli’s Law1:
If Force is away from the origin ( intersection of co – ordinate axis X&Y ) and making an angle with either of the axis, the corresponding axis component is always “cos” the opposite axis component is always “sin” using the sign symbols of corresponding quadrant.
Explanation: In above diagram P is in first quadrant, the sign symbols for both components are positive. If an angle makes with X-axis then the resolution component of P corresponding to X-axis is Pcosθ, opposite component is Psinθ related to Y-axis, if an angle makes with Y-axis then the resolution component of P corresponding to Y-axis is Pcosθ, opposite component is Psinθ related to X-axis
If angle with X-Axis Px = + Pcosθ, Py= +Psinθ ; If angle with Y-Axis Px = + Psinθ, Py= +Pcosθ
Nallimilli’s Law2:
If Force is towards the origin ( intersection of co – ordinate axis X&Y ) and making an angle with either of the axis, shift the force component into opposite quadrant and away from the intersection of co-ordinate axis, and perfectly shift the angle also with the same axis at the
initial quadrant position then implement law1
Explanation: In above diagram P is in first quadrant & towards origin, shifts P to opposite quadrant i.e. third quadrant, the sign symbols for both components are Negative. If an angle makes with X-axis then shift the angle with same X-axis in opposite quadrant, using law1 resolution component of P corresponding to X-axis is Pcosθ, opposite component is Psinθ related to Y-axis, If an angle makes with Y-axis then shift the angle with same Y-axis in opposite quadrant, using law1 resolution component of P corresponding to Y-axis is Pcosθ, opposite component is Psinθ related to X-axis
If angle with X-Axis in first quadrant after shifting same angle with X-axis in third quadrant
Px = - Pcosθ, Py = -Psinθ
If angle with Y-Axis in first quadrant after shifting same angle with Y-axis in third quadrant
Px = - Psinθ, Py = -Pcosθ
Resolution component of force P Px Py
With X-axis in first quadrant + Pcosθ +Psinθ
With Y-axis in first quadrant +Psinθ + Pcosθ
With X-axis in second quadrant -Pcosθ +Psinθ
With Y-axis in second quadrant -Psinθ + Pcosθ
With X-axis in third quadrant -Pcosθ -Psinθ
With Y-axis in third quadrant -Psinθ -Pcosθ
With X-axis in third quadrant +Pcosθ -Psinθ
With Y-axis in third quadrant +Psinθ -Pcosθ
Nallimilli’s Law1:
If Force is away from the origin ( intersection of co – ordinate axis X&Y ) and making an angle with either of the axis, the corresponding axis component is always “cos” the opposite axis component is always “sin” using the sign symbols of corresponding quadrant.
Explanation: In above diagram P is in first quadrant, the sign symbols for both components are positive. If an angle makes with X-axis then the resolution component of P corresponding to X-axis is Pcosθ, opposite component is Psinθ related to Y-axis, if an angle makes with Y-axis then the resolution component of P corresponding to Y-axis is Pcosθ, opposite component is Psinθ related to X-axis
If angle with X-Axis Px = + Pcosθ, Py= +Psinθ ; If angle with Y-Axis Px = + Psinθ, Py= +Pcosθ
Nallimilli’s Law2:
If Force is towards the origin ( intersection of co – ordinate axis X&Y ) and making an angle with either of the axis, shift the force component into opposite quadrant and away from the intersection of co-ordinate axis, and perfectly shift the angle also with the same axis at the
initial quadrant position then implement law1
Explanation: In above diagram P is in first quadrant & towards origin, shifts P to opposite quadrant i.e. third quadrant, the sign symbols for both components are Negative. If an angle makes with X-axis then shift the angle with same X-axis in opposite quadrant, using law1 resolution component of P corresponding to X-axis is Pcosθ, opposite component is Psinθ related to Y-axis, If an angle makes with Y-axis then shift the angle with same Y-axis in opposite quadrant, using law1 resolution component of P corresponding to Y-axis is Pcosθ, opposite component is Psinθ related to X-axis
If angle with X-Axis in first quadrant after shifting same angle with X-axis in third quadrant
Px = - Pcosθ, Py = -Psinθ
If angle with Y-Axis in first quadrant after shifting same angle with Y-axis in third quadrant
Px = - Psinθ, Py = -Pcosθ
Resolution component of force P Px Py
With X-axis in first quadrant + Pcosθ +Psinθ
With Y-axis in first quadrant +Psinθ + Pcosθ
With X-axis in second quadrant -Pcosθ +Psinθ
With Y-axis in second quadrant -Psinθ + Pcosθ
With X-axis in third quadrant -Pcosθ -Psinθ
With Y-axis in third quadrant -Psinθ -Pcosθ
With X-axis in third quadrant +Pcosθ -Psinθ
With Y-axis in third quadrant +Psinθ -Pcosθ
Sunday, October 3, 2010
Foundation of Non Circuit Engineering (Engineering Mechanics)
Before Mechanics
Measurement of angel’s : There are two common systems of measuring angel’s
1.sexagesimal measure : According to this system, divide a right angle 90 into equal parts called degrees. Each degree is divided into sixty equal parts called minutes and each minute is divided into sixty equal parts called seconds. Denoting one degree, one minute and one second by the symbols 10 1’1”.
2. Circular measure : The unit of measurement is called radian . ∏ is an irrational number. Its approximate value is 22/7. Its value correct to 5 decimal places is 3.14159. Sometimes1/∏ value also required & is given by 0.31831.
Relation between degree & radian {1 radian = 1800 x 1/∏ = 57017’44.8”}; 10 = ∏ /180 radian
Formulas from Trigonometry:
1. sin2A + cos2A = 1 ; sin2A = 1- cos2A ; cos2A = 1- sin2A
2. 1+tan2A = sec2A ; tan2A = sec2A -1 ; tan2A - sec2A = 1
3. sin(A+B) = sin A . cos B + cos A . sin B
4. sin(A - B) = sin A . cos B - cos A . sin B
5. cos(A+B) = cos A . cos B – sin A . sin B
6. cos(A - B) = cos A . cos B + sin A . sin B
7. sin(A+B) . sin(A - B) = sin2A-sin2B = cos2B- cos2A
8. cos(A+B) . cos(A - B) = cos2A – sin2B = cos2B-sin2A
9. sin2θ = 2 sinθ cosθ = 2tan θ / 1+tan2θ
10. cos2θ = cos2θ – sin2θ =1- tan2θ / 1+tan2θ = 1-2 Sin2θ =2cos2θ -1
Formulas from Differentiation:
1. y = xn, dy/dx = nxn-1
2. y = ex, dy/dx = ex
3. y = log x, dy/dx = 1/x
4. y = ax, dy/dx = ax log a
5. y = sinx , dy/dx = cos x
6. y = cosx, dy/dx = - sinx
Scalars & Vectors
Those quantities which have only magnitude and are not related to any direction in space are called scalars. Whereas those which have both magnitude and direction are called vector quantities.
1. Vectors are said to be like vectors when they have the same sense of direction, unlike vectors when they are in opposite direction.
2. When two or more vectors are said to be collinear vectors when they act along the same line of action & parallel vectors when they are in parallel lines
3. Three or more vectors are said to be coplanar when they are parallel to the same plane or lie in the same plane whatever their magnitudes be (**two vectors are always coplanar)
4. Two vectors are said to be equal when they have the same length(magnitude &are parallel having the same sense of direction)are called as equal vectors.
5. If the origin and terminal points of a vector coincide, then it is said to be a zero vector
6. { Unit vector = Force vector / Magnitude of vector}
7. The vectors having the same initial point are call co –initial vectors.
8. A vector drawn parallel to a given vector through a specified point in space is called a localized vector. But if the origin of vectors is not specified the vectors are called free vectors.
Formulas from Vectors
1. a.b = b.a = ab cosθ
if the scalar product is of two vectors is zero, then at least one of the vectors is a zero vector or they are perpendicular.
2. a.(b+c) = a.b + a.c
3. i2=j2=k2=1
4. i.j=j.k=k.i=0
5. a x b ≠ b x a but a x b = - b x a
6. i x i = j x j = k x k =0
7. i x j = k = - j x i ; j x k = i = - k x j; k x i = - i x k
8. if a = a1i+a2j+a3j ; b = b1i+b2j+b3k then a x b is given by
a x b = (a2b3 – a3b2) i +(a3b1-a1b3) j + (a1b2 – a2b1) k
Conversion Equivalents:
Length 1in = 2.540cm ; 1ft =12in =30.48cm
1mile=5280ft=1.609km
Force 1lb= 0.4536kg = 4.448N
Velocity 88fps=60mph=96.54km/hr
Acceleration g = 32.2fps2 = 9.81m/s2
Pressure 1atm = 14.7psi=760mmof Hg= 1.013 x 105 N/m2
Volume 1cuft=7.481gallons=28.32litres
Sign Conventions:
| | I Quadrant | II Quadrant | III Quadrant | IV Quadrant |
| X -Axis | + | - | - | + |
| y-Axis | + | + | - | - |
Fresh Engineers are Innovative Designers for Future
Hai! Young Engineers
we warm welcomes you, into the designers of science and technology, with your innovative thoughts and implementation of technology to greater extent and useful to human life and environment. Suggestions and comments are welcome.visit frequently this site for tutorials,assignments,question papers,objective type etc... Best of luck every one
yours truly
N.SRINIVASA REDDYM.TECH
9849964005
we warm welcomes you, into the designers of science and technology, with your innovative thoughts and implementation of technology to greater extent and useful to human life and environment. Suggestions and comments are welcome.visit frequently this site for tutorials,assignments,question papers,objective type etc... Best of luck every one
yours truly
N.SRINIVASA REDDYM.TECH
9849964005
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