CHAP1 General principle

Mechanics Mechanics Definition Definition A physical science studies the state of rest or motion of bodies subjected to the action of forces A physical science studies the state of rest or motion of bodies subjected to the action of forces

CHAP1 General principle Classfication Classfication Mechanics Rigid BodyDeformable Body Fluids Statics Dynamics Incompressible Compressible Deformation/ stress Material Behavior

CHAP1 General principle Fundamental Concepts Fundamental Concepts Basic Quantities Basic Quantities Length Length The position of a point The position of a point The size of a physical system The size of a physical system Time Time A succession of events A succession of events Mass Mass A property of matter A property of matter Force Force A push or pull exerted by one body on another A push or pull exerted by one body on another

CHAP1 General principle Idealizations or Models Idealizations or Models Simplify application of the theory of mechanics Simplify application of the theory of mechanics Particle 質點 Particle 質點 A particle has a mass with a neglected size A particle has a mass with a neglected size Ex: orbital motion of earth Physical problem model Solution Rr r<<R Earth a particle Earth a particle

CHAP1 General principle Rigid body 剛體 Rigid body 剛體 A rigid body is a combination of a large number of particles in which all particles remain at a fixed distance from one another both before and after applying a load A rigid body is a combination of a large number of particles in which all particles remain at a fixed distance from one another both before and after applying a load p2 p1 p3 a b c p1 p3 p2 b’b’ c’c’ a’a’ F F beforeafter

CHAP1 General principle Concentrated Force 集中力 Concentrated Force 集中力 A force is assumed to act at a point in a body A force is assumed to act at a point in a body F Real physical problemIdealization model Loading area <<< the size of body Distributed load Concentrated force

CHAP1 General principle Newton's Three Laws of Motion Newton's Three Laws of Motion First law First law Second law Second law Third law Third law F M =0 F=m. a F action =-F reaction

CHAP1 General principle Unit of Measurement Unit of Measurement Quantity SI Units FPS Units Quantity SI Units FPS Units Length m ft Time s s Mass kg Slug(lbs 2 /ft) Force N (kgm/s 2 ) 1b

CHAP1 General principle International System of Units International System of UnitsPrefixes Exponential form prefix SI Symbol Multiple giga G giga G mega M mega M kilo K kilo K Submultiples milli m milli m micro micro nano n nano n

CHAP1 General principle Numerical calculations Numerical calculations Dimensional Homogeneity Dimensional Homogeneity Each terms of any equation must be expressed in the same unit Each terms of any equation must be expressed in the same unit 例 : 例 : Significant figures 有效數字 Significant figures 有效數字 A significant figure is any digit, including a zero, provided it is not used to specify the location of the decimal point for the number. (Ex & significant figures) A significant figure is any digit, including a zero, provided it is not used to specify the location of the decimal point for the number. (Ex & significant figures) Numbers begin or end with zeros, then the number should be reported using power of 10. (Ex. 40, 4(10) 1 or 0.4(10 2 )) Numbers begin or end with zeros, then the number should be reported using power of 10. (Ex. 40, 4(10) 1 or 0.4(10 2 ))

CHAP1 General principle Rounding off Numbers 四捨五入 Rounding off Numbers 四捨五入 The accuracy of the calculated result < the accuracy of the problem data The accuracy of the calculated result < the accuracy of the problem data Rules for rounding off a number to n significant figure Rules for rounding off a number to n significant figure (n+1)th digit Round off Rule Example <5 Drop the (n+1)th digit and others following it 2.326(n=2) Ans.: 2.3 =5 with zeros following it Round off the nth digit to an even number (n=3) Ans.: >5 or =5 with no zeros following it Increase the nth digit by 1 Drop (n+1)th digit and others following it (n=3) Ans.: (n=3)Ans.:566

CHAP1 General principle Calculations: Calculations: In general we round off final answers to three significant figures since the data for geometry, loads, etc, are often reported with this accuracy. In general we round off final answers to three significant figures since the data for geometry, loads, etc, are often reported with this accuracy.