CHAP 1 General principle CHAP 1 General principle

CHAP 1 General principle

CHAP 1 General principle n Mechanics n Definition n A physical science studies the state of rest or motion of bodies subjected to the action of forces

CHAP 1 General principle n Classfication Mechanics Rigid Body Statics Deformable Body Dynamics Fluids Incompressible Deformation/ stress Material Behavior Compressible

CHAP 1 General principle n Fundamental Concepts n Basic Quantities n Length n n n Time n n A succession of events Mass n n The position of a point The size of a physical system A property of matter Force n A push or pull exerted by one body on another

CHAP 1 General principle n Idealizations or Models n Simplify application of theory of mechanics n Solution model Physical problem Particle質點 A particle has a mass with a neglected size Ex: orbital motion of earth n r<<R R r Earth a particle

CHAP 1 General principle F p 1 a p 2 n p 1 b c p 3 Rigid body 剛體 n b’ a’ p 2 F c’ p 3 A rigid body is a combination of a large number of particles in before after which all particles remain at a fixed distance from one another both before and after applying a load

CHAP 1 General principle n Concentrated Force 集中力 n A force is assumed to act at a point in a body F Distributed load Real physical problem Concentrated force Idealization model Loading area <<< the size of body

CHAP 1 General principle n Newton's Three Laws of Motion n First law F n Second law =0 M =0 F=m. a n Third law F action=-F reaction

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

CHAP 1 General principle n International System of Units Prefixes Exponential form prefix SI Symbol giga mega kilo G M K Multiple Submultiples milli micro nano m n

CHAP 1 General principle n Numerical calculations n Dimensional Homogeneity n n n Each terms of any equation must be expressed in the same unit 例: Significant figures 有效數字 n n 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. 5604 & 34. 52 4 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(102))

CHAP 1 General principle n Rounding off Numbers 四捨五入 n n The accuracy of the calculated result < the accuracy of the problem data 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 0. 8655(n=3) Ans. : 0. 866 >5 or =5 with no Increase the nth digit zeros following it by 1 Drop (n+1)th digit and others following it 0. 86551(n=3) Ans. : 0. 866 565. 5003(n=3) Ans. : 566

CHAP 1 General principle n Calculations: n In general we round off final answers to three significant figures since the data for geometry, loads, etc, are often reported with this accuracy.