Chapter one A. Lecturer Saddam K. Kwais Introduction to statics 1-1 What Is Mechanics? Mechanics can be defined as that science which describes and predicts the conditions of rest or motion of bodies under the action of forces. Mechanics Rigid bodies Statics Deformable bodies Dynamics Fluid Compresible Incompresible Statics deals with bodies at rest or moving with acceleration equal is zero. Dynamics deals with bodies at motion where acceleration ≠ 0. 1/2 Fundamental Concepts and Applications The study of elementary mechanics rests on six fundamental principles based on experimental evidence. 1. The parallelogram law for the addition of forces: This states that two forces acting on a particle may be replaced by a single force , called their resultant, obtained by drawing the diagonal of the parallelogram which has sides equal to the given forces. 2. The principles of transmissibility: This states that the conditions of equilibrium or of motion of a rigid body will remain unchanged if a force acting at a given point of the rigid body is replaced by a force of the same magnitude and same 1 Chapter one A. Lecturer Saddam K. Kwais Introduction to statics direction, but acting at different point. Provided that the two forces have the line of action. 3. Newton's three fundamental laws: i. First law If the resultant force acting on a particle is zero, the particle remain at rest (if originally at rest) or will move with constant speed in a straight line (if originally is motion). ii. Second law If the resultant force acting on a particle is not zero, the particle will have an acceleration proportional to the magnitude of the resultant and in the direction of this resultant force. = . (1.1) = . , = . , = . iii. Third law The forces of action and reaction between bodies in contact have the same magnitude, same line of action, and opposite sense. 4. Newton's law of gravitation: This states that two particles of mass M and m are mutually attracted with equal and opposite forces F and –F Fig. (1-1) of magnitude F given by the formula = . . (1.2) Where F = the mutual force of attraction between two particles G = universal constant called the constant of gravitation. M, m = the masses of the two particles r = distance between the two particles. The magnitude W of the weight of a particle of mass m may be expressed as: 2 Chapter one A. Lecturer Saddam K. Kwais Introduction to statics = . (1.3) m r F -F M Fig. (1-1) 1/3 System of Units System of Units International System of Units (SI Units) U.S. Customary Units In mechanics we use four fundamental quantities called dimensions. These are length, mass, force, and time. The four fundamental dimensions and their units and symbols in the two systems are summarized in the following table. SI UNITS U.S. CUSTOMARY UNITS Dimensional Quantity Symbol Unit Symbol unit symbol Length L meter m foot ft Mass M Kilogram kg slug - Time T Second s second sec 3 Chapter one Force A. Lecturer Saddam K. Kwais F Newton N Introduction to statics Pound Ib International system of unit The unit of force is a derived unit. It is called the Newton (N) and is defined as the force which gives an acceleration of 1 m/s2 to a mass 1 kg Fig. (1-2) from Eq. (1.1) we write: = (1). (1 ⁄ ) = 1. ⁄ (1.4) a =1 m/s2 m = 1 kg F =1 N Fig. (1.2) The weight of the body, or the force of gravity exerted on the body, should, like any other force, be expressed in Newton. From Eq. (1.3) it follows that the weight of a body of mass 1 kg Fig. (1-3) is = . = (1). (9.81 ⁄ ) = 9.81(1.5) m = 1 kg a =9.81 m/s2 W =9.81 N Fig. (1.3) 4 Chapter one A. Lecturer Saddam K. Kwais Introduction to statics Exponential Form Prefix SI Symbol 109 106 103 giga mega kilo G M k 10-3 10-6 10-9 milli micro nano m µ n Multiple 1 000 000 000 1 000 000 1 000 Submultiples' 0.001 0.000 001 0.000 000 001 Units of Length 1dm = 0.1 m = 10-1 m 1cm = 0.01 m = 10-2 m 1mm = 0.001 m = 10-3 m Units of Area decimeter centimeter millimeter 1dm2 = (1dm)2 = (0.1 m)2 = 10-2 m2 1cm2 = (1cm)2 = (0.01 m)2 = 10-4 m2 1mm2 = (1mm)2 = (0.001 m)2= 10-6 m Units of Volume square Decimeter square Centimeter square Millimeter 1dm3 = (1dm)3 = (0.1 m)3 = 10-3 m3 1cm3 = (1cm)3 = (0.01 m)3 = 10-6 m3 1mm3 = (1mm)3 = (0.001 m)3= 10-9 m3 Cubic Decimeter Cubic Centimeter Cubic Millimeter U.S. Customary unit The unit of mass is a slug can be derived from the equation F = m.a after substituting 1 Ib and 1 ft/s2 for F and a respectively Fig. (1-4). We write F = m.a 1 Ib = (1 slug). (1 ft/s2) And obtain 1 = 1 ! = 1 !. ⁄"# (1.6) 1"#⁄ a =1 ft/s2 m = 1 slug (=1Ib.s2/ft) Fig. (1.4) 5 F =1 Ib Chapter one A. Lecturer Saddam K. Kwais Introduction to statics Other U.S. Customary units mile (mi) = 5280 ft inch (in) = (1/12) ft kilopound (kip) = 1000Ib Note: acceleration of gravity in U.S. Customary unit (g = 32.2 ft/s2) 1/4 Conversion from one system of unit to another Units of Length 1"# = 0.3048(1.7) 1 mi = 5280 ft = 5280 (0.3048) = 1609 m 1' = 1.609(1.8) 1 in = (1/12) ft = (1/12) (0.3048) = 0.0254 m 1'( = 25.4 = 2.54)(1.9) Units of Force 1*+(, = 0.4536(1.10) According to the equation (1.3) W=m.g 1 Ib = (0.4536 kg). (9.81 m/s2) = 4.448 kg. m/s2 1 ! = 4.448(1.11) Units of Mass 1 slug = 1 Ib . 1 s2/ft = (1 Ib)/(1ft/s2) = (4.448 N)/(0.3048 m/s2) = 14.59 N.s2/m 1 = 14.59(1.12) Example No.(1) : Converts the moment of force (M = 47 Ib. in) into SI Units. Solution : we use formulas (1.9) and (1.11) and write: = 47 !. '( = 47(4.448). (25.4) = 5310. = 5.31. -(. 6 Chapter one A. Lecturer Saddam K. Kwais Introduction to statics Example No.(2) : Converts the moment of force (M = 40 N. m) into U.S. Customary Units. Solution : we use formulas (1.7) and (1.11) and write: = 40. = (40. ). 1 ! 1"# /.. / 4.448 0.3048 = 29.5 !. "#-(. 7
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