Statics Statics is concerned with the equilibrium of bodies that are at rest or moving with a constant velocity Dynamics is concerned with bodies that are undergoing acceleration

Basic quantities used throughout mechanics Length Length –locates the position of a point in space –able to describe the size of a physical system Time Time –succession of events –statics problems are time independent Mass Mass –property of matter –provides quantitative measure of the resistance of matter to a change in velocity Force Force –“push” or “pull” exerted by one body on another –characterized by magnitude, direction, sense, and point of application

Idealizations Particle Particle –has mass, but a size that can be neglected –geometry of the body not involved in the analysis Rigid body Rigid body –can be considered a combination of a large number particles –particles remain at the same fixed distance from one another both before and after applying a load Concentrated force Concentrated force –a loading which is assumed to act at a point on a body

Units of measure International System of Units (modern version of the metric system) - SI International System of Units (modern version of the metric system) - SI US Customary System of Units – FPS US Customary System of Units – FPS W = m g W = m g (g is the acceleration due to gravity, 9.81 m/s 2 or 32.2 ft/s 2 ) Angular units may be expressed in radians Angular units may be expressed in radians quantitySIFPS length meter (m) foot (ft) time second (s) mass kilogram (kg) slug ((lb-s 2 )/ft) force Newton (N, (kg-m)/s 2 ) pound (lb)

SI unit prefixes multiple/submultiple exponential form prefix SI symbol gigaG megaM kilok millim microμ nanon

Rules for use of units/symbols and prefixes Never written with a plural “s” Never written with a plural “s” Always written in lowercase letters, except M, G, and units named after a person (i.e. Newton, N) Always written in lowercase letters, except M, G, and units named after a person (i.e. Newton, N) Quantities defined by several units which are multiples of one another are separated by a dot (a dash will be used in these slides, i.e. m-s represents meter-seconds, while ms represents milliseconds) Quantities defined by several units which are multiples of one another are separated by a dot (a dash will be used in these slides, i.e. m-s represents meter-seconds, while ms represents milliseconds) μN 2 = (μN) 2 = μN * μN μN 2 = (μN) 2 = μN * μN When performing calculations, begin by representing numbers in terms of base units and/or derived units When performing calculations, begin by representing numbers in terms of base units and/or derived units (50 kN)(60 nm) = (50)(10 3 )(N) * (60)(10 -9 )(m) = (10 -6 ) N-m = 3 (10 3 )(10 -6 ) N-m = 3 N-mm Compound prefixes should not by used (kμs) Compound prefixes should not by used (kμs) Avoid use of prefix in denominator of composed units, except kg Avoid use of prefix in denominator of composed units, except kg

Significant figures Accuracy of a number is specified by the number of significant figures it contains Accuracy of a number is specified by the number of significant figures it contains 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 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 763,000 ??? if only four significant digits 763,000 ??? if only four significant digits –Use scientific notation, x 10 5, one digit to the left of decimal point with the remaining digits to the right –Use engineering notation, x 10 6 – the exponent is displayed in multiples of three (to facilitate conversion of SI units to those having an appropriate prefix)

Rounding If the n + 1 digit is less than 5, the n + 1 digit and others following it are dropped If the n + 1 digit is less than 5, the n + 1 digit and others following it are dropped If the n + 1 digit is greater than 5 (or is equal to 5 with nonzero numbers following the 5), then increase the nth digit by 1 and drop the n + 1 digit and others following it If the n + 1 digit is greater than 5 (or is equal to 5 with nonzero numbers following the 5), then increase the nth digit by 1 and drop the n + 1 digit and others following it If the n + 1 digit is equal to 5 (with no numbers or zeroes following the 5) If the n + 1 digit is equal to 5 (with no numbers or zeroes following the 5) –And the nth digit is an even number, then the nth digit is not rounded up –And the nth digit is an odd number, then the nth digit is rounded up In text, the answers to problems are generally rounded down to three significant figures In text, the answers to problems are generally rounded down to three significant figures

General procedure for analysis Read the problem carefully and try to correlate the actual physical situation with the theory studied. Read the problem carefully and try to correlate the actual physical situation with the theory studied. Draw any necessary diagrams and tabulate the problem data. Draw any necessary diagrams and tabulate the problem data. Apply the relevant principles, generally in mathematical form. Apply the relevant principles, generally in mathematical form. Solve the necessary equations algebraically as far as practical, then making sure they are dimensionally homogeneous, use a consistent set of units and complete the solution numerically. Report the answer with no more significant figures than the accuracy of the given data (generally three significant figures for problems in this text). Solve the necessary equations algebraically as far as practical, then making sure they are dimensionally homogeneous, use a consistent set of units and complete the solution numerically. Report the answer with no more significant figures than the accuracy of the given data (generally three significant figures for problems in this text). Study the answer with technical judgment and common sense to determine whether or not it seems reasonable. Study the answer with technical judgment and common sense to determine whether or not it seems reasonable.