Statics

1. 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

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

3. Idealizations • Particle • has mass, but a size that can be neglected • geometry of the body not involved in the analysis • 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 • a loading which is assumed to act at a point on a body

4. Units of measure • International System of Units (modern version of the metric system) - SI • US Customary System of Units – FPS • W = m g (g is the acceleration due to gravity, 9.81 m/s2 or 32.2 ft/s2) • Angular units may be expressed in radians

5. SI unit prefixes

6. Rules for use of units/symbols and prefixes • Never written with a plural “s” • 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) • μN2 = (μN)2 = μN * μN • When performing calculations, begin by representing numbers in terms of base units and/or derived units (50 kN)(60 nm) = (50)(103)(N) * (60)(10-9)(m) = 3 000 (10-6) N-m = 3 (103)(10-6) N-m = 3 N-mm • Compound prefixes should not by used (kμs) • Avoid use of prefix in denominator of composed units, except kg

7. Significant figures • 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 • 763,000 ??? if only four significant digits • Use scientific notation, 7.630 x 105, one digit to the left of decimal point with the remaining digits to the right • Use engineering notation, 0.7630 x 106 – the exponent is displayed in multiples of three (to facilitate conversion of SI units to those having an appropriate prefix)

8. 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 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) • 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

9. General procedure for analysis • 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. • 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). • Study the answer with technical judgment and common sense to determine whether or not it seems reasonable.