StaticsStatics

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

Dynamics is concerned with bodies that are undergoing Dynamics is concerned with bodies that are undergoing accelerationacceleration

Basic quantities used throughout Basic quantities used throughout mechanicsmechanics

Length Length – locates the position of a point in spacelocates the position of a point in space– able to describe the size of a physical systemable to describe the size of a physical system

TimeTime– succession of eventssuccession of events– statics problems are time independentstatics problems are time independent

MassMass– property of matterproperty of matter– provides quantitative measure of the resistance of matter provides quantitative measure of the resistance of matter

to a change in velocityto a change in velocity ForceForce

– ““push” or “pull” exerted by one body on anotherpush” or “pull” exerted by one body on another– characterized by magnitude, direction, sense, and point of characterized by magnitude, direction, sense, and point of

applicationapplication

IdealizationsIdealizations

Particle Particle – has mass, but a size that can be neglectedhas mass, but a size that can be neglected– geometry of the body not involved in the analysisgeometry of the body not involved in the analysis

Rigid bodyRigid body– can be considered a combination of a large number can be considered a combination of a large number

particlesparticles– particles remain at the same fixed distance from one particles remain at the same fixed distance from one

another both before and after applying a loadanother both before and after applying a load Concentrated forceConcentrated force

– a loading which is assumed to act at a point on a bodya loading which is assumed to act at a point on a body

Units of measureUnits of measure

International System of Units (modern version of the International System of Units (modern version of the metric system) - SImetric system) - SI

US Customary System of Units – FPSUS Customary System of Units – FPS

W = m gW = m g(g is the acceleration due to gravity, 9.81 m/s(g is the acceleration due to gravity, 9.81 m/s2 2 or 32.2 or 32.2 ft/sft/s22))

Angular units may be expressed in radians Angular units may be expressed in radians

quantityquantity SISI FPSFPS

lengthlength meter (m)meter (m) foot (ft)foot (ft)

timetime second (s)second (s) second (s)second (s)

massmass kilogram (kg)kilogram (kg) slug ((lb-sslug ((lb-s22)/ft))/ft)

forceforce Newton (N, (kg-Newton (N, (kg-m)/sm)/s22))

pound (lb)pound (lb)

rad 2deg 360

SI unit prefixesSI unit prefixes

multiple/multiple/

submultiplesubmultipleexponential exponential

formformprefixprefix SI symbolSI symbol

1 000 000 0001 000 000 000 101099 gigagiga GG

1 000 0001 000 000 101066 megamega MM

1 0001 000 101033 kilokilo kk

0.0010.001 1010-3-3 millimilli mm

0.000 0010.000 001 1010-6-6 micromicro μμ

0.000 000 0010.000 000 001 1010-9-9 nanonano nn

Rules for use of units/symbols and Rules for use of units/symbols and prefixesprefixes

Never written with a plural “s”Never written with a plural “s” Always written in lowercase letters, except M, G, and Always written in lowercase letters, except M, G, and

units named after a person (i.e. Newton, N)units named after a person (i.e. Newton, N) Quantities defined by several units which are multiples of Quantities defined by several units which are multiples of

one another are separated by a dot (a dash will be used one another are separated by a dot (a dash will be used in these slides, i.e. m-s represents meter-seconds, while in these slides, i.e. m-s represents meter-seconds, while ms represents milliseconds)ms represents milliseconds)

μμNN22 = ( = (μμN)N)22 = = μμN * N * μμNN When performing calculations, begin by representing When performing calculations, begin by representing

numbers in terms of base units and/or derived unitsnumbers in terms of base units and/or derived units(50 kN)(60 nm) = (50)(10(50 kN)(60 nm) = (50)(1033)(N) * (60)(10)(N) * (60)(10-9-9)(m) =)(m) =3 000 (103 000 (10-6-6) N-m = 3 (10) N-m = 3 (1033)(10)(10-6-6) N-m = 3 N-mm) N-m = 3 N-mm

Compound prefixes should not by used (kCompound prefixes should not by used (kμμs)s) Avoid use of prefix in denominator of composed units, Avoid use of prefix in denominator of composed units,

except kgexcept kg

Significant figuresSignificant figures

Accuracy of a number is specified by the number of Accuracy of a number is specified by the number of significant figures it containssignificant figures it contains

A significant figure is any digit, including a zero, A significant figure is any digit, including a zero, provided it is not used to specify the location of the provided it is not used to specify the location of the decimal point for the numberdecimal point for the number

763,000 ??? if only four significant digits763,000 ??? if only four significant digits– Use scientific notation, 7.630 x 10Use scientific notation, 7.630 x 1055, one digit to the left , one digit to the left

of decimal point with the remaining digits to the rightof decimal point with the remaining digits to the right– Use engineering notation, 0.7630 x 10Use engineering notation, 0.7630 x 1066 – the exponent is – the exponent is

displayed in multiples of three (to facilitate conversion of displayed in multiples of three (to facilitate conversion of SI units to those having an appropriate prefix)SI units to those having an appropriate prefix)

RoundingRounding

If the n + 1 digit is less than 5, the n + 1 digit and If the n + 1 digit is less than 5, the n + 1 digit and others following it are droppedothers following it are dropped

If the n + 1 digit is greater than 5 (or is equal to 5 with If the n + 1 digit is greater than 5 (or is equal to 5 with nonzero numbers following the 5), then increase the nth nonzero numbers following the 5), then increase the nth digit by 1 and drop the n + 1 digit and others following itdigit 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 If the n + 1 digit is equal to 5 (with no numbers or zeroes following the 5)zeroes following the 5)– And the nth digit is an even number, then the nth digit is And the nth digit is an even number, then the nth digit is

not rounded upnot rounded up– And the nth digit is an odd number, then the nth digit is And the nth digit is an odd number, then the nth digit is

rounded uprounded up In text, the answers to problems are generally rounded In text, the answers to problems are generally rounded

down to three significant figuresdown to three significant figures

General procedure for analysisGeneral procedure for analysis

Read the problem carefully and try to correlate the actual Read the problem carefully and try to correlate the actual physical situation with the theory studied.physical situation with the theory studied.

Draw any necessary diagrams and tabulate the problem Draw any necessary diagrams and tabulate the problem data.data.

Apply the relevant principles, generally in mathematical Apply the relevant principles, generally in mathematical form.form.

Solve the necessary equations algebraically as far as Solve the necessary equations algebraically as far as practical, then making sure they are dimensionally practical, then making sure they are dimensionally homogeneous, use a consistent set of units and complete the homogeneous, use a consistent set of units and complete the solution numerically. Report the answer with no more solution numerically. Report the answer with no more significant figures than the accuracy of the given data significant figures than the accuracy of the given data (generally three significant figures for problems in this text).(generally three significant figures for problems in this text).

Study the answer with technical judgment and common Study the answer with technical judgment and common sense to determine whether or not it seems reasonable.sense to determine whether or not it seems reasonable.