FOR PHYSICS ENGINEERS 1 (PHY 2043) FALL 2011
Prerequisite course required MAC 2281 or MAC 2311
Instructor: Dr. Grigoriy Kreymerman
COURSE TEXT BOOK:
PHYSICSFORSCIENTISTANDENGINEERS,Vol-1,SixthEdition
Authors:PaulA.TiplerandGeneMosca
Publisher:W.H.FreemanandCompany(http://whfreeman.com/tipler/)
ThebiggestpartofthisbookisMechanicsfallowingbyOscillations
WavesandThermodynamics.
There will be four tests and four 15 minutes quizzes.
First,secondandthirdtestswillbegradedas105pointsmax.The
finalcumulativetestwillbegradedas120pointsmax.Thetotal
pointsforfourtestsare435max.Quizzeseach21pointstotal84
pointsmax.
Homeworkassignments60pointstotalmax.Totalcoursepoints
1
possibleare579.
WELCOME TO PHYSICS!
The required textbook
for this course is
PHYSICS
For Scientists
and Engineers
Sixth Edition
by Paul A. Tipler and Gene
Mosca
(2008,W.H.Freeman&Company)
2
1-CHAPTER
MEASUREMENT AND VECTORS
Units
ConversionofUnits
DimensionsofPhysicalQuantities
Vectors
GeneralPropertiesofVectors
3
Toexpressmeasurementquantitativelyweneedintroduceunits.
Physical unit is the define standard for measurement of physical
quantity or value.
Forexample
Time _____ seconds,minutes,hours,days,
Distance_____
meters,kilometers,feet,yards,miles.
Mass_______kilograms,grams,milligrams,pounds,slugs.
U.S.customarysysteminches,feet,yards,miles,pounds,.
FootoriginallydefinedasthelengthofthekingsfootinFrance.
The basic standard, which use in physics is
The International System of Units
In1960,aninternationalcommitteeestablishedasetofstandards
forthescientificcommunitycalledSI(forSystem International).
4
TherearesevenbasequantitiesintheSIsystem.Theyarelength,
mass,time,electriccurrent,thermodynamictemperature,amountof
substance(mole),andluminousintensity.
For now we define only three base units or fundamental quantities:
Time, Length, and Mass
Time-----second(s)Historicallyitis(1/60)(1/60)(1/24)of
themeansolarday
ModernetalonofthetimedefinebyfrequencyofE.M.radiationemitted
fromacertainlevelexcitationincesium(9192631770cyclespersecond)
5
Length-----meter(m)Historicallylengthwasdefineas1/10,000000
10 7
orofthedistancebetweentheequatorandNorthPole.
Standard1mbetweentwoscratchesonplatinumiridiumalloyat
constanttemperatureadapted1889.
Todaylengthdefinebyspeedoflight(299792458m/s)in
emptyspace.Themeteristhedistancewhichlighttravel
1/299792458second.
6
Mass-----kilogram(kg)Historicallywasdefinedasthemassof
oneliterofdistillatedwaterat4C.
Thekilogramisnowdefinedtobethemassofa
specificplatinum-iridiumalloycylinder,which
storeintheInternationalBureauofWeightsand
MeasuresinSvres,France.
7
TheclassicalexampleofimportanceofunitsisNASAfiascowith
Marsprobein1999.TheJetPropulsionLaboratoryinCaliforniaand
LockheadMartininColoradousedifferentunitsofmeasurement.
Units Prefixes
8
ConversionofUnits
Example:
Howmanycentimetersarethereinonefoot?Howmanycentimetersare
thereinonemile?
Wecanusethefactsthatthereare2.540centimetersin1inchand12
inchesin1foottoshowthatthereare30.48cmperft.Wecanthenuse
thefactthatthereare5280feetin1miletofindthenumberof
centimetersinonemile.
Multiply2.540cm/inby12in/fttofindthenumberofcmperft:
cm in
2.540 12 = 30.48 cm/ft
in ft
Multiply30.48cm/ftby5280ft/mitofindthenumberofcentimetersin
onemile:
cm
ft
30.48 5280 = 1.609 105 cm/mi
ft
mi
9
DimensionsofPhysicalQuantities
Wegoingusenextnotation:fordistance=[L],
fortime=[T],mass=[M]
We can multiply or divide physical quantities (values)
in deferent units.
Examplespeed=[L]/[T]
When we adding or subtracting physical quantities (values)
dimensions of this quantities should be same.
Exampletotallength=[L1]+[L2]
Dimensionalanalysis.Fallingtimeasfunctionofhighand
10
Example:
Forcehasdimensionsofmasstimesacceleration.Accelerationhas
dimensionsofspeeddividedbytime.Pressureisdefinedasforce
dividedbyarea.Whatarethedimensionsofpressure?Express
pressureintermsoftheSIbaseunitskilogram,meterandsecond.
Usethedefinitionofpressureandthedimensionsofforceandareato
obtain:
ML
[F] = T 2 = M
[ P] =
2
LT 2
[ A] [ L ]
ExpresspressureintermsoftheSIbaseunitstoobtain:
m
kg 2
N
s = kg
=
m2
m2
m s2
11
Whatcombinationofforceandoneotherphysicalquantityhasthe
dimensionsofpower?Wherepoweris[ ] P = [ F ] [ L]
[T ]
LetXrepresentthephysicalquantityofinterest.
ExpresstherelationshipofXtoforceandpowerdimensionally:
[ F ] [ X ] = [ P]
Solvefor [ X ]
[ X ] = [ P]
[F]
Substitutethedimensionsofforceandpowerandsimplifytoobtain:
[ F ] [ L]
[ X ] = [T ] = [ L ]
[ F ] [T ]
BecausethedimensionsofvelocityareL/T,wecanconcludethat:
[ P] = [ F ] [v]
12
Trueorfalse:
(a)Twoquantitiesmusthavethesamedimensionsinordertobeadded.
(b)Twoquantitiesmusthavethesamedimensionsinordertobe
multiplied.
(a)True.Youcannotaddapplestoorangesoralength(distance
traveled)toavolume(litersofmilk).
(b)False.Thedistancetraveledistheproductofspeed(length/time)
multipliedbythetimeoftravel(time).
13
Example:
Indoingacalculation,youendupwithm/sinthenumerator
andm/s^2inthedenominator.Whatareyourfinalunits?
(a)m^2/s^3,(b)1/s,(c)s^3/m^2,(d)s,(e)m/s.
14
Uncertaintyofmeasurement
Problem:
Acircularholeofradius8.470 101cmmustbecutintopanel.The
1 103
toleranceofradiusiscm.Iftheactualholeislargerthanthe
desiredradiusbytheallowedtolerance,whatisthedifference
betweentheactualareaandthedesiredareaofthehole?
Solution:
(
A = r02 r 2 = r02 r 2
)
A = ( r0 r ) ( r0 + r )
(
)[
(
A = 1.0 10 3 cm 8.470 10 1 cm + 8.470 10 1 cm + 1.0 10 3 cm
= 5.3 10 3 cm 2
15
)]
OrderofMagnitude
Roundingnumbertothenearestpowerof10calledanorder
ofmagnitude.
10 5 g
9 10 g isapproximately
4
9 10 5 g
isapproximately
?
Problem:
Assume,percentageofHumanBodythatisWaterUpto60percent.
Themassofawatermoleculeis30 10^-27kg.Ifthemassofa
personis60kg,estimatethenumberofwatermoleculesinthatperson.
N representthenumberofwatermoleculesinapersonofmass m
N=
N=
mhuman body
m water molecule
0.6
60 kg
30 10 27
kg
molecule
0.6
= 1.2 1027 molecules
16
VECTORS
Vectordefinebymagnitude(displacementorlength)anddirection.
EqualVectors
17
AdditionandSubtractionofVectors
Head-to-Tailmethodaddition.
Vectorsum,orresultant.
Parallelogrammethodaddition
Vector addition obeys the commutative law
18
Vector addition is associative. A+ B + C = A+ B + C
C = A+ B
A
B
C = A+ B itisnotequalto. Exceptwhenandareparallel.
19
SubtractionofVectors
20
Avectorpointsinthe+xdirection.Showgraphicallyatleastthree
A
choicesforavectorsuchthatpointsinthe+ ydirection.
B+ A
B
21
Thevectorequationthatdescribes
therelationshipamongvectors A, B and C
is
A.
B.
C.
D.
E.
B =C + A
B =C A
C = A B
A= B C
A= B +C
22
ComponentofVector
Componentofvectorindefinedirectionistheprojectionofthe
vectorontoanaxisinthatdirection.
23
Theprocessoffindingthex,y,andzcomponentofvectoris
calledresolvingthevector
Wecanfindangle ifweknowAx andAy.
tan =
Ay
Ax
= arctan
Ay
Ax
2
A = Ax + A 2
y
Inthreedimensions.
2
A = Ax + A2 + Az2
y
24
C = A+ B
C X = AX + B X
CY = AY + BY
25
Problem:
AvectorA 7.00unitslongandavectorB 5.50unitslongareadded.
TheirsumisavectorC 10.0unitslong.Determinetheanglebetween
theoriginaltwovectors.
26
= 180
Applythelawofcosines
C 2 = A2 + B 2 2 AB cos
A2 + B 2 C 2
= cos 1
2 AB
1 7.00
= cos
= 105.6
2
+ 5.50 2 10.0 2
2( 7 ) ( 5.5)
= 180 105.6 = 74
27
UnitVectors
AUnitVectorofvectorisvectorwhichisinsamedirectionas
A
A
A
vectorbutwithoutdimensionsandwithmagnitudeequalto1.
= A where A = A2 + A2 + A2
A
x
y
z
A
A = Ax + Ay + Az k
i
j
A + B = Ax + Ay + Az k + Bx + B y + Bz k =
i
j
i
j
(
(
)
)(
)
= ( Ax + Bx ) + Ay + B y + ( Az + Bz ) k
i
j
28
+ 4.7
B = (7.7)i + 3.2
j
Giventhefollowingvectors:,and
A = 3.4i
j
(a)Findthevector,inunitvectornotation,
D
C = 5.4i + (9.1)
j
suchthat
D + 2 A 3C + 4 B = 0
(b)ExpressyouranswerinPart(a)intermsofmagnitude.
(c)FindunitvectorforD vector.
(a) Solvethevectorequationthatgivestheconditionthatmustsatisfied
for D
D = 2 A + 3C 4 B
Substitutefor A,C andB
(
)(
)(
D = 2 3.4i + 4.7 + 3 5.4i 9.1 4 7.7 i + 3.2
j
j
j
= ( 6.8 + 16.2 + 30.8) i + ( 9.4 27.3 12.8)
j
= 40.2 i 49.5
j
(b)UsethePythagoreanTheorem
2
D = Dx + D 2
y
(c )
D=
( 40.2) 2 + ( 49.5) 2
= D = 40.2i 49.5 j 0.63i 0.78
D
j
D
63.8
= 63.8
29
)
30