MechanicsLecture1,Slide1

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ClassicalMechanics

MechanicsLecture1,Slide2

Modus Operandi

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MechanicsLecture1,Slide3

MechanicsLecture1,Slide7

Q:Whatarethebenefitsofpar?cipa?ng?A:Youlearnmore

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43.478347.826152.173956.521760.869665.217469.565273.91378.260982.608786.956591.304395.6522 100

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MechanicsLecture1,Slide4

Clicker Question 1

Doyouhaveyouri>clickerwithyoutoday?

A) Yes

B) No

C) Maybe

D) I like pudding

MechanicsLecture1,Slide5

Clicker Question 2

Whichofthefollowingbestdescribesyourhigh-schoolphysicsclass?

A) Great

B) Pretty good

C) So-so

D) Not so good

E) Awful

Classical Mechanics Lecture 1

Today'sConcepts:a)Displacement,Velocity,Accelera?on

b)1-DKinema?cswithconstantaccelera?on

MechanicsLecture1,Slide8

Your CommentshowtoidenNfyanduNlizeintegralsinformulasandquesNons,justthewholeconcept.

CanyougivememorequesNonstopracNceandnotbemarked,justpracNcequesNonwithrightanswersandexplain.thankssomuch.

thepartexplaininghowdistancewasrelatedtovelocityregardlessofNmewentabittoofast

“themostdifficultthingiswhenwelookatthev-tgraph,thenaskwhatweknowaboutthex-tora-tgraph,especiallyitisnotaconstantspeed.”

“PerhapstheintroducNonofthecalculusconceptisseXngusupforlaterinthecourse?”

Text

You betcha

Start by visualizing the graphical representation

Start by visualizing the graphical representation

Textbooks are a good source

Use the controls to repeat.

Formal Problem SolvingFormalProblemSolving

ForthenextseveralassignmentswhileyouareworkingwithUnit4andthenextunityouwillbedoingasetofkinemaNcsproblems.Thesehelpyoulearnabouttheelementsofformalproblemsolving.

Part1:DiagramsandGraphs

Part2:TablesandEquaNons

Part3:AlgebraandSubsNtuNon

Part4:Checks:ComputaNonandUnits

ThisapproachwasdevelopedbyBobMorsea

Formal Problem Solving

AnexampleofhowtoworkatypicalkinemaNcsproblemistheSAMPLECONSTANTACCELERATIONPROBLEM.Thenthereisapacketof5problems.EachproblemisprintedatthetopofasheetenNtledCONSTANTACCELERATIONPROBLEMWORKSHEET.Youaretodopartsofeachofthe5problemsduringthenextfewassignmentsunNlallthepartsarecompleted.

• ThisapproachwasdevelopedbyBobMorse,ateacheratSt.

AlbansSchoolinWashingtonDC.

MechanicsLecture1,Slide11

Displacement

Timetaken

Displacement and Velocity in One Dimension

MechanicsLecture1,Slide12

DefiniNon:

Speed = |v(t)|

The v(t) vs. t plotisjustthe slopeofthe x(t) vs. t plot

Displacement and Velocity in One Dimension

MechanicsLecture1,Slide13

A)YESB)NO

Aretheplotsshownatthele\correctlyrelated

Displacement and Velocity in One Dimension

MechanicsLecture1,Slide14

Thevelocityvs.?meplotofsomeobjectisshowntotheright.

WhichdiagrambelowcouldbetheDisplacementvs.?meplotforthesameobject?

A B C

Clicker Question

MechanicsLecture1,Slide15

Acceleration

MechanicsLecture1,Slide16

FortheDisplacementandVelocitycurvesshownonthele\,whichisthecorrectplotofaccelera?onvs.?me?

A

B

Checkpoint 1

MechanicsLecture1,Slide17

A

B

Because a(t)= dv(t)/dt, according to the graph of velocity vs. time, acceleration vs. time graph should be the slope of the velocity vs. time graph. Thus, the answer should be the first graph.

TypicalAanswer

The velocity starts at a high positive value and then decreases to about zero before increasing again. Since the velocity graph curves first down then up, the acceleration decreases and then increases instead of just increasing for the entire time.

TypicalBanswer

VoteagainClicker Question 4

A B

MechanicsLecture1,Slide18

Constant Acceleration

constanta(t) = a

MechanicsLecture1,Slide20

1ft4ft

9ft

?

16ft

At t = 0 aball,ini?allyatrest,startstorolldownarampwithconstantaccelera?on.Supposeitmoves 1 ft between t = 0 sec and t = 1 sec.

Howfardoesitmovebetween t = 1 sec and t = 2 sec?

A)1\B)2\C)3\D)4\E)6\

Clicker Question 5

MechanicsLecture1,Slide21

Forthefirstsecond,thevelocityis1h/s.ThereforeifacceleraNonisconstant,thenvelocitywillhaveincreasedto2h/sat2seconds.Therefore,intheNmeintervalbetween2and1seconds,theballwouldhavemoved2feet.

TypicalBanswer

AcceleraNonis1h/s2andthevelocityattheendofthefirstintervalis2h/ssoatthesecondintervalthedistanceis3hfromtheequaNond=v+1/2at2

TypicalCanswer

Ifitmoves1hin1sec,usingx=xo+vt,v=1/1or1m/s.Usingv=vo+at,a=1/1or1h/s2.Sointheintervalof1second,theballwillmove1foot.

TypicalAanswer

1ft4ft

9ft

3

16ft

Checkpoint 2 Responses

A B D E

MechanicsLecture1,Slide21

SinceacceleraNonisconstant,wecansolveforacceleraNonusingtheformulax=v(iniNal)*t+0.5at2.DoingthiswesolveacceleraNonfor0.6096m/s2,ahergeXngthiswecanplugthisinfortotaldistancetravelledandtheanswercomesoutto4hifcalculatedproperly.

TypicalDanswer

1ft4ft

9ft

3

16ft

Checkpoint 2 Responses

A B C D E

TheequaNonvf=vo+atwillgiveusthefinalvelocityandwiththatthefinaldisplacement.Giventhatvo=1foot/second,a=4.9(thisistrueduetothegravitaNonalpullfromtherampassuminga30°ramp)andttobe1s.Thiscalculatestothefinalanswerbeingapproximately5.9m.

TypicalEanswer

Question asks for distance from t=1 s to t=2.

g≠9.8 ft/s2 — angle not necessarily 30°

MeasureposiNonwithruler.

EsNmatetenthsofmm

ConverttoactualposiNoninmetres

Notethatt0ist=0sbutnotx=0m.

Where to plot <v> and <a>?

PlottheaveragevelociNes,<vi>,halfwaybetweentheendpointsoftheinterval.

PlottheaverageacceleraNons,<ai>,atthesameNmesasxi