Always solve problems by writing a logical and. Under what conditions they are useful. Under what conditions they are true

Size: px

Start display at page:

Download "Always solve problems by writing a logical and. Under what conditions they are useful. Under what conditions they are true"

Bertram Sharp
5 years ago
Views:

1 Aleady accmplished Read Te Chape Read Te Chape Read Te Chape 3 Read CPS (Cmpeen Pblem Sle) Chap. 3 Wked Te Pblems Chap. - 3 Wked CPS Pblems Chap. 3 Pblems m Lab I & Ne Weeks Cnnec Min (Chape & 3) wih Ineacins (Chape 4 & 5) using Vecs Read Te Chape 4 & 5 Read CPS Chape 4 Wk pblems in Chape 4 Wk pblems in Chape 5 Wk pblems in CPS Chape 4 Pblems m Lab 3 & Wha - iscussin Secin Ge a peec sce n he ne quiz gup pblem (and a highe sce n he indiidual pa ). In discussin secin pacice wiing a peec pape.» Make sue eey membe yu gup cmes pepaed. Yu need eeyne cnibue!» Make sue eey membe he gup agees n eey sep. I eey membe yu gup des n cmpleely undesand hw sle he pblem m wha is wien n he pape I is eihe wng ply eplained. (bh gie a p quiz gade)» Pacice wiing as lile as pssible ha eplains as much as needed. USE picues and diagams ( A picue is wh 000 wds. )» Pacice yu gup les. T ge a peec sce yu need A manage keep ack ime and pgess. A ecde checke wie an ganized sluin and make sue ha eeyne agees wih each sep. A skepic make sue ha he sluin des n assume ha smene can ead yu mind. Eeyne guiding he sluin. nes m quiz Bh pblems n indiidual quiz wee m hmewk Pblem 87 Chape Pblem 40 Chape 3 Cmmn iiculies leading lw sces Oganizain» Undeined symbls» Equains m nwhee» N eplanains abu why an equain wuld apply» P picues (n physics cnen)» P nn-eisen diagams» Sling he wng quaniy» Sluin lgic n eplained» N algebaic plan ge a sluin» iiculy llwing algebaic plan ge an answe Physics» N disincin beween aeage elciy and insananeus elciy.» Use gemey and ig insead physics» A l ime wased hinking abu and ding ielean hings.» N cmpaisn answe he epeience lgic wih eplanain Wha - A Hme Sle all suggesed pblems as i i wee a es. Read he e is. Wie dwn he smalles numbe undamenal pinciples in he chape using equains whee pssible.» Oen ne equain pe chape.» Alms nee me han hee equains.» The equains used in he lecue and n eample pblem sluins.» Ask i in dub. Me TAs Aemp sle a leas ne pblem eey d» Only use equains epesening he undamenal pinciples.» Alws wie he sluin in a lgical and well eplained manne m he beginning.» n sle ne w and y wie i up.» Wk as (n me han 0 minues/pblem)» n ee back he e.» n lk a he answe sluin uline.» I suck unsue, ge help. ( diec quesins & as espnse) Re-ead he chape & lecue nes. Sudy gup TAs Me» I yu g help, wk anhe pblem he same diiculy in he same secin. n wy - Ac Wha Neihe Physics n gd pblem sling is naual. Lean hw and undesand why. Sling pblems in a pessinal manne will eel uncmable a while.» Like leaning die. Sling pblems wihu clea wien cmmunicain hes is useless.» OK a hbby N a pessin. Impemen cmes hugh pacice and epeiin. Alws pacice sling a pblem as i i wee a es.» A hme» In discussin secin. Alws sa m basic pinciples (he equains we gie yu.)» Undesand hem cmpleely Wha he symbls eally mean Unde wha cndiins hey ae ue Unde wha cndiins hey ae useul. Alws sle pblems by wiing a lgical and cmplee sluin m he beginning.» Nee use scach pape. Wha - In Lab Cme pepaed Read ebk Pass pe-quiz Read assigned lab pblems» Wie dwn hings unclea m he eading Read elean appendices Wie up mehds quesins assigned pblems. Wie up he pedicin as i yu wee sling a es pblem. Cmpae yu pedicin sluin and mehds quesin answes wih yu gup. iscuss and esle dieences and hings yu wee unsue. Make sue ha he qualiaie behai bjecs in he lab agees wih yu cmmn sense Eplain secin is ey impan I hee is a disageemen, ecgnize i and esle i by discussin wih he gup membes and TA. Make sue ha he quaniaie behai bjecs agees wih yu pedicins. Undesand he uncins yu use i he daa.» Relainship undamenal pinciples» Meaning all ceiciens. Finish all analysis and make cnclusin bee ding ne pblem. Pacice wking apidly and eicienly as a gup.

2 Wha - In Lecue Undesand he need he undamenal pinciples pesened eemine he cnnecin he hings yu knw. Check yu undesanding hem by answeing» Hw d yu knw i is ue?» Unde wha cndiins des i apply?» Wha is i useul? S a leas ne sep ahead eample pblem sluins Hw is wha is pesened he same as wha yu wuld d? Hw is wha is pesened dieen m wha yu wuld d?» Hw impan ae he dieences? n ead my lecue nes in class. G e hem bee class eiew peius lecues» Wie dwn any quesins yu hae and ask hem G e hem ae class eince impan issues echniques yu. Cnclusins Time hi he gund is same whehe yu hw i hiznally yu dp i. The launch cndiins he eical (y) min ae he same eical iniial psiins (yi ) same eical iniial elciies (y I) same eical acceleains same ( = g). The bjec mes eically m yi yf he same w n mae wha happens hiznally. Thus i akes he same ime. The min bjecs in he eical diecin is independen hei min in he hiznal diecin Is he min bjecs in he hiznal diecin independen hei min in he eical diecin? Wha - In Oice Hus Cme help when suck unsue Leae ime a leas ½ hu pe pblem. Cme a imes ha ae unppula i yu can Ty dieen TAs and ind ne ha is ms in une wih wha yu need. Cme wih a small sudy gup i yu can» iscuss he help yu wee gien amng yuseles aewads. Shw hw yu sled he pblem m he beginning n epec anyne be able jump in he middle yu sluin n allw smene shw yu hw hey wuld sle he pblem. Insis hey see hw yu wee ying sle i. Insis hey use yu lgic shw yu why yu lgic is wng. es Hiznal Min epend n Veical Min? Tw bjecs me wih he same cnsan hiznal elciy bu ne bjec has a eical elciy and a eical acceleain. Which bjec ends up ahes m he saing pin when i his he gund? ya y, A AF F,F + a ya yaf a ya AF B Cmbining Hiznal Min and Veical Min Hw des eical min depend n hiznal min? Suppse yu hw an bjec hiznally and a he same ime dp an idenical bjec. Which bjec his he gund is? y I = 0 I = 0 y I, I y I = 0 I y F, F y F I I F= 0 F + F Cnclusin Hiznal displacemen an bjec is he same i i has he same hiznal elciy whehe n i has a eical elciy. The launch cndiins he hiznal () min ae he same hiznal iniial psiins (I ) ae same hiznal iniial elciies ( I) ae same hiznal acceleains ae same (a = 0). The bjec mes hiznally m I F he same w n mae wha happens eically. Thus i akes he same ime. The min bjecs in he hiznal diecin is independen hei min in he eical diecin

3 Pjecile Min: he They Hiznal min : is cnsan es n depend n ppeies (size, mass, densiy,...) he bjec. es n depend n he eical min epends nly n iniial hiznal elciy Veical min: is cnsan (called g) es n depend n ppeies (size, mass, densiy,... ) he bjec. es n depend n he hiznal min epends nly n iniial eical elciy and eical acceleain. Pjecile min is cmpleely deemined by he launch cndiins ( I and y I). The min a baseball, a bulle, and a balle dance die nly because he launch elciies die. The abe saemens ae clealy alse i ai esisance is impan Is I A Fce? I yu hink a ce acs n an bjec yu MUST Ideniy anhe bjec causing he ce. Ideniy he diecin he ce. Ideniy he ype he ce Cnac Gaiainal Tensin Sping Ficinal Magneic Elecic Fce A is he GRAVITATIONAL PULL he EARTH n he BALL. Wha Causes his Min? Wha ineacs wih a hwn bjec? (emembe we assumed he ineacin wih he ai is negligible) The nly ineacin is wih he Eah Called Gaiy iecin Gaiainal Ineacin a hwn bjec wih he Eah Veical - wn Hw d we knw? Veical min: cnsan acceleain Hiznal min: ze acceleain Guess a hey: An ineacin ne bjec wih anhe causes ha bjec acceleae in he diecin he ineacin. They Fces The sum he cmpnens Fces Σ F aecs ONLY he cmpnen acceleain Σ F causes a The sum he y cmpnens Fces Σ Fy aecs ONLY he y cmpnen acceleain Σ Fy causes The sum he z cmpnens Fces Σ Fz aecs ONLY he z cmpnen acceleain Σ Fz causes az Fce A me pecise w descibing an ineacin WHAT WE KNOW ABOUT FORCES An bjec cann change is elciy unless a ce is eeed n i by anhe bjec A ce n an bjec is ALWAYS caused by anhe bjec. Indicas a Fce n an bjec Cnac wih anhe bjec The bjec is acceleaing The bjec is n acceleaing bu knwn ces ae unbalanced Mahemaical escipin Need a cdinae sysem s mahemaics makes sense. Call he hiznal cdinae and y he eical cdinae. The psiie diecin is deined n he dawing he cdinae sysem y I, I I The hiznal elciy nee changes F y F, F I y = yf -yi = F -I = F -I F F y F + F

4 Hiznal Min Hiznal min: is cnsan a = 0 Because hee is n ineacin wih he bjec in he diecin use he deiniin aeage elciy a = = a = Vecs Mahemaics deal wih independen pependicula pas is called ecs Pependicula pas ae called cmpnens. Vec quaniies Psiin:, y = î + yĵ Velciy:, y = + y Acceleain: a, a = a + a y isplacemen:, y Velciy change:, y = î + yĵ = + y ĵ Time des n hae cmpnens. The min ccus duing he same ime ineal as he y min. Time is called a scala Veical Min Veical min: a y is cnsan y is changing Because he bjec ineacs wih he Eah in he diecin use he deiniin acceleain a y = d y d a y = d d (dy d ) y = a() + y0 + y 0 use he deiniin aeage acceleain a ya = y a yae a = y = y y Taking Min Apa y + The bjec mes m psiin psiin The magniude he displacemen is The psiin changes m. The displacemen is The y psiin changes m y y. The y displacemen is y isplacemen, is he "sum" and y NOT= + y Fm he dawing,, y, and make up a igh iangle. Tha is ne easn we use pependicula cdinaes. Pyhagean, () = () + (y) Relean Equains N hiznal ineacin = Hiznal min cnsan A eical ineacin Veical min y = a() + y0 + y 0 a y cnsan a y = y y changes is he same hiznal and eical min Jus ne bjec psiin: y Cmpnens = + y y + Sin = y y = Sin Cs = = Cs Velciy: + y y β Sin β = y y = Sin β Cs β = + = Cs β = + y Acceleain: +a y a a φ a a = a Sin φ = a = a Sin φ a Cs φ = +a a a = a Cs φ + a y î î ĵ ĵ î

5 Change Psiin = - + Wha mus be added gie? + = Wha is Eample Yu ae seing n a ciizen s panel ealuae a ppsal seach lie n Mas. A eam bilgiss has suggesed ha Maian lie migh be ey agile and decmpse quickly in he hea m he Mas lande. They sugges ha any seach lie shuld begin a leas 9 mees m he base he lande. This bilgy eam has designed a pbe ha is sh m he lande by a spinechanism in he lande.0 mees abe he suace Mas. T eun he daa, he pbe cann be me han mees m he bm he lande. Addiinal daa acquisiin and bilgical cnsideains equie he pbe impac he suace wih a elciy 8.0-m/s a an angle 30 degees m he eical. Can his pbe wk as designed? The Maian gaiainal acceleain is 0.40g. Change Velciy + y + + = - Wha mus be added gie? = Wha is Fcus.0 m 0.4 g Quesin: d g 8.0 m/s Is he disance he pbe his beween 9 and m? Appach: Use kinemaics. Hiznal min independen eical min. Hiznal: cnsan elciy N ce n he bjec in he hiznal diecin Igne ai esisance Veical: cnsan acceleain Only he gaiainal ce dwn Min and Ineacins Type min esuls m he ineacin he bjecs wih he bjec inees F simpliciy assume nly ne ineacin N ineacin Cnsan elciy - saigh line min Cnsan ineacin alng elciy Changing elciy - saigh line min Cnsan ineacin n alng elciy Changing elciy - pjecile min Changing ineacin in diecin bu n magniude - alws pependicula he elciy, y min diagam y y =.0 m = 0 = 0 =? y = 0 =?? = 0.40g, + = 8.0 m/s = 60 Cmpnens y + + y sin = y cs = sin = y cs = =

6 Tage: Hiznal : cnsan elciy = = = = Veical: cnsan acceleain = y y 0 = + y + y 0 = cs sin cs + y 0 = cs an + y check unis m s m s [ m ]+ [ m ]+ [ m ]= [ m ] k Use quadaic equain sle = an ± an 4 cs cs y Plan unknwns Find = [], Find cs = [] Find 0 = + y + y [3] y Find y = y y [4] y Find y sin = y [5] n new unknwns 5 unknwns, 5 equains k = an ± an cs cs y pu in numbes = an ( 60 )± an ( 60 ) m s 8. 0 m s m s 8. 0 m s cs ( 60 ) cs ( 60 ) (. 0m ) 0.58 ± = 0.5 m = 3. 76m 0.96m This will n wk, back he dawing bad Eecue he Plan [5] sin = y In [4] = sin y y = sin + In [3] 0 = g m + ( sin + ) + y 0 = sin + y insead sling his and pu in cs = eese he seps = cs 0 = cs sin cs + y Ealuae The disance is gien in he cec unis, m. The disance is n uneasnable since smehing n he de mees was pediced by he design. Fm he answe: = an ± an cs cs y The disance is ininie i is ze Reasnable since ha means hee is n gaiainal ce pull he pbe dwn. The disance is ze i is ze Reasnable since ha means hee is n hiznal cmpnen elciy iniially. The quesin is answeed, he plan will n wk

7 Eample Yu ae wiing swae a new cmpue baseball game. Yu mus deemine an equain wih which he cmpue can deemine i a bae his a hme un based n he size he ballpak and he w he ball is hi. The cmpue chses easnable andm numbes he disance he ba m he gund when i hi he ball, he angle m he hiznal ha he ball leaes he ba, and he iniial speed he ball he ba. The heigh he uield wall and is disance m he bae is als knwn. Cmpnens: A iniial ime 0 sin = y 0 y + cs = 0 A inal ime sin φ = y φ + cs φ = y = Fcus he pblem h b g Quesin: Is he eical psiin he ball geae han he heigh he wall when i is a he hiznal psiin he wall? Appach: eical and hiznal min ae independen N ce in he hiznal diecin Neglec ai esisance Hiznal cmpnen elciy is cnsan Gaiainal ce in he eical diecin Acceleain is eical and cnsan Find y Plan unknwns y eical min ball y = ( g )( ) + y0 ( ) + y 0, y0 Find 0y sin = y0 0 Find hiznal min ball = 3 Find cs = 4 n new unknwns 0 4 unknwns, 4 equains k + y iagam y 0 y0 g g y0 = b 0 = 0 0 = 0 0 = knwn = knwn = a y y = g =? =? =? Tage quaniy is y Is y > heigh wall? Quaniaie elainships: hiz: cns. elc. e: cns. accel. = y = y ( g )( ) + y0 ( ) + 0 -g = - y y Eecue he Plan 4 0 cs = In [3] cs = = cs In [] alng wih [] y = ( g )( cs ) + 0 sin( cs ) + y 0 y = g( cs ) + sin( cs ) + y 0 check unis m s [ m ] m s + [ m ]+ [ m ]= [ m ] OK

8 A Recap cnsan eical acceleain y = a( 0 ) + y0 ( 0 ) + y 0 B deiniin sin iniial elciy ec sin = y C 0 deiniin aeage hiznal elciy cnsan hiznal elciy = 0 0 = deiniin cs iniial elciy ec cs = 0 Pjecile Min Tajecy eemine he pah (ajecy) a pjecile. Lks like The pah (ajecy) descibed by an equain gies he elainship beween The bjec s hiznal psiin and The bjec s eical psiin Ealuae y = g( cs ) + sin( cs ) + y 0 Is his uneasnable? Imagine sme easy siuains whee yu knw he answe I g = 0 (n gaiainal ce) y = sin ( cs ) + y 0 y -y = an y y Saigh line min cec i n gaiainal ce pulling dwn Reasnable Wha deemines he ajecy? he iniial elciy he bjec he acceleain he bjec he iniial psiin he bjec Wan an equain ha has Veical psiin n ne side and hiznal psiin, g,, and n he he side Appach: Use deiniin elciy Use deiniin acceleain Hiznal min independen eical min Hiznal min: cns. elciy Veical min: cns. acceleain Appimain: igne ineacin wih ai y = g( cs ) + sin( cs ) + y 0 I angle = 0 y = g( g( ) + y 0 = S / = y -y = g( ) Cec alling saigh dwn Reasnable n iniial eical cmpnen elciy Min diagam: y F y g + g = 0 y= 0 F F F = knwn F = knwn = knwn yf =? = 0 g = knwn F =? F Cmpnens =? + y + y 0 y0 F + φ yf + F iniial elciy inal elciy,,

9 Tage quaniy: y F as uncin F,,, g Quaniaie elainships (Tls): hiznal eical Cnsan elciy Cnsan acceleain is cnsan a y is cnsan = a y = y y F = a y () + y + y 0 Velciy cmpnens: Iniial ime Final ime sin= y0 cs= 0 sinφ = yf F csφ= F = F F y F = g( + F an cs F This is he equain a paabla y = a + b + c Ealuae he uncin wih speciic alues = 45, = 4m/s, g = -0m/s Gaph i in m y in m in mees + In mees Plan unknwns Find y F y F bjec s eical min y0 y F = g F + y F F Find y0 sin = y0 Find F bjec s hiznal min 0 = F 3 F 0 Find 0 cs = unknwns, 4 equains Eecue he Plan 4 cs = 0 cs = 0 in 3 cs = F F F = F cs in y F = g( F cs + y F cs sin = y0 sin = y0 in y F = g( F cs + sin F cs y F = g( + F an cs F ) ) ) )

11. HAFAT İş-Enerji Power of a force: Power in the ability of a force to do work

11. HAFAT İş-Enerji Power of a force: Power in the ability of a force to do work MÜHENDİSLİK MEKNİĞİ. HFT İş-Eneji Pwe f a fce: Pwe in he abiliy f a fce d wk F: The fce applied n paicle Q P = F v = Fv cs( θ ) F Q v θ Pah f Q v: The velciy f Q ÖRNEK: İŞ-ENERJİ ω µ k v Calculae he pwe