Physics 111 Lecture 04. Force and Motion I: The Laws of Motion. SJ 8th Ed.: Ch Newton s First Law: zero net force

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1 Phsics Lectue 04 oce nd Motion I: he Lws of Motion SJ 8th Ed.: Ch Dnics - Soe histo oce Cuses Acceletion ewton s ist Lw: zeo net foce Mss ewton s Second Lw ee Bod Digs Gvittion ewton s hid Lw Appliction to Sple Pobles 5. he Concept of oce 5. ewton s ist Lw nd Inetil es 5.3 Mss 5.4 ewton s Second Lw 5.5 Gvittionl oce nd Weight 5.6 ewton s hid Lw 5.7 Using ewton s Second Lw Copight R. Jnow Sping 0

2 Dnics - ewton s Lws of Motion Kinetics descibed otion onl no el Phsics. Wh does pticle hve cetin cceletion? ew concepts (in 7th centu: oces - pushes o pulls - cuse cceletion Ineti (ss esues how uch tte is being cceleted esistnce to cceletion ewton s 3 Lws of Motion: Codified kinetics wok b Glileo nd othe el epeientes Intoduced thetics (clculus s the lnguge of Phsics Allowed detiled, quntittive pediction nd contol (engineeing. Usheed in the Enlightenent & Clockwok Univese. Ae ccute enough (with gvit to pedict ll coon otions plus those of celestil bodies. il onl fo v ~ c nd quntu scle (ve sll. Si Isc ewton oulted bsic lws of echnics Invented clculus in pllel with Liebnitz Discoveed Lw of Univesl Gvittion Mn discoveies deling with light nd optics Rn the Rol Mint fo n es duing old ge Mn ivlies & conflicts, few fiends, no spouse o childen, pototpe geek Copight R. Jnow Sping 0

3 oce: cuses n chnge in the velocities of pticles ewton s definition: A foce is tht which cuses n cceletion Contct foces involve phsicl contct between objects - k ield foces ct though ept spce without phsicl contct Action t distnce though intevening spce? How? Given toic phsics, Is thee n such thing s el contct foce? he fou fundentl foces of ntue e: Gvittion, Electognetic, ucle, nd Wek foce Copight R. Jnow Sping 0

4 oce: wht cuses n chnge in the velocities of pticles Units: ewton foce tht cuses kg to ccelete t /s Pound foce tht cuses slug to ccelete t ft/s oces e VECORS Opete with vecto ules Replce foce cting t point b its coponents t the se point. Supeposition: A set of foces t point hve the se effect tht thei vecto esultnt foce would 3 ottion: v net ĵ î i i net Definition: A bod is in EQUILIBRIUM if the net foce pplied Copight to it R. Jnow equls Sping 0 zeo

5 Reltive otion - Inetil Refeence es in Diension A fe of efeence ounts to selecting coodinte sste. Descibe point P in both fes using, v, nd, v,. Oigins coincide t t 0 Constnt v eltive velocit of oigin of in fe is the distnce between oigins t soe tie t. nsfo the coodintes: (t nsfo the velocities: d dt d dt d dt (t (t v v v ind the cceletions: dv dt dv hen 0 nd dt dv dt dv dt dv dt 0 v P he cceletion of oving object is the se fo pi of inetil fes. Eple: An cceleting c viewed fo tin nd the gound, with the tin itself oving t constnt velocit Inetil fes cn not be otting o cceleting eltive to one nothe o to the fied sts. on-inetil fes fictitious foces. Copight R. Jnow Sping 0

6 ewton s ist Lw (686 Don t oving objects coe to stop if ou stop pushing? Stopping iplies negtive cceletion, due to fiction o othe foces opposing otion. Wht effect does ineti hve on cuve on n ic od? he Lw of Ineti : A bod s velocit is constnt (i.e., 0 if the net foce cting on it equls zeo Altente stteent: A bod eins in unifo otion long stight line t constnt speed (o eins t est unless it is cted on b net etenl foce. Above ssue n inetil efeence fe : Equtions of phsics look siplest in inetil sstes. on-inetil fes (e.g., otting equie fictitious foces & cceletions in phsics equtions (e.g., centifugl nd Coiolis foces. ist Lw (ou tet: An object tht does not intect with othe objects (no net foce, isolted cn be put into efeence fe in which the object hs zeo cceletion (i.e., it s otion cn be tnsfoed to n inetil fe if it is not in one led. Copight R. Jnow Sping 0

7 Mss: the Mesue of Ineti Appl the se foce to diffeent objects. Diffeent cceletions esult. Wh? Eple: Appl se foce to bsebll, bowling bll, utoobile, RR tin Mss esues ineti: the ount of tte in bod (i.e., how n tos of ech tpe esistnce to chnges in velocit (i.e., cceletion when foce cts o given foce pplied to nd : A ss nd esulting cceletion on it e invesel popotionl Mss is scl: Attch to he esult behves with Mss is intinsic to n object: it doesn t depend on the envionent o stte of otion (fo v << c, o tie. Don t confuse ss with weight ( foce: W g If kg then W eth 0. but W oon 3.3. he se inetil ss vlue lso esues gvittionl ss - pticle s effect in poducing gvittionl pull Copight on othe R. Jnow sses Sping 0

8 ewton s Second Lw SIMPLE PROPORIOALIY WHE I A IERIAL RAME Suizing: Vecto su of foces cting O pticle net i i Ineti of pticle Acceletion esulting fo net DIRECIO O ACCELERAIO AD E ORCE ARE HE SAME Ctesin coponent equtions: net, i i net, i i net,z Othe ws to d Wite nd dp Lw: net i whee p v dt net dt Units fo oce: i [ ] [][] ML / i iz z SYSEM ORCE MASS ACCELERAIO SI ewton ( Kg /s CGS Dne g c/s Bitish Pound (lb slug ft/s kg WEIGHS. lb dne 0-5 g 0-3 kg lb 4.45 kg slug kg Copight R. Jnow Sping 0

9 ug of w 4-: hee students cn ll pull on the ing (see sketch with identicl foces of gnitude, but in diffeent diections with espect to the is. One of the pulls long the is with foce s shown. Wht should the othe two ngles be to iniize the gnitude of the ing s cceletion? θ 0, θ 3 0 b θ 80, θ 3-80 c θ 60, θ 3-60 d θ 0, θ 3-0 e θ 50, θ 3-50 θ 3 3 θ 4-: Wht should the othe two ngles be to iize the gnitude of the ing s cceletion? θ 0, θ 3 0 b θ 80, θ 3-80 c θ 60, θ 3-60 d θ 0, θ 3-0 e θ 50, θ 3-50 Copight R. Jnow Sping 0

10 Eple: A hocke puck whose ss is 0.30 kg is sliding on fictionless ice sufce. wo foces ct hoizontll on it s shown in the sketch. ind the gnitude nd diection of the puck s cceletion. Appl nd Lw to nd diections net, net, cos( sin( 0 0 cos( sin( kg Evlute: net, 8.7 net, / s net, 5. net, / s Convet to pol coodintes: / - [ ] 34 /s θ tn ( / 3 he net foce nd cceletion vectos hve the se diection A unit vecto in tht diection is: â 9 7 î ĵ î ĵ 0.85 î ĵ o BD Copight R. Jnow Sping 0

11 Mesuing oce nd Mss On fictionless sufce (e.g., i tck: Appl enough hoizontl foce 0 to give the stndd ss 0 the stndd cceletion 0 0 kg 0 /s he (stndd foce unit theeb defined ote: -coponents onl bove, & e in se diection Mesuing nothe ss: Appl stndd foce, ecod esulting cceletion / / 0 0 Wht bout foces in the diection, left out bove? Copight R. Jnow Sping 0

12 Gvittionl oce, Weight, ol oce Mss in fee fll on Eth s sufce cceletes t g: g gĵ g BD " the weight" g hs the se diection (towd cente of Eth nd gnitude fo ll sses (in volue lge coped to hun. g 9.8 /s 3. ft/s t the Eth s sufce Action t distnce he weight is independent of how ss is oving (pehps othe foces lso ct. Mss in contct with hoizontl sufce (tble, i tck, be in equilibiu fo : Equilibiu" fo 0 BD " 0 g ( does not ccelete g gĵ "nol foce" pependicul to sufce is contct foce tht djusts to g g pushes on the sufce - the sufce pushes bck with If not 0, does not equl g Copight R. Jnow Sping 0

13 ewton s hid Lw Bodies intect b pushing o pulling on ech othe 3 d Lw (ntique vesion: Ech ction hs n equl nd opposite ection Moe oden vesion: When two bodies intect the foces tht ech eets on the othe e lws equl in gnitude nd opposite in diection Eple: gvit cting t distnce foce on object foce on object due to object due to object Eple: bo on level sufce g gĵ s g is the pull of Eth on the bo (weight he 3 d lw ection is e - the bo s pull on the Eth is the sufce s push on the bo s is the bo s push on the sufce OLY foces on the bo ( g & ffect it s otion g & e O 3 d lw pi ( sb & e pi Wh then does g??? e If ou eve find foce w/o the 3 d lw ection, ou cn build pepetul otion chine Copight R. Jnow Sping 0

14 ee Bod Digs (BDs Dwing the BDs is the ost ipotnt step in nlzing otion. DRAW BDs IRS befoe ou stt witing down equtions. Pictoil sketches e not the se s BDs. Model bodies in ou sste s point pticles. hee be sevel. Soeties ou cn tet the sste s one object. Choose coodintes. Include in BDs onl foces tht ct O ou sste. Eclude foces eeted BY bodies in ou sste on othe bodies. eglect intenl foces. When ou bek up sste fo nlsis, ICLUDE foel intenl foces tht becoe etenl. Don t foget ction-t--distnce foces (fields such gvit g g M g Mgĵ Is this BD? ' g gĵ Copight R. Jnow Sping 0

15 iction ictionless BDs: show onl foces on bodies Sliding o sttic fiction f (lte g f g o fiction pllel to sufce iction is esistive foce pllel to sufce / ( f / f Contct foce - lws opposed to otion Cods ension onl, no copession Pulling cetes tension the foce tnsitted b the cod is the se evewhee in zeo-ss, unstetchble cod Suppot BD fo bod g 3 d lw pi Equilibiu g ' BD fo cod 3 d lw pi BD fo suppot Copight R. Jnow Sping 0

16 ewton s Lws - Su ewton s ist Lw A bod s velocit is constnt ( 0 if the net etenl foce on it is zeo - Motion is long stight line - ind nd use n inetil fe of efeence ewton s Second Lw net In Ctesin coponents: i i net foce vecto z z ewton s hid Lw If bod A eets foce on bod B, then bod B eets nd equl nd Opposite foce on bod A. Copight R. Jnow Sping 0

17 Method fo solving ewton s Second Lw pobles Dw o sketch sste. Adopt coodintes. e the vibles, Dw fee bod digs. Show foces cting on pticles. Include gvit (weights, contct foces, nol foces, fiction. Appl Second Lw to ech pt net i Mke sue thee e enough ( equtions; Et conditions connecting unknowns (constint equtions be pplicble Siplif nd solve the set of (siultneous equtions. Intepet esulting fouls. Do the ke intuitive sense? Ae the units coect? Refe bck to the sketches nd oiginl poble Clculte nueicl esults, nd snit check nwes (e.g., ight ode of gnitude? Sstes with sevel coponents hve sevel unknowns. nd need n equl nube of independent equtions Copight R. Jnow Sping 0

18 Eple: ffic Light in Equilibiu Conceptulize: cbles e ssless nd don t bek no otion Ctegoize: equilibiu poble cceletions 0 Model s pticles in equilibiu BDs g BD of Knot BD of Light 3 g BD of light ields 3 g ( light 0 BD of knot ields: 0 cos( Solve uppe fo : 0 cos( cos( [sin( o o o sin( o o cos( 37 o o 53 sin( sin( 53 o ] Copight R. Jnow Sping 0

19 Eple: Pticle Motion Unde et oce Mss is oving on fictionless hoizontl sufce, cted on b n etenl foce of gnitude, king n ngle θ with the -is. ind epessions fo the cceletion long the hoizontl nd veticl diections θ Along : cos( θ cos( θ Along : Is zeo, o does pticle ccelete upwd? sin( θ W Set 0. Cossove to > 0 when lso 0, i.e, when W W weight 0 sin( θ W sin( θ W When is > the weight, the sin( θ pticle cceletes upwd W 0 When is < the weight, the pticle does not ccelete 0 W sin( θ Copight R. Jnow Sping 0

20 Bootstps 4-3: he n nd the pltfo weigh totl of 500. He pulls upwd on the ope with foce. Wht foce would he need to eet in ode to ccelete upwd with 0. g? Is this possible? 50 b 000 c 550 d 500 e He cnnot lift hiself b his own bootstps t ll. Copight R. Jnow Sping 0

21 Eple: Sliding nd Hnging Blocks Block S, ss M is sliding on fictionless hoizontl sufce. Block H, ss hngs fo ssless, unstetchble cod wpped ove ssless pulle. ind epessions fo the cceletions of the blocks nd the tension in the cod. W Mg o fiction, o ss Appl nd Lw to blocks S & H septel fo & BD fo Block S W Mg s M W M s s 0 BD fo Block H choose positive down W g 0 h h h W' ' ' Constints:, Eliinte,, ind foul fo M M M g could lso use sste ppoch o find this W' M g M W g M g Copight R. Jnow Sping 0

22 Eple: Block Sliding on Rp [ Inclined Plne ] Mss is cceleting long fictionless inclined sufce s shown, king n ngle θ with the hoizontl. ind epessions fo the cceletion nd the nol foce oces cting O the block e nd W is nol to the sufce W is veticl s usul Choose - es ligned to p, fo which: Assue W 0, Appl nd Lw to nd Wcos( W θ W W gcos( θ Wsin( gcos( gsin( gsin( θ Does not depend on (positive down & ight θ θ θ 0 W g θ Wh does the block ccelete? Do ou epect to equl W? BD 90θ W Check: Wht hppens s θ 90 o s θ 0 o θ W W Copight R. Jnow Sping 0 θ

23 Eple: Atwood s Mchine with Mssless Pulle Both sses hve the se cceletion (constint. he tension in the unstetchble cod is the se on both sides of the ssless pulle (nothe constint. ind epessions fo the cceletion nd the tension In the cod. ind the foce W tot suppoting the pulle BD fo g g Add the equtions g g BD fo g g o foces o otion long 0 fo is clockwise fo > g fo 0 o - g fo 0 g W tot Subtct the equtions g g g 0 fo o equls zeo. g fo BD fo pulle W tot W tot 0 W tot 4 g W tot g if Othewise not so Copight R. Jnow Sping 0

24 Eple: You Weight in n Elevto A pssenge whose ss 7. kg is stnding on pltfo scle in n elevto. Wht weight does the scle ed fo hi s the elevto (nd hiself cceletes up nd down? BD fo pssenge o foces o otion long g g is the el weight, which doesn t chnge he building is n inetil fe, s is the elevto when tveling t constnt speed. When the elevto nd pssenge e cceleting thei non-inetil fe fictitious foces is the scle eding ppent weight Appl Second Lw in the building s efeence fe g Intepettions: ( g g g fo 0 ol weight fo elevto t est o oving with constnt v > g fo > 0 Incesed ppent weight fo elevto cceleting up < g fo < 0 Decesed ppent weight fo elevto cceleting down 0 fo -g ee fll - weightless g foce eeted b gvit g velocit hs no effect on ppent weight ictitious foce ppes in non-inetil fe Copight R. Jnow Sping 0

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