Force and Motion II Friction, Circular Motion. Uniform Circular Motion - Free Body Diagrams Sample Problems. Properties of Friction.
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1 Phi 111 Letue 05 oe and Motion II ition, Ciula Motion SJ 8th Ed.: Ch. 5.8, Dnai Sua ition Bai Stati ition Kineti ition Popetie o ition Saple Poble Unio Ciula Motion - Centipetal oe ee Bod Diaa Saple Poble on-unio Ciula Motion Aeleated ae o Reeene Da oe and Teinal Speed 5.8 ition oe 6.1 Etendin the Unio Ciula Motion Model 6. on-unio Ciula Motion 6.3 Motion in Aeleated ae Copiht R. Janow Spin 01
2 Sua Dnai o a Conept Ma: inetia, eitane to aeleation, inheent popet oe: puhe o pull on bodie, ontat o thouh ield, aue a bod to aeleate et oe: eto u o all oe atin O a bod (upepoition. net i BD: ee Bod Diaa, ital to poble anali. Inlude ALL oe atin on a bod i ewton 3 Law hold in inetial (un-aeleated eeene ae it Law: A bod eloit i ontant i the net etenal oe atin on it i zeo (equilibiu Seond Law: o eah Cateian oponent net a Aeleation eultin o net Thid Law: I bod A eet a oe on bod B, then bod B eet a oe equal in anitude and oppoite in dietion on bod A. Unit: SYSTEM ORCE MASS ACCELERATIO SI ewton ( K / CGS Dne / Bitih Pound (lb lu t/ ow: Add ition. Copiht R. Janow Spin 01
3 ition Bai A ontat oe between uae due to thei ouhne ition oe alwa oppoe the otion Motion a be: Atual otion ineti (lidin ition Ipendin otion tati ition Model o olid uae in ontat: Suae ouhne eaued b ition oeiient µ and µ ition oe popotional to peue between uae and µ ition oe independent o peed Othe diipatie oe (e.. in liquid depend on peed and ioit KIETIC RICTIO µ 0 W STATIC RICTIO µ W el-aie to anel, up to a beaawa liit µ < µ <,a Copiht R. Janow Spin 01
4 ition oe a a untion o applied oe W Stati ition: a 0 Ipendin otion: a 0 i i W a Slowl ineae and obee ition oe,a µ µ 0 Kineti ition ate beaawa :,a and <,a µ a 0 a > 0 µ and µ depend on uae ondition and ateial µ < µ othewie beaawa ould not happen Copiht R. Janow Spin 01
5 ition oe a a untion o applied oe Slowl ineae and obee ition oe a 0 o W,a BREAKAWAY µ,a µ W <,a µ < µ µ Copiht R. Janow Spin 01
6 Soe ition Coeiient µ < µ Copiht R. Janow Spin 01
7 Eaple: Kineti ition The led and load ae pulled at ontant eloit ind the tenion T in the od µ led Appl Seond Law + T in( φ 0 a T in( φ (1 ition oe depend on the noal oe whih oten doe OT the weiht To( φ a 0 i ontant T o( φ µ ( Subtitute (1 into ( To( φ µ T [ o( φ + µ µ T o( φ in( + µ φ µ ] T in( φ µ in( φ Ealuate: T 91. M led 75 µ 0.10 φ 4 o BD Copiht R. Janow Spin 01
8 Do ou puh o pull (o allet? Aue hild lide at ontant eloit, and a 0 How uh oe i equied to oeoe ition o o( 30 µ 0 µ o( 30 o 30 o 30 o W o W in( 30 a 0 W + in( 30 o > W ' W o ' W + in( 30 a 0 W in( 30 o < W Lae, Lae ition Salle, alle ition Copiht R. Janow Spin 01
9 Eaple: Stati ition on a Rap A oin i jut about to lide down the boo when the anle 15 o. ind the tati ition oeiient µ. i Model a a blo on a ap Chooe -ai alon the ap uae the noal oe i alon -ai Weiht at taiht down,a µ weiht o oin The and aeleation 0 i neatie i poitie (oppoe otion BD o( 0 o( (1 µ in( a 0 (ipendin otion µ in( ( Diide ( b (1 µ in( o( µ tan(.3 Copiht R. Janow Spin 01
10 Aeleation o Conneted Objet with ition A blo o a on a ouh hoizontal uae i onneted to hanin ball 1 b a od pain oe a ale pulle. oe i applied to blo at an anle. Deteine the anitude o the aeleation a. Aue a i poitie (ihtwad and the ae o both BD a 1 1 T 1 T a T 1 (a + (1 BD T a + in( a µ 0 in( ( o( T a o( T (3 a [o( + µ in( 1 ] [ 1 o 0, a i neatie + + µ ] o µ 0 a o( I alo 0 a 1 Copiht R. 1 + Janow Spin 01
11 ition oe o a wall 5 1: A tudent pee he phi boo aaint a ouh etial wall, with he hand eetin a oe noal to the wall. What i the dietion o the ition oe eeted b the wall on the boo? A. oal to the wall, oppoite to the oe o he hand B. Downwad C. Upwad D. Into the wall E. The oe i zeo, ine the boo i in equilibiu Copiht R. Janow Spin 01
12 Eaple: Blo Slidin alon a Wall blo etial wall Cae A: i up W The blo i ee to lide up o down alon the etial wall. It weiht i 100. The tati ition oeiient i The anle 30 o A What i the iniu oe that will peent the blo o lidin down the wall? B What iniu oe will tat the blo oin up the wall? Both ae ae ipendin otion: i µ,a a + 0 a 0,a 0 W 0 in( in( o( (ae o ae B W A [o( + µ in( A 107. ] Cae B: i down W,a W 0 I µ 0, both eult o to the ae eult: W/o( W B [o( µ in( B 1493 ] Copiht R. Janow Spin 01
13 Unio Ciula Motion Manitude,, & a ontant Veto,, a alwa point to P a ω " entipetal anula aeleation" peed The entipetal aeleation ut be aued b a entipetal oe and othewie it into the nd Law. π π /T T ω Looin down on a pu oed to oe in a ile on a table P a T Appliation o Seond Law to poble: T a [ all eal adial oe ] The a ide o nd Law The atual phial oe Centipetal oe hane the dietion but not the anitude o a bod eloit; i.e. o 0 ( Copiht R. Janow Spin 01
14 Appliation to nd Law Poble, ontinued Eaple: Pu on the end o a ope (hoizontal T T (tenion in the ope I ope bea, T anihe a doe a. Ma lie o tanent to ile Eaple: Paene in a a tunin let T ition with the eat, oe o eat belt o o doo ontat Paene i in a otatin (non-inetial eeene ae and eel a ititiou entiual oe Poble Solin Method P a T Ue ae poe a o othe nd Law poble inludin BD oulate poble in inetial (non-otatin eeene ae Teat adial dietion at oe oent a an ai Dnaial quantitie otate how naphot BD Soetie poble need eeal naphot Set the u o eal adial oe / te (peiou lide T a [ all eal adial oe ] Copiht R. Janow Spin 01
15 Eaple: Eath Satellite in Ciula Obit Gien: Altitude h 50 Obital peed 7.6 / 7600 / Ma 1000 ind: Centipetal aeleation a oe eeted b Eath Solution: a a T EARTH a Teat Eath a a point a at it ente (ia Shell Theoe Cente o obit i at Eath ente h + e 6890 h Centipetal aeleation: altitude, a 6 e 6370 T / Gaitational oe: a / 8400 T IDEPEDET O MASS OBJECTS ISIDE THE SATELLITE EEL WEIGHTLESS SICE THEY ALL HAVE THE SAME ACCELERATIO Copiht R. Janow Spin 01
16 Eaple: Conial Pendulu The ball win aound in a iula path L and ae aued nown (initial ondition ind the peed Seth and BD how a naphot o otion Lin( adiu o iula Vetiall, ball i in equilibiu To( T o( (1 a path 0 Hoizontall, ball i in unio iula otion T in( Diide ( b (1: a tan( Lin( tan( ( tan( i independent o a I ou tat with 0, then 0 (zeo path adiu ut be ininite o to appoah 90 o Copiht R. Janow Spin 01
17 Eaple: The Aueent Pa Roto Ride tand aound the wall o a lae linde while it pin. Then the loo dop out. What iniu tanential peed in ut the ide hae in ode to not all thouh? The noal oe i the entipetal oe a R Vetiall, ide ut be ept in equilibiu b tati ition balanin the weiht. The allet alue o oepond to ipendin otion µ,a µ a,a µ µ in R R in µ 0 in µ R R Copiht R. Janow Spin 01
18 Eaple: Baned Roadwa w/o ition Road ae baned at ue o that a do not hae to el on ition to ta on the oad a the o aound ue. Aue: iula ue adiu, 70 hoizontal plane dein peed 60 i/h 6.8 / no ition at all µ 0 ind the ban anle. in( o( Requie equilibiu in the dietion W a 0 o( W (1 in( W Centipetal aeleation alon adial ( dietion: in( Diide ( b (1: ( tan( Ban anle i independent o a (luil 46.3 o W o lae, a lide up o alle, a lide down Copiht R. Janow Spin 01 tan( What peed hould I hae on thi i, baned ue?
19 Eaple: Weiht on a ei Wheel, Tanential Aeleation botto a a u b top R a The appaent weiht o paene at the top and botto o a ei wheel ae dieent. Model the ei wheel a a etial di (adiu 7. otatin at ontant peed, opletin 1 eolution in 8. Aue the eat eain hoizontal a the Wheel otate. ind the appaent weiht at the top ( u and botto ( b. All oe ae adial at top and botto RADIAL Top:,top u R o R the weiht u Botto:,bot b R u b 0 alle than [ ] u 50 R and paene lie o lae than [ + ] b 560 R o, and hae adial and tanential oponent o( t in( o( t in( R [ + Ro( ] Redue to Aboe o 0 o 180 TAGETIAL a t t t a t R tan( Copiht R. Janow Spin 01 Speed would a (not in UCM i a t not anelled b et, inetia o whole wheel, bae
20 on-unio Ciula Motion The aeleation and oe an hae tanential a well a adial (entipetal oponent at point alon a iula path. + ad tan podue entipetal aeleation a ad podue tanential aeleation a tan We oe the eloit to eain tanent to the path, but the peed hane due to a t The net adial oe an not hane the peed a lon a the eloit i tanent to the path o 0 ( ad ad t Copiht R. Janow Spin 01
21 Helial Loop-the-Loop Teat the ide a a etial ile. Speed aie alon the path, a tanential oe eit. oal oe i alwa adiall inwad, equialent to tenion Siila: Ball pun in a etial ile on a od unde tenion Copiht R. Janow Spin 01
22 Eaple: Loop-the loop: otion aound a etial iula ta u a botto u a top OT Unio Ciula Motion: aie with poition. All oe ae adial at top and botto. Elewhee b R b a t (e.., at weiht ha tanential oponent. The noal oe o the ta i adiall inwad; no tanential oponent a ition i abent. Top: Botto: o point, weiht ha adial and tanential oponent: RADIAL TAGETIAL R a t t o,top < R the noal oe < u u,bot b + u o( a t in( R b R u u b [ 0 [ What hould b be at botto to ta on ta at top?: Ue ene. What hane i thee i ition? 1 1 R + b b [ + o( R t in( ] R anda all o u b R Redue to top & botto ae aboe o 180 o 0 Copiht R. Janow Spin 01 ] ] CCW poitie o a t i CW hee alle than b lae than u
23 Motion in Aeleated ae o Reeene A ititiou oe due to inetia appea when the ae o eeene i aeleatin (non-inetial. Objet appea to epond to a oe but Thee i no objet eetin the oe. Real oe ae alwa inteation between objet. Lineal aeleatin te ipl ititiou linea oe: Roet in pae iin oto. People and objet inide ee to eel atiiial ait. Tain o a aeleatin alon a linea path. Paene and looe objet ae puhed towad the ba Rotatin te (UCM o with anula aeleation ipl entiual oe at ontant adiu, due to entipetal aeleation: Paene in a a tunin eel entiual oe:. ititiou outwad adial oe when otatin inide a du ide, pae tation, Alo in otatin te: Coioli oe appea to delet objet hanin adiu o the otation ente: Whilpool, loni to, oean uent low CCW in othen Heiphee Ball thown adiall in pinnin e-o-ound appea to delet Inetial ae ae piileed in that ewton Law ae obeed without inentin ititiou oe Copiht R. Janow Spin 01
24 Eleato a non-inetial te 5-: A peon weihin 0.70 ide in an eleato that ha an upwad aeleation o 1.5 /. What i the anitude o the oe o the eleato loo on the peon? A B C D E Copiht R. Janow Spin 01
25 Eaple: ititiou oe in a Lineal Aeleatin Tain Tain i aeleatin to the iht alon -ai. Pendulu han eel. Both inetial and non-inetial obee aee: od anle equilibiu o the -dietion diaee alon 0 To( To( - Inetial ae obee: aeleate due to hoizontal oponent o T Tin( a (no ititiou oe on-inetial ae obee: i in equilibiu alon : zeo aeleation 0 Tin( - it (ut intodue ititiou oe to eplain the equilibiu Ue pendulu to eaue a: a tan( Copiht R. Janow Spin 01
26 Eaple: Centiual oe in a a ain a let tun A a i ain a let tun on a iula etion o leel oad at ontant peed. Obee in inetial and otatin ae aee that a paene a lide to the iht ide o the a. Inetial ae o the Eath: the a eat eet a eal entipetal oe on paene towad the ente o otation, due to ition. ad eat a I the ition oe i not lae enouh, paene tend to oe tanent to the path due to ewton it Law eal entipetal oe on-inetial ae (aeleatin with the a: paene i in equilibiu, with ititiou entiual oe in adial outwad dietion, aneled b eat ition puhin letwad. 0 ad eat it it R ititiou entiual oe Inetial ae ae piileed in that ewton Law ae obeed without inentin ititiou oe Copiht R. Janow Spin 01
27 Eaple: Coioli oe in a otatin te An objet oin in a otatin oodinate te a hane it adial ditane o the otation ai. In an inetial te it ollow ewton it Law. In the non-inetial (otatin te, objet epond to a ititiou Coioli oe, eultin in ued path. Eaple (CW otation Eaple: Ai o wate oin alon Eath uae (oth o Equato to: oth eel Wetwad Coioli oe South eel Eatwad Coioli oe A a eult: Wate pial CCW aound a dain Huiane, tonadoe, Monoon, et pial CCW Coioli eet eee to CW South o the Equato. Copiht R. Janow Spin 01
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