Circular Motion Problem Solving

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Alan George
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iula Motion Poblem Soling Aeleation o a hange in eloity i aued by a net foe: Newton nd Law An objet aeleate when eithe the magnitude o the dietion of the eloity hange We aw in the lat unit that an

1 iula Motion Poblem Soling Aeleation o a hange in eloity i aued by a net foe: Newton nd Law An objet aeleate when eithe the magnitude o the dietion of the eloity hange We aw in the lat unit that an objet peed up o low down when a net foe at in the ame o oppoite the dietion of it motion (tangential to the motion x net x ma In thi unit, we examine the aeleation due to a hange in dietion of the eloity. An objet hange dietion o moe in a ue when a net foe at pependiula to the dietion of motion, towad the ente of the ue. A net foe pependiula to the dietion of motion i alled a entipetal (enteeeking foe,, and the aeleation it gie ie to i a entipetal aeleation, a. entipetal aeleation i a hange in the eloity dietion only and it an be hown to be equal to / whee i the peed and i the adiu of the ue. he entipetal foe i found by adding all the foe in the adial dietion (pependiula to the ue Note that "entipetal foe" i jut a fany name fo the adial omponent of the net foe. It i not a new kind of foe and i NO dawn on foe diagam. A net foe ould hae both tangential and adial omponent; the omponent tangential to the dietion of motion aue the objet to peed up o low down and the adial omponent aue the objet to moe in a ue. In thi unit, we fou on the aeleation aoiated with a hange in dietion only. In othe wod, an objet that moe with ontant peed but ontinuouly hange dietion UNIORM IRULAR MOION. An objet in unifom iula motion ha ontant peed,, entipetal aeleation, a, and undegoe peiodi motion with peiod and fequeny, f. tangential o linea peed: = d/t = / = f angula peed: =/t= / = f entipetal aeleation: a = / = Poblem: 1. he angula peed of a eod playe i 33 otation pe minute. It ha a diamete of 1 inhe (0.305m. a What i the peiod and fequeny of otation of the eod? f 33ot / min 0.55e 0.55Hz 1/ f 1.8e b What i the angula peed in ad/ What i the tangential peed of the oute mot pat of the eod? x ma and d What i the tangential peed halfway out to the edge of the eod? tangential peed i dietly popotional to o the peed would be half what it i on the oute pat: = 0.65m/ y net y m( / m f 3.45ad e 3.45( m ma y a m

2 . A 900 kg ae a make one lap aound a tak of adiu 50. m in 11.0 a What i the a aeage peed? (50 a 8.6m 11 b What i the a angula peed? What i the a entipetal aeleation? d What i the entipetal foe ating on the a and whih foe poide it? Stati fition between the tie and the oad poide the 14,670N entipetal foe ma ( 900( , 670N 3. a A a goe aound a ue at 0.0 m/. If the adiu of the ue i 50.0 m, what i the entipetal aeleation of the a? 0 a 8m 50 b If the peed of the a wee haled, how muh diffeent would a be to tael the ame adiu ue? Beaue the entipetal aeleation depend on the quae of the peed, if the peed wee haled and the adiu tayed the ame, a would deeae by a fato of 4 4. A peed kate goe aound a tun with a 31 m adiu. he kate ha a peed of 14m/ and expeiene a entipetal foe of 460N. What i the ma of the kate? m( m 7.8kg 5. Noman Neuton wing a ubbe ball attahed to a ting oe hi head in a hoizontal, iula path. he piee of ting i 1.5 m long and the ball make 10 omplete tun eah minute. a What i the aeage peed of the ball? 1min 60 ( yle 10yle ( m 0.5 b What i the ball entipetal aeleation? a a ad ma 16.3m m 36m 6. alulate the entipetal aeleation of the Eath towad the Sun. ( = 1.5 x m don t know the peed of the Eath, but we know the peiod (1yea 365day 4h ( 1yx x x 3.154x10 1y 1y 1h 10yle a ( (1.5 x10 7 (3.154x m

3 7. A 0.50 kg ma i attahed to a ting 1.0 m long and moe in a hoizontal ile at a ate of.0 Hz. a alulate the entipetal aeleation of the ma. f = Hz. = 1/f = 0.5 ( 4 4 (1 a 158m 0.5 b alulate the tenion in the ting. he tenion in the ting i what poide the entipetal foe. ma ( 0.5(158 79N 8. A penny, plaed on a pinning eod, otate at 33 1 / 3 eolution pe minute when it i plaed 10 m fom the ente of the eod (ma of penny =.5 gam. a What i the tangential and angula peed of the penny a it moe aound the ente of the eod? 10m 0.10m ( m f 33.3e / min 0.555e 1/ f 1.80e b What i the magnitude of the entipetal foe neeay to keep the penny moing in a iula path? How muh fitional foe i applied to the penny by the ufae of the eod? It i tati fition between the penny and tuntable that poide all of the entipetal foe. heefoe, f = = N d Daw a fee body diagam howing all the foe ating on the otating penny oe Diagam ad 0.35 ma m N 0.1 N eod f g e What i the minimum oeffiient of tati fition equied to keep the penny fom liding off the eod? Newton Seond Law Appliation N mg f ma mg /

4 9. A ei wheel with a 38 m adiu and tangential peed of 5.0 m/ ha a 76 kg paenge iding it. a What i the magnitude of the entipetal foe ating on the ei wheel paenge at the top and at the bottom? Same m, and at top and bottom, o i the ame magnitude at the top and bottom. 5 ma m 76 50N 38 b omplete the feebody diagam howing all the foe ating on the paenge at the top and at the bottom of the ei wheel. Label the foe. Indiate whethe the appaent weight of the paenge (the nomal foe i geate, equal to, o le than thei tue weight at the top and at the bottom. oe Diagam fo top Note that at the top, the entipetal foe mut be dietly down, towad the ente of the ile. heefoe N < g to get a net foe down (like the eleato aeleating downwad. oe Diagam fo bottom Note that at the bottom, the entipetal foe mut be dietly up, towad the ente of the ile. heefoe N > g to get a net foe up (like the eleato aeleating upwad. N N g Appaent wt < ue wt g Appaent wt > ue wt How big i the nomal foe exeted on the paenge the top and at the bottom? Note: he poitie adial dietion i taken a the dietion towad the ente of the ile beaue foe pointed into the ile ADD to entipetal foe he negatie adial dietion i away fom the ente of the ile. NSL Appliation ma ( / At the top ma g N N mg N Stat with Newton nd Law fo the adial omponent of the net foe. Ue you BD aboe to guide you in umming up the adial foe to find the entipetal foe and the nomal foe. entipetal foe i upplied by the ombination of gaity pointing into the ente of the ile and the nomal foe pointing out of the ile ( g - N. It i 50 N ( / he nomal foe i what a ale would ead of you weight. Hee the nomal foe i you tue weight minu a tem due to the entipetal aeleation. You appaent weight i lighte due to the aeleation, jut a in the eleato

5 At the bottom ma N g N mg N entipetal foe i upplied by the ombination of gaity pointing out of the ile and the nomal foe pointing into the ile ( N - g. It i 50 N ( / he nomal foe i what a ale would ead of you weight. Hee the nomal foe i you tue weight plu a tem due to the entipetal aeleation. You appaent weight i heaie due to the aeleation, jut a in the eleato d How fat would the ei wheel hae to go fo the paenge to feel double thei tue weight at the bottom of the ei wheel? What the paenge feel i the nomal foe puhing on them. If the nomal foe (appaent weight wa double the tue weight (G at the bottom, the net foe pointing into the ente of the ile (the entipetal foe, would be geate due to the ei wheel moing fate (ine the adiu and ma of paenge annot hange ma N g g g g mg g 14m e At the peed found in pat d how heay would the paenge feel at the top of the ei wheel (thi i the nomal foe? At the peed found aboe, the entipetal foe at the bottom (the net adial foe i g Sine = g i the ame at eey point on the ei wheel (what hange i the ontibution of N and g to the entipetal foe, at the top whee g i pointing into the ile, the nomal foe mut be zeo and the paenge feel weightle. You an alo find thi by alulating At the top ma m N 0 g N N (70( N

6 10. azan (m = 85 kg tie to o a ie by winging fom a 10-m-long ine. Hi peed at the bottom of the wing (a he jut lea the wate i 8.0 m/. azan doen t know that the ine ha a beaking tength of 1000 N. Doe he make it afely ao the ie? Jutify you anwe ma g mg (858 (85( N No, azan doen t make it ine the tenion equied to poide the neeay entipetal foe exeed 1000N g

Recitation PHYS 131. must be one-half of T 2

Recitation PHYS 131. must be one-half of T 2 Reitation PHYS 131 Ch. 5: FOC 1, 3, 7, 10, 15. Pobles 4, 17, 3, 5, 36, 47 & 59. Ch 5: FOC Questions 1, 3, 7, 10 & 15. 1. () The eloity of a has a onstant agnitude (speed) and dietion. Sine its eloity is