1. A 4.00-kg stone is whirled at the end of a 2.00-m rope in a horizontal circle at a speed of 15.0 m/s. Ignoring the gravitational effects;
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1 AP Physics Centripetl Pcket 1. A 4.00-kg stone is whirled t end 2.00-m rope in horizontl circle t speed 15.0 m/s. Ignoring grvittionl effects; A. Clculte centripetl ccelertion B. Clculte centripetl force. 2. A 1500 kg cr moving t 86.0 km/hr goes round curve 325 m rdius. A. Wht is centripetl ccelertion? B. Wht is centripetl force on cr? 3. An electron is moving t speed 2.00 X 10 6 m/s in circle rdius 0.05 m. Wht is force on electron? 4. A boy sits on edge polished wooden disk. The disk hs rdius 3.00 m nd coefficient friction between his pnts nd disk is Wht is mximum speed disk t moment boy slides f? 5. A 1200-kg cr begins to skid when trveling t 80.0 km/hr round level curve 125 m rdius. centripetl ccelertion nd coefficient friction between tires nd rod. 6. A motorcyclist goes round curve 100-m rdius t speed 95.0 km/hr, without lening into turn. A. Wht must coefficient friction between tires nd rod be in order to supply necessry centripetl force? B. If rod is iced nd motorcyclist cn not depend on friction, t wht ngle from verticl should motorcyclist len to supply necessry centripetl force?
2 AP Physics Centripetl Pcket 7. At wht ngle should highwy be bnked for crs trveling t speed 100 km/hr, if 6.8 Newton's Lw Universl 11. A 3200-lb cr begins to skicl when rdius rod is 400 m nd no frictionl forces re involved? trveling t 60.0 mph round" level Grvittion curve SOO-ft rdius. 20. Two lrge metl spheres re centripetl ccelertion nd seprted by distnce 2.00 m coefficient friction between from center to center. If ech sphere tires nd rod. hs10.0 msskg mss. SOOOkg, wht is 8. Acr5.0 kg mss is 1.00 m from 12. A 1200-kg begins to skid when grvittionl force between m? trveling t 80.0 km/hr round 21. A S.OO-kg mss is 1.00 m from level curve 12S-m rdius. A. Wht is grvittionl forcemss. tht() 5.0is kg 10.0-kg Wht mss exerts on 10.0 kg mss? centripetl ccelertion nd grvittionl force tht S.OO-kg coefficient friction between exerts on 10.0-kg mss? tires nd rod. B. Wht is grvittionlmss force tht 10.0-kg mss exerts on 5.0 kg mss? (b) Wht is grvittionl force 13. At wht ngle should bobsled turn tht 10.0-kg mss exerts on be bnked if sled, moving t 26.0 mss? wht (c) If both re If both msses re free S.OO-kg to move, will msses ir initil ccelertion be? mis, is to roundc. turn rdius 100 free to move, wht will ir initil m? ' ccelertion be? 14. A motorcyclist goespoint roundmsses curve 9. Three kg,Three 20.0 kg,msses nd30.0 kg20.0 re locted on line t 10.0 cm, point 10.0 kg, 400-ft rdius t speed 60.0 kg, nd 30.0 kg re locted on line 50.0 cm, nd 80.0 cm, respectively. mph, without lening into turn. t 10.0 cm, SO.Ocm, nd 80.0 cm, () Wht must coefficient respectively. resultnt friction betweena. tires nd resultnt grvittionl 10.0-kg mss, grvittionlforce force on on () 10.0-kg rod be in order to supply mss, (b) 20.0-kg mss, nd necessry centripetl force? (b) If (c) 30.0-kg mss. resultnt grvittionl force on 20.0-kg mss, rod is icedb. nd motorcyclist 23. Pete meets Eileen for first time cn not depend on friction, t wht nd is immeditely ttrcted to her. ngle from verticl should If Pete hs force mss on 7S.0 nd C. resultnt grvittionl kg30.0-kg mss. motorcyclist len to supply Eileen hs mss SO.O kg nd necessry centripetl force? y re seprted by distnce 15. A motorcyclist roundeileen curve for first time nd is immeditely ttrcted to her. If Pete hs 10. Petegoes meets 3.00 m, is ir ttrction purely 100-m rdius t speed 9S.0 physicl? mss 75.0 kg nd Eileen hs mss 50 kg nd y re seprted by distnce km/hr, without lening into turn. () Wht must coefficient ttrction purely physicl? 3.00 m, is ir friction between tires nd rod be in order to supply necessry centripetl force? (b) If rod is iced nd motorcyclist cn not depend on friction, t wht ngle from verticl should motorcyclist len to supply necessry centripetl force? 16. At wht ngle should highwy be bnked for crs trveling t speed 3m 60.0 mph, if rdius rod is 1000 ft nd no frictionl forces re involved? 24. Wht is grvittionl force 17. At wht ngle should highwy be proton nd n electron in 11.forWht is tgrvittionl force between between proton nd n electron in hydrogen tom if bnked crs trveling speed hydrogen tom if y re seprted 11 m? 100 km/hr, rdius yifre seprted by distnce 5.29xS m? by distnce X 10rod is 400 m nd no frictionl forces re involved? The Accelertion Due 18. An irplne is flying in circle with to Grvity speed 200 knots. (A knot is nuticl mile per hour.) The ircrft 25. Wht is vlue g t distnce weighs 2000 Ib nd is bnked t n from center erth () I ngle rdius erth rdius, (b) 2 erth rdii, (c) 10 turn in feet. erth rdii, nd (d) t distnce 19. An irplne is flying in circle with moon? speed 6S0 km/hr. At wht ngle with horizon should pilot mke turn rdius 8.00 km such tht component lift ircrft supplies necessry centripetl force for turn? vittion, nd Stellites 185
3 h y d e f n AP isphysics Pcket 26. Wht weightcentripetl body, in Additionl Problems t42. A rope is ttched to pil wter terms its weight t surfce nd pil is n rotted in t36. A rock ttched to string hngs erth, t distnce from verticl circle 80.0-cm rdius. from ro moving trin. If center erth () 1 erth 12. A rock ttched to string hngs from ro moving trin. If Wht trin is trveling must minimum speed trin is trveling t 50.0 mph rdius, (b) 2 erth rdii, (c) 10 erth pil wter be such tht t 50.0 mph round level curve 500 ft rdius, find ngle tht string mkes round level curve 500-ft rdius, rdii, nd (d) t distnce wter will not spill out? find ngle tht string mkes nverticl. moon?with How cn object in 43. A mss is ttched to string nd is with verticl. stellite, t sy 2 erth rdii, be swung in verticl circle. At considered to be weightless? prticulr instnt mss is moving 27. Clculte ccelertion grvity t speed v, nd its velocity vector on surfce Mrs. Wht would mkes n ngle 0 with horizontl. mn who weighs 180 Ib on erth Show tht norml component weigh on Mrs? ccelertion is given by U8. It is yer 2020 nd bse hs T + w sino = rnv2/r been estblished on Mrs. An enterprising businessmn decides to nd tngentil component buy cfee on erth t $5.00/lb nd ccelertion is given by sell it on Mrs for $1O.00/lb. How T = -gcoso much does he mke or lose per Ib Hence show why this motion in when he sells it on Mrs? Ignore verticl circle is not uniform circulr cost trnsporttion from erth to motion. Mrs. t44. A 10.0-N bll ttched to string 29. The sun's rdius is 110 times tht 1.00 m long moves in horizontl erth, nd its mss is 333,000 circle. The string mkes n ngle times s lrge. Wht would be Additionl Problems t42. A rope is ttched to pil wter 60.0 with verticl. () weight I.OO-kgobject t nd pil is n rotted in t36. A rock ttched to string hngs 37. centripetl force due to in string. (b) surfce sun, ssuming tht it verticl circle 80.0-cm rdius. from ro centripetl moving trin. If rottion erth cting on component 13. rottion cting on erth 100 kgperson tht does not melt or' evporte re? force due to Wht must minimum speed trin is trveling t 50.0 mph 100kgpil person t () equtor, supplies necessry centripetl wter be such tht round level curve 500-ft rdius, (b)wter 45.0 will ltitude, nd (c) force. (c) speed bll. not spill out? A. t find ngle tht equtor string mkes Stellite Motion pole.is ttched to string nd is 43. A mss with verticl. 38. vector ccelertion 30. Wht is velocity moon swung resultnt in verticl circle. At by ccelertion dueistomoving B. t round erth in 45.0 circulr orbit? ltitude cused prticulr instnt mss grvity nd centripetl Wht is time for one revolution? t speed v, nd its velocity vector ccelertion for person locted t 31. Clculte velocity erth in mkes n ngle 0 with horizontl. C. circulr t orbit pole. ()Show equtor, 45.0 component n pproximte bout tht (b) norml ltitude, nd (c) is sun. Clculte time for one ccelertion given pole. by A pilot who weighs 180 Ib pulls out revolution. 14. A rope is ttched to pilt39. wter nd+ pil is w tsino rnv2n /rlong rotted in verticl circle verticlt dive 400=mph 32. A stellite orbits erth 700 mi 80.0-cm rdius. Wht speed pil rc tngentil circle 5280-ft rdius. nd component wter be such tht bove surfce. its speed nd must nminimum centripetl ccelertion, ccelertion is given by its period revolution. wter will not spill out? centripetl force, nd net norml 33. Clculte speed stellite T = -gcoso force on pilot t bottom orbiting 100 km bove surfce 15. A 10.0-N bll ttched to string 1.00 m long dive. Hence show why thismoves motion inin horizontl circle. The string Mrs. Wht is its period? circle is not uniform circulr t34. An Apollo spce cpsule orbited mkes n ngle 60.0 with verticl verticl. motion. moon in circulr orbit t height 45. A mss rna = 35.0 g is on smooth t44. A 10.0-N bll ttched to string 112 km bove surfce. The A. in string. horizontl tble. It is connected by 1.00 m long moves in horizontl time for one complete orbit, string tht psses through center circle. The string mkes n ngle period T. ws 120 min with verticl. () tble to mss rnb = 25.0 g. mss moon. B. force component force. orbits centripetl. At wht uniform speed should rna in tht string.supplies (b) centripetl t35.37.a stellite erth indue to rottion erth cting on move in circle rdius r = 40.0 component tht circulr orbit in 130 min. Wht is 100 kg person t () cm such tht mss rnb remins equtor, bll.supplies necessry centripetl distnce C. stellite tospeed (b) 45.0 ltitude, nd (c) motionless? force. (c) speed bll. center erth? Wht is its pole. t46. Three point msses 30.0 kg, 50.0 height bove surfce? Wht is its 38.speed? resultnt vector ccelertion kg, nd 70.0 kg re locted t cused by ccelertion due to 40. A 90-kg pilot pulls out verticl vertices n equilterl tringle grvity nd centripetl dive t 685 km/hr long n rc 1.00 m on side. resultnt ccelertion for person locted t circle 1500-m rdius. grvittionl force on ech mss. () equtor, (b) 45.0 centripetl ccelertion, centripetl t47. Four metl spheres re locted t ltitude, nd (c) pole. force, nd net force on pilot corners squre sides t39. A pilot who weighs 180 Ib pulls out t bottom dive. m. If ech sphere hs mss 10.0 verticl dive t 400 mph long t41. Wht is minimum speed n kg, find force on sphere in n rc circle 5280-ft rdius. irplne in mking verticl loop lower right-hnd corner. centripetl ccelertion, such tht n object in plne will centripetl force, nd net norml not fll during pek loop? \ force on pilot t bottom The rdius loop is 1000 ft. dive A mss rna = 35.0 g is on smooth horizontl tble. It is connected by string tht psses through center tble to mss rnb = 25.0 g.. At wht uniform speed should rna Mechnics
4 AP Physics Centripetl Pcket 1. Mr. Gobbles (Mss = 4kg) is swinging from rope (length = 2.3m). If t bottom verticl circulr pth speed Gobbles is 5.9 m/s, find in rope. T= 2. Wht is minimum speed to get Gobbles over top? Hint: Wht would be in string if Gobbles just mkes it round circle? Tmin= vmin=
5 AP Physics Centripetl Pcket 5. For more fun, turkey (Mss = 11kg) goes on ride t elementry school plyground (rdius = 2.3m). gretest velocity he cn hve if coefficient friction for ride nd turkey is V = 6. A turkey (mss = 6kg) is spinning round on n ice pond μ = 0, tied to rope (length = 8m). How mny times does bird circle ech minute, if bird feels centripetl ccelertion 5 g? v = rev/min =
6 AP Physics Centripetl Pcket 3. A strnge mn (m = 80 kg) in turkey costume goes on Rotor ride (r = 3.2m). As y lower floor ride, ride completes turn every 4.1 s. Wht is necessry vlue μ so tht turkey-mn will not fll? v = μmin = 4. This turkey (m = 10kg) is on sfer ride t musement prk. As ride opertes, chin cretes 75 o ngle with ground, nd pth with 3.9m rdius. in chin, nd velocity turkey T = V =
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