( ) 2. Chapter 3 Review, pages Knowledge

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1 Chapte 3 Review, pages Knowledge 1. (a). (a) 3. (b) 4. (b) 5. (c) 6. (d) 7. False. An amusement pak ide moving down with a constant velocity is an example of an inetial fame of efeence. 8. Tue 9. False. The diection of centipetal acceleation fo a ca on a banked cuve is always hoizontal into the tun. 10. False. The magnitude of an object s centipetal acceleation inceases with the mass and the velocity of the object, but not the adius of the cicula path. 11. Tue 1. False. The Moon is an example of an object in unifom cicula motion. 13. False. Objects moving in a otating fame of efeence expeience a foce pependicula to the velocity of the object in the otating fame. 14. False. A Foucault pendulum demonstates that Eath is a otating fame of efeence. 15. Tue 16. (a) Substitute v new v in the equation fo centipetal acceleation: a c v new v ( ) a c 4 v The centipetal acceleation is fou times its oiginal value. (b) Substitute new in the equation fo centipetal acceleation: a c v new v v a c 1 The centipetal acceleation is half its oiginal value. 17. The faste ca expeiences the geate foce because centipetal foce inceases with speed. 18. Centifuges ae used to sepaate blood into its components pats. Copyight 01 Nelson Education Ltd. Chapte 3: Unifom Cicula Motion 3-

2 19. (a) The souce of the centipetal foce on the Moon is Eath s gavitational foce. (b) The souce of the centipetal foce on a ca tuning a cone is static fiction. (c) The souce of the centipetal foce on a ock on a sting is tension. Undestanding 0. (a) You must hold the acceleomete exactly hoizontal, so that the angle the bead makes with the vetical is 0 when the ca is at est. If it is tilted slightly, a non-zeo angle will intoduce an eo into all measuements. (b) The bead will be at an angle of 0 with espect to the vetical. (c) The bead will oll to the west side of the acceleomete, o towad you. (d) The bead will be at an angle of 0 with espect to the vetical. (e) The bead will oll to the east side of the acceleomete, o away fom you. (f) Given: θ 13 Requied: a Analysis: Look at the situation fom an Eath (inetial) fame of efeence. The hoizontal component of the tension F T balances the acceleation and the vetical component of the tension F T balances the gavitational foce. Expess the components of the tension in tems of the hoizontal and vetical applied foces. Then calculate the magnitude of the acceleation. Solution: Vetical component of foce:!f y 0 F T cos" mg 0 F T mg cos" Hoizontal component of foce:!f x ma F T sin" ma mg cos" ( sin" ma g sin" cos" ( a g tan" a a ( 9.8 m/s )tan13 a.3 m/s Statement: The magnitude of the ca s acceleation is.3 m/s. 1. (a) Given: 13 cm 0.13 m; f 33.5 pm Requied: a c Analysis: a c 4! f Solution: Convet the fequency to hetz: f 33.5 pm min! 1 min 60 s f Hz (two exta digits caied) Copyight 01 Nelson Education Ltd. Chapte 3: Unifom Cicula Motion 3-3

3 Detemine the centipetal acceleation: a c 4! f ( )( Hz) 4! 0.13 m a c 1.6 m/s Statement: The centipetal acceleation is 1.6 m/s. (b) Given: 4.3 m; T 1. s Requied: a c Analysis: a c 4! T Solution: a c 4! T ( ) 4! 4.3 m ( 1. s) a c 1. "10 m/s Statement: The centipetal acceleation of the lasso is m/s. (c) Given: v m/s; d m m Requied: a c Analysis: a c v Solution: a c v ( ).18!106 m/s ( 5.30!10 "11 m) a c 8.97!10 m/s Statement: The magnitude of the centipetal acceleation is m/s.. Given: 15 m; a c 33.8 m/s Requied: v Analysis: a v c v a c Solution: v a c ( 33.8 m/s )( 15 m ) v 65 m/s Statement: The speed of the ca is 65 m/s. 3. Given: v 50.0 km/h; d 33.5 m o m Requied: a c Analysis: a c v Copyight 01 Nelson Education Ltd. Chapte 3: Unifom Cicula Motion 3-4

4 Solution: Convet the speed to metes pe second: v 50.0 km h! 1000 m 1 km! 1 h 60 min! 1 min 60 s m/s (two exta digits caied) v 13.9 m/s Detemine the centipetal acceleation: a c v m/s ( m) a c 11.5 m/s ( ) Statement: The magnitude of the centipetal acceleation is 11.5 m/s. 4. Given: d 0 m o 10 m; F net 1 3 F g Requied: v ; F g mg; F net + F g F net 1 3 F g + F g 1 3 F g! 3 F g mv! 3 mg v! mg 3 m v! 3 g Solution: v! 3 g ( ) 10 m ( )!!9.8 m/s 3 v 8.1 m/s Statement: The speed of the olle coaste is 8.1 m/s. Copyight 01 Nelson Education Ltd. Chapte 3: Unifom Cicula Motion 3-5

5 5. Substitute m locomotive 3m cago ca in the equation fo centipetal foce: F locomotive m locomotive v ( 3m cago ca )v 3 m cago ca v F locomotive 3ago ca The centipetal foce on the locomotive is thee times the foce on the cago ca. 6. (a) Given: m.0 kg; v 0 m/s; 16 m Requied: Solution: (90 kg)(0 m/s) (16 m)!10 3 N Statement: The centipetal foce is 10 3 N. (b) Given: m.0 kg; v 0 m/s; 10 m Requied: Solution: (90 kg)(0 m/s) (10 m) 4!10 3 N Statement: The centipetal foce is N. (c) Given: m.0 kg; v 5 m/s; 10 m Requied: Solution: (90 kg)(5 m/s) (10 m)!10 N Statement: The centipetal foce is 10 N. Copyight 01 Nelson Education Ltd. Chapte 3: Unifom Cicula Motion 3-6

6 7. Given: m.0 kg;.8 10 N; 1.00 m Requied: v F c m Solution: v F c m.8!10 kg " m s ( ( 1.00 m) (.0 kg ) v 1 m/s Statement: The speed of the discus is 1 m/s when eleased. 8. (a) Given: m.0 kg; 0.5 m; f 1.0 pm 1 60 Hz Requied: ma c ; a c 4! f ; 4! mf Solution: 4! mf " 1 4! (.0 kg)(0.5 m) 60 Hz N Statement: The centipetal foce is N. (b) Given: m.0 kg; 0.5 m; f 5.0 pm 1 1 Hz Requied: ma c ; a c 4! f ; 4! mf Solution: 4! mf " 1 4! (.0 kg)(0.5 m) 1 Hz 0.7 N Statement: The centipetal foce is 0.7 N. 1 (c) Given: m.0 kg; 0.5 m; f 1.0 pm 10 Hz Requied: ma c ; a c 4! f ; 4! mf Copyight 01 Nelson Education Ltd. Chapte 3: Unifom Cicula Motion 3-7

7 Solution: 4! mf " 1 4! (.0 kg)(0.5 m) 10 Hz N Statement: The centipetal foce is N. 9. The peson s weight equals mg, so if the nomal foce of N is the esult of g, then half the nomal, o N is the peson s weight. Analysis and Application 30. Given: m; f 60 pm 1.0 Hz Requied: a c Analysis: a c 4π f Solution: a c 4! f ( )( 1.0 Hz) 4! m a c 1. m/s Statement: The centipetal acceleation is 1. m/s. 31. Given: 0.50 m; m 1.5 kg; F T 5 N Requied: maximum v Analysis: The maximum speed of otation is when the centipetal foce equals the maximum tension befoe the sting beaks. v F c m Solution: v F c m " 5 kg! m s ( 0.50 m ) ( 1.5 kg ) v.9 m/s Statement: The maximum speed of otation befoe beaking the sting is.9 m/s. 3. Given: F N 3.5F g ; v 6 m/s Requied: ; F g mg; F N + F g Copyight 01 Nelson Education Ltd. Chapte 3: Unifom Cicula Motion 3-8

8 Solution: F N + F g 3.5F g + F.5F g.5mg mv.5mg v.5g ( ) ( ) 6 m/s m/s 8 m Statement: The adius of the tack s cuvatue is 8 m. 33. (a) Given: m 35 kg; d m o 11 m; f 3.5 pm Hz Requied: F N at the top 4π mf ; F N F g Solution: F N F g! mg! 4" mf ( 35 kg) ( 9.8 m/s )! 4" ( 35 kg) ( 11 m) 3.5 F N.9 ) 10 N Statement: The foce of the seat is.9 10 N. 60 Hz ( (b) Given: m 35 kg; d m o 11 m; f 3.5 pm Hz Requied: F N at the bottom 4π mf ; F N F g + Solution: F N F g + mg + 4! mf " ( 35 kg) ( 9.8 m/s ) + 4! ( 35 kg) ( 11 m) Hz F N 3.9 ( 10 N Statement: The foce of the seat is N. 34. Given: m 1.5 kg;.0 m Requied: F T at the bottom Analysis: Since the tension at the top of the loop equals the gavitational foce, but the speed constant, the centipetal foce must equal the gavitational foce at all points along the cicula path: mg; F T F g + Copyight 01 Nelson Education Ltd. Chapte 3: Unifom Cicula Motion 3-9

9 Solution: F T F g + mg + mg mg 1.5 kg ( ) ( ) 9.8 m/s F T 9 N Statement: The tension when the ock is at the bottom is 9 N. 35. (a) Ovehead: Side view: (b) (c) The centipetal foce is the sum of the tension and the gavitational foce. Given the angle, the centipetal foce is equal to F T cos θ. (d) Given: 1.5 m; v 10.0 m/s Requied: θ tan! F g mg mv g v g! tan "1 ( v ; F g mg g Solution:! tan "1 v ( m 9.8 kg ) s ( ( 1.5 m ) ( tan "1 ( 10.0 m ( s ( (! 8.4 Statement: The sting makes an 8.4 angle with the hoizontal. Copyight 01 Nelson Education Ltd. Chapte 3: Unifom Cicula Motion 3-10

10 36. Given: m kg; 35 m; v 1 m/s Requied: F s Solution: F s ; F s ( )( 1 m/s) ( 35 m) 1.7! 103 kg F s 7.0! 10 3 N Statement: The fiction foce is N. 37. Given: m 50.0 kg; 0.75 m; F T 50.0 N Requied: maximum v Analysis: The maximum speed of otation is when the centipetal foce equals the maximum tension befoe the sting beaks. v F c m Solution: v F c m " 50.0 kg! m s 0.75 m ( 0.30 kg ) ( ) v 11 m/s Statement: The maximum speed of otation befoe beaking the sting is 11 m/s. 38. Given: m 70.0 kg; v.0 m/s; 1.0 m Requied: Solution: 70.0 kg ( )(.0 m/s) ( 1.0 m).8! 10 N Statement: The centipetal foce is.8 10 N. Copyight 01 Nelson Education Ltd. Chapte 3: Unifom Cicula Motion 3-11

11 39. Given: m 30.0 kg; d 0.0 m o 10.0 m; 3 N Requied: v v F c m Solution: v F c m " 3 kg! m s 10.0 m 30.0 kg ( ) ( ) v 3.3 m/s Statement: The speed of the child cycling is 3.3 m/s. 40. Given: v 55 m/s; m 15 kg; 5 m Requied: Solution: 15 kg ( )( 55 m/s) ( 5 m) 1.5! 10 4 N Statement: The centipetal foce is N. 41. (a) Given: m; v m/s; 16 N Requied: m m F c v Solution: m F c v " 16 kg! m s " m s m ( ) m 8 kg Statement: The mass of the boat is 8 kg. Copyight 01 Nelson Education Ltd. Chapte 3: Unifom Cicula Motion 3-1

12 (b) Given: m; m 8 kg; 4 N Requied: v v F c m Solution: v F c m " 4 kg! m s ( m) ( 8 kg ) v 1 m/s Statement: The speed should be deceased to 1 m/s. 4. (a) Substitute v v 1 in the equation fo centipetal foce: F mv ( ) m v 1 4 mv 1 F 4F 1 The centipetal foce on the ca is fou times the foce at half the speed. (b) If thee wee no fiction, the ca would not be able to tun and would continue in the same diection. 43. Given: m 105 kg; v 7.0 m/s; 15 m Requied: Solution: 105 kg ( )( 7.0 m/s) ( 15 m) 3.4! 10 N Statement: The centipetal foce is N. 44. Given: T.00 s; m kg; m 5.00 kg; m; 6.00 m Requied: 4! m T Copyight 01 Nelson Education Ltd. Chapte 3: Unifom Cicula Motion 3-13

13 Solution: Detemine the tension in sting B: F B 4! m T ( )( 6.00 m) (.00 s) 4! 5.00 kg F B 96 N Detemine the tension in sting A: F A 4! m F B T ( )( 4.00 m) + 96 N (.00 s) 4! 3.00 kg F A 414 N Statement: The tension in sting A is 414 N and the tension in sting B is 96 N. 45. (a) Given: m 1.0 kg; m 5.0 kg; µ s 0.30; 5.0 m Requied: maximum v ; F s µ s mg; The maximum speed is the point at which the centipetal acceleation on mass 1 equals the foce of static fiction keeping mass 1 on top of mass. Solution: F s mv! s mg v! mg s m v! s g ( ) 9.8 m/s ( )( 5.0 m ) 0.30 v 3.8 m/s Statement: The maximum speed is 3.8 m/s. (b) Given: m 1.0 kg; m 5.0 kg; µ s 0.30; 5.0 m Requied: F T Solution: ( F T m + m 1 )v.0 kg kg ( )( m/s) ( 5.0 m) F T 1 N Copyight 01 Nelson Education Ltd. Chapte 3: Unifom Cicula Motion 3-14

14 Statement: The tension in the sting at the maximum speed is 1 N. 46. Given: T 4.0 s; m kg; m 1800 kg; m; 4.0 m m 7.0 m Requied: F T at the bottom fo each suppot 4! m ; F T F g + T Solution: Detemine the tension in suppot B: F TB F g + F TB mg + 4! m T ( 1800 kg) 9.8 m/s ( ) + 4! ( 1800 kg) ( 7.0 m) ( 4.0 s) 4.873" 10 4 N (two exta digits caied) 4.9 " 10 4 N Detemine the tension in suppot A: F TA F g + + F TB F TA mg + 4! m T ( 100 kg) 9.8 m/s 7. " 10 4 N ( ) + 4! ( 100 kg) ( 4.0 m) " 10 4 N ( 4.0 s) Statement: The tension in suppot A is N and the tension in suppot B is N. 47. (a) The ide feels the gavitational foce, centipetal foce, and the foce due to static fiction. (b) Given: 3.0 m; µ s 0.40 Requied: minimum v Analysis: In this scenaio the nomal is hoizontal and opposite the centipetal foce instead of the gavitational foce. Detemine the speed at which the foce due to static fiction equals the gavitational foce; ; F s µ s Copyight 01 Nelson Education Ltd. Chapte 3: Unifom Cicula Motion 3-15

15 Solution: F g F s mg! s! mv mg! s " g! s v v g! s v g! s ( 9.8 m/s )( 3.0 m ) ( ) 0.40 v 8.6 m/s Statement: The minimum speed of otation to keep the peson stuck to the wall 8.6 m/s. 48. Given: m 6.0 kg; A 5.0 m; B 5.0 m; h 8.0 m; v 1 m/s Requied: F T in each sting Analysis: In this scenaio the tensions will not be equal because of the gavitational foce. The x- components of the tensions will balance the centipetal foce while the x-components of the tensions balance the gavitational foce; ; F s µ s. The adius of the cicula path is one side of a ight tiangle with sting A as the hypotenuse and half the height cylinde as the othe side. Solution: Detemine the adius of the cicula path using the Pythagoean theoem: + 1! " h A! A 1 " h! A 1 " h 5.0 m! " ( ) 1 ( 8.0 m ) 3.0 m Detemine the angle the stings make with the hoizontal: cos! 4.0 m 5.0 m! Also, we can use cos θ 0.8 (and theefoe sin θ 0.6) late in the solution. Copyight 01 Nelson Education Ltd. Chapte 3: Unifom Cicula Motion 3-16

16 Detemine the centipetal foce on the mass: 6.0 kg ( )( 1 m/s) ( 3.0 m) 88 N Expess the balancing of the hoizontal foces and isolate one of the tensions: F TAx + F TBx F TA sin! + F TB sin! 88 N F TA 88 N " F TB sin! sin! Expess the balancing of the vetical foces and solve fo the tension on sting B: F TA y! F TBy F g F TA cos"! F TB cos" mg 88 N! F TB sin" sin" ( cos"! F TB cos" 6.0 kg ( ) cos" 88 N sin"! F sin" cos" TB! F TB cos" 58.8 N sin" ( 88 N)cos"! F sin" TB cos" 58.8 N ( 88 N) ( 0.8 )! F ( 0.6) TB ( 0.8) 58.8 N 384 N!1.6F TB 58.8 N Solve fo the tension on sting A: F TA 88 N! F sin" TB sin" 88 N! ( 03. N) ( 0.6 ) ( 0.6) F TA.8 10 N ( ) ( ) 9.8 m/s 58.8 N! 384 N F TB! N F TB.0 )10 N Statement: The tension in sting A is.8 10 N and the tension in sting B is.0 10 N. Copyight 01 Nelson Education Ltd. Chapte 3: Unifom Cicula Motion 3-17

17 49. Given: f pm 60 Hz; 30.0 m; m kg Requied: ma c ; a c 4! f Solution: ma c m( 4! f ) 4! ( 9.8 " 10 kg) ( 30.0 m) 1.3 " 10 3 N 60 Hz ( Statement: The dive will feel a foce of N. 50. Given: m.0 kg; 0.35 m; f 50.0 pm Hz Requied: ma c ; a c 4! f Solution: ma c m 4! f ( ) " 4! (.0 kg) ( 0.35 m) N 60 Hz Statement: The foce acting on the clothes is 19 N. 51. Given: f 0.30 ps 0.30 Hz; 15 cm 0.15 m Requied: µ s ; F s µ s mg; The speed is the point at which the centipetal acceleation on the coin equals the foce of static fiction. Solution: F s 4! mf! s mg 4! f! s g! s 4! f g ( )( 0.30 Hz) 4! 0.15 m ( 9.8 m/s )! s Statement: The coefficient of static fiction is Copyight 01 Nelson Education Ltd. Chapte 3: Unifom Cicula Motion 3-18

18 5. Given: 0.0 m; F N 3.00F g Requied: v ; F g mg; The nomal foce at the bottom of the loop is the sum of the centifugal foce and the gavitational foce. Solution: + F g 3.00F g.00f g mv.00mg v.00g v.00g ( )( 0.0 m ) m/s v 19.8 m/s Statement: The speed at the bottom of the loop is 19.8 m/s. 53. Given: v 1 m/s; a c 0.500g Requied: ; F c ma c Solution: ma c mv ma c v 0.500g v 0.500g ( 1 m/s) 0.500( 9.8 m/s ) 9 m Statement: The adius of the station is 9 m. 54. (a) The bucket moves in a cicle because of the fictitious centifugal foce. (b) The souce of the centifugal foce is the tension in the ope. (c) Given: m 15 kg; v m/s; m Requied: Copyight 01 Nelson Education Ltd. Chapte 3: Unifom Cicula Motion 3-19

19 Solution: 15 kg ( )( m/s) ( m) 30 N Statement: The magnitude of the foce is 30 N. 55. (a) Given: d 4 m o m; m 65 kg + 95 kg 160 kg; f pm 60 Hz Requied: µ s ; F s µ s ; The foce of static fiction needs to offset the gavitation foce. Solution: F g F s mg! s mg! s 4! mf g! s 4! f! s g 4! f ( 9.8 m/s ) " ( ) 4! m 60 Hz! s 0.9 Statement: The coefficient of static fiction is 0.9. (b) The fequency of the ide is Hz o 0.37 loops/s. 60 (c) Given: m; m 65 kg + 95 kg 160 kg; v 6 m/s Requied: F N at top and bottom ; The foce at the top of the sphee is the diffeence between the centifugal foce and the gavitational foce: F N F g. The foce at the bottom of the sphee is the sum of the centifugal foce and the gavitational foce: F N + F g. Solution: Detemine the foce at the top of the sphee: F N F s! F g! mg 160 kg ( )( 6.0 m/s) ( m) F N 1.3" 10 3 N! ( 160 kg) ( 9.8 m/s ) Copyight 01 Nelson Education Ltd. Chapte 3: Unifom Cicula Motion 3-0

20 Detemine the foce at the bottom of the sphee: F N F s + F g + mg 160 kg ( )( 6.0 m/s) ( m) F N 4.4! 10 3 N + ( 160 kg) ( 9.8 m/s ) Statement: The nomal foce at the top of the sphee N. The nomal foce at the bottom of the sphee N. 56. Given: 3.0 m; f.0 pm Hz; m 54 kg Requied: 4! mf Solution: 4! mf 4! ( 54 kg) ( 3.0 m) 7.1 N 60 " 60 Hz Statement: The magnitude of the centipetal foce is 7.1 N. 57. Given: m 450 kg; f 1 pm 1 60 Hz; 48 N Requied: 4! mf Solution: 4! mf F c 4! mf 48 N " 1 4! ( 450 kg) 60 Hz 9.7 m Statement: The length of the lead ope is 9.7 m. 58. Given: 5 m; a c 1.0g Requied: v Analysis: a c v Copyight 01 Nelson Education Ltd. Chapte 3: Unifom Cicula Motion 3-1

21 Solution: a c v v a c 1.0g ( )( 5 m ) m/s m s! 60 s 60 min!! 1 km 1 min 1 h 1000 m v 56 km/h Statement: The speed of the hose is 56 km/h. Evaluation 59. (a) The centifugal foce is the fictitious foce that occus in a otating fame of efeence that is diected away fom the cente of otation. (b) The Coiolis foce is the fictitious foce in a otating fame of efeence that acts pependicula to an object s velocity. (c) Fictitious foces ae not actual foces; they only appea when the natual fame of efeence fo a given situation is itself acceleating and they ae always popotional to the mass of the object on which they act. 60. (a) As a peson ides an elevato to the top of the CN Towe, the fame of efeence acceleates upwad. The peson will expeience an incease in the nomal foce and thei appaent weight inceases. (b) As a peson is in fee fall while skydiving, the nomal foce acting on the peson is zeo and the peson also has an appaent weight of zeo. 61. (a) Equations fo Centipetal Acceleation Equation Vaiables in equation Vaiables not in equation v, T, f a c v a c 4! T, T v, f a c 4! f, f v, T (b) The fist equation follows fom the definition of aveage acceleation, simila tiangles, and looking at vey small peiods of time. The second equation follows fom the fist equation by inseting the cicumfeence of the cicula path fo distance and using peiod of evolution fo the time inteval in the basic equation fo speed. The thid equation follows fom the second equation by simply substituting 1 f fo T. 6. (a) Twiling the ope allows he to incease its speed while it tavels in a cicula path. (b) By spinning the ope faste, she can ensue it has a geate speed when it is eleased. This will help the ope go fathe. (c) The ope will tavel away fom the odeo pefome in a staight-line path in the diection it was moving when she let go. Copyight 01 Nelson Education Ltd. Chapte 3: Unifom Cicula Motion 3-

22 63. Banked off- and on-amps on highways use centipetal foces to allow vehicles to stay on cuved paths. The banked cuve povides a component of the nomal foce in the diection of the centipetal acceleation towads the cente, making it moe difficult fo a ca diving on a cuve to leave the oad. The angles ae calculated to ensue safe diving conditions when the coefficient of static fiction between ties and the oad is high (dy conditions) and low (wet o icy conditions). 64. Answes may vay. Sample answe: I would use the analogy of a bucket of wate being swung aound in a cicle. Just as the wate stays in the bucket, a otating space station foces astonauts to the oute walls with the centifugal foce acting to simulate gavity. Reflect on You Leaning 65. Answes may vay. Sample answe: The thing I found most supising was the speeds equied fo atificial gavity on a spacecaft and that a small adius on the spacecaft means that the atificial gavity will feel diffeent at one s feet compaed to one s head. 66. Answes may vay. Sample answe: I was not comfotable woking with fequency and peiods. Also I did not fully undestand the diffeence between a centipetal foce and a centifugal foce. 67. Answes may vay. Sample answe: Know What I Leaned What I Would Like to Lean gavity I expeience with the pull that Eath exets on me atificial gavity is a manmade situation whee the value of gavity is changed atificially appopiate fequency can simulate the effects of Eath s gavity oes the cuent space station use otation to ceate atificial gavity? 68. Answes may vay. Sample answe: I leaned that centifugal foces ae fictitious foces. They help to bette explain atificial gavity and objects moving as a fame of efeence acceleates. 69. Answes may vay. Students should epot on topic fom the chapte that has an impact on them. Fo example, dives will be inteested in the impotance of banked cuves fo diving and how the angle must be caefully selected so that it is safe fo dy and slippey conditions when the coefficient of static fiction deceases. Reseach 70. Answes may vay. Students answes should include histoic moments such as the ealiest olle coastes, the fist cicula loops, and the intoduction of clothoid loops. Students may wish to go into ecent developments in olle coastes and eseach maximum speeds and foces of acceleation. 71. Answes may vay. Students should addess that stoms such as huicanes tend to otate counteclockwise in the Nothen Hemisphee and clockwise in the Southen Hemisphee as a esult of the Coiolis foce. Copyight 01 Nelson Education Ltd. Chapte 3: Unifom Cicula Motion 3-3

23 7. Answes may vay. Students answes should include the concept of geotopism (sometimes called gavitopism), wheeby seedlings gow upwad in esponse to gavity. In a otating fame of efeence, plants would theefoe gow in esponse to the fictitious centifugal foce, into the cente of otation. 73. Answes may vay. Students should explain how the centifuge sepaates the heavie isotopes fom the lighte ones while the uanium is in gaseous fom as uanium hexafluoide, helping to get highe concentations of the desied uanium-35 isotope. With highe concentations of uanium-35, nuclea powe plants ae moe efficient because enegy is not wasted woking with othe uanium isotopes. 74. Answes may vay. Students may exploe changes in taining pogams, which equies astonauts to be capable of enduing the intense acceleation of take-off and the disoientation of woking in the fee fall conditions of the space station. Ealy astonauts wee tained test pilots while moden astonauts ae moe likely to be academics. Thanks to the intoduction of shuttles, astonauts ae no longe etuning to Eath at sea, so thee has been a de-emphasis on suvival skills. Students should also discuss the knowledge equiements in addition to the physical testing. Students should discuss health isks such as muscle loss and deceased bone density, and how astonauts must execise in space to avoid excessive muscle loss. To combat the health isks associated with extended space tavel, eseach into atificial gavity, bette execise equipment, and impoved life-suppot systems is being conducted. 75. (a) Answes may vay. Students should pesent infomation on the histoical use of centifuges in an industy. Fo example, simple, hand-canked centifuges have been used to sepaate the ceam in fesh milk since the 19th centuy. The technology is still used today, howeve the centifuges ae automated and moe efficient. (b) Answes may vay. Centifuges have been useful fo sepaating and puifying fo ove a centuy. Students may list medical eseach, cance teatment, fuel puification, sewage teatment, o something as simple as a home washing machine. 76. Answes may vay. Students concept maps should include that although the olle coaste does not include any loops, it does have multiple tight tuns (with banked tacks) whee ides will expeience a centipetal foce that is the sum of the gavitational foce and the nomal foce. Rides will also expeience a centifugal foce since the olle coaste is a non-inetial fame of efeence. 77. (a) Fo optimal pefomance, a wind tubine o windmill is pointed diectly at the diection the wind is coming fom. The kinetic enegy of wind is tansfeed into the cuved blades of the wind tubine. The blades ae attached to a oto that otates with them. The otation of the oto causes a shaft into the body of the wind tubine to otate. A geneato in the head of the wind tubine tansfes the cicula motion of the shaft into altenating cuent. Students diagams must include the blades, attached to the oto, pointing into the wind, the otating shaft, and the geneato. (b) Using wind powe educes the envionmental impact of powe geneation by educing pollutants associated with nuclea o fossil fuel plants. Wind powe does not equie coal mining o oil dilling. One negative aspect is the effect on migatoy bids that can be injued o killed by flying into wind tubines. 78. Answes may vay. Students designs should take advantage of mateial they have leaned in this chapte, such as the advantage of clothoid loops and the benefits of banked cuves fo maintaining geate speeds. Copyight 01 Nelson Education Ltd. Chapte 3: Unifom Cicula Motion 3-4