# 14. Which shows the direction of the centripetal force acting on a mass spun in a vertical circle?

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1 Physics 3204 Public Exam Questins Unit 1: Circular Mtin NAME: August Which describes unifrm circular mtin? 13. A circular race track has a radius f 159 m. If the centripetal frce acting n a 65.0 kg cyclist is 4.16 N, hw lng des it take t cmplete ne lap arund the track? (A) 9.91 s (C) 313 s (B) 98.2 s (D) 785 s 14. Which shws the directin f the centripetal frce acting n a mass spun in a vertical circle? The diagram belw represents a kg car driving int the bttm f a small valley. If the car is travelling at 9.0 m/s and the radius f the valley is 12.0 m, what is the nrmal frce acting n the car? (A) N (B) N (C) N 4 (D) N 16. At what speed can a car safely negtiate a frictinless curve f radius 115 m if the rad is banked at an angle f 35.0? (A) 8.97 m/s (C) 28.1 m/s (B) 19.9 m/s (D) 40.1 m/s

2 3% 51.(c) A 2.00 kg bject is attached t the end f a 3.00 m lng rpe and is spun in a vertical circle. Calculate the speed f the bject, at the bttm f the circle, if the tensin in the rpe is 49.0 N. 3% (d) A 1500 kg car runds a curve n a flat rad f radius 55 m at a speed f 16 m/s. Determine whether the car will make the turn n an icy rad where = Shw yur calculatins. June A 25.0 kg girl is spinning arund at 1.25 m/s n a merry-g-rund with a radius f 2.39 m. What is the centripetal frce n the girl? (A) 13.1 N (C) 32.5 N (B) 16.3 N (D) 47.8 N 14. An bject is mving in unifrm circular mtin at a speed f 6.20 m/s arund a path having radius 3.85 m. Hw lng des it take t make ne cmplete revlutin? (A) s (C) 1.61 s (B) s (D) 3.90 s 15. A 1.20 kg ball n a string is swung at a speed f 3.57 m/s in a vertical circle f radius 1.10 m. What is the tensin in the string at the tp f the circle? (A) 2.1 N (C) 13.9 N (B) 11.8 N (D) 25.7 N

3 16. A rller caster car f mass, m, is n a track that frms a circular lp f radius r in a vertical plane. If the car is t just maintain cntact with the track, what expressin represents the minimum speed at the tp f the lp? (A) rg (B) (rg) (C) rmg (D) (rmg) 3% 51 (d) A 0.40 kg stne is tied t a string and whirled arund in a circle f radius 0.75 m with a cnstant speed f 5.0 m/s. In which situatin is the string mst likely t break? Explain. August An bject travels alng a hrizntal circular path at a cnstant speed. By what factr will the centripetal frce change if the radius is halved? (A) ¼ (C) 2 (B) ½ (D) What is the acceleratin f a car that ges arund a curve f radius 150 m at a cnstant speed f 30.0 m/s? 2 2 (A) 0 m/s (C) 5.0 m/s (B) 0.20 m/s2 2 (D) 6.0 m/s

4 12. The diagram belw shws an bject mving at a cnstant speed in a hrizntal circle. What is the directin f the acceleratin at pint P? (A) A (C) C (B) B (D) D 13. What is the centripetal frce n an bject f mass kg, that is spinning at 6.40 m/s in a hrizntal circle f radius m? (A) 2.87 N (C) 23.4 N (B) 3.66 N (D) 117 N 14. What banking angle is required fr a car t cmplete a m radius frictinless turn at 24.5 m/s withut skidding? (A) 29.1 (C) 56.2 (B) 33.8 (D) A persn f mass, m, n a carnival ride stands inside a large drum that begins t rtate. When a safe speed is reached, the flr f the drum falls away and the rider is left stuck t the wall. What is the minimum speed at which the drum can turn s that the persn des nt fall? 3 4% 51.(e) A car f mass kg travelling at 18 m/s, tps a hill having a radius f curvature f 50.0 m. i) Calculate the nrmal frce n the car at the tp f the hill.

5 ii) Calculate the maximum speed that will allw the car t stay n the rad at the tp f the hill. June A rubber stpper spins in a hrizntal circle n the end f a 1.2 m lng string. If the stpper mves at a speed f 3.2 m/s, what is its acceleratin? 2 2 (A) 0.12 m/s (C) 2.7 m/s 2 2 (B) 0.38 m/s (D) 8.5 m/s 13. The diagram belw shws a ball n the end f a string mving at a cnstant speed in a hrizntal circle. A target is lcated near the path f the ball as shwn. At which pint shuld the ball be released in rder t hit the target? (A) A (B) B (C) C (D) D What is the speed f a planet that travels in a circular path f radius m, and has a perid f 27.3 days? 2 4 (A) m/s (C) m/s 3 4 (B) m/s (D) m/s 15. The diagram belw shws a ball, suspended by a string, travelling in a hrizntal circular p ath at a cnstant speed. Which is the free bdy diagram fr the ball at P? 5

6 2 16. A pilt mving at a speed f m/s, experiences a nrmal frce f seven times his weight at the bttm f a vertical dive. What is the radius f curvature f the dive if it fllws a semi-circular path as shwn? (A) 425 m (B) 797 m (C) 911 m (D) 1060 m 3% 51 (d) In an autmatic clthes dryer a hllw drum mves the clthes in a vertical circle f diameter 0.75 m. The dryer is designed s that the clthes tumble and d nt simply stick t the drum as it rtates. Calculate the speed at which the drum must rtate s that a kg sweater at the tp f the drum will just begin t tumble. August What is the directin f the centripetal acceleratin fr an bject mving in a hrizntal circle? (A) up (C) away frm the center (B) dwn (D) twards the center 12. A ball attached t a string is swung in a vertical circle. If the string breaks at pint X, which path will the ball fllw at the instant the string breaks? (A) A (B) B (C) C (D) D 6

7 13. A ball n a string is spun in a hrizntal circle. If the speed remains cnstant and the radius is halved, by what factr will the centripetal acceleratin change? (A) ¼ (C) 2 (B) ½ (D) An bject f mass 20.0 kg underges 50 rtatins in 25 s making a circle f radius 0.95 m. What is the centripetal frce experienced by the bject? 2 3 (A) N (C) N 2 3 (B) N (D) N 15. A 4.0 kg ball n a string is swung in a hrizntal circle at a speed f 3.5 m/s. If the tensin in the string is 51 N, what is the radius f the circular path traced ut by the ball? (A) 0.43 m (B) 0.67 m (C) 1.3 m (D) 1.5 m 4% 51 (d) A rller caster cart is at the tp f a vertical circular lp and is travelling at 9.30 m/s. The ttal mass f the cart and passengers is 435 kg. (i) If the radius f the lp is 4.50 m, calculate the nrmal frce acting n the cart at the tp f the lp. ii) Calculate the minimum speed required at the tp f the lp t keep the cart n the track. 7

8 June Which is the centripetal frce fr a car in a frictinless banked curve? (A) hrizntal cmpnent f the nrmal frce (C) vertical cmpnent f the nrmal frce (B) hrizntal cmpnent f the weight (D) vertical cmpnent f the weight 12. The diagram belw shws an bject, attached t a string, mving at a cnstant speed f 4.00 m/s in a hrizntal circle. What is the magnitude f the centripetal acceleratin f the bject? (A) m/s 2 (B) 2.00 m/s 2 (C) 5.00 m/s 2 (D) 20.0 m/s Which shws the velcity vectr fr an bject in unifrm circular mtin? (A) (B) (C) (D) 14. In a series f test runs, a car travels arund the same circular track at different velcities. Which graph shws the relatinship between its centripetal acceleratin, a, and its velcity v? c 15. The diagram belw shws a pail f water being swung in a vertical circle f radius 1.3 m. What is the minimum speed, v, at the tp f the circle that will keep the water frm spilling? (A) 3.6 m/s (B) 7.5 m/s (C) 9.8 m/s (D) 13 m/s 8

9 3% 51 (d) A 1500 kg car travels at 25 m/s arund a circular curve n a flat rad. If the cefficient f static frictin is 0.750, calculate the minimum radius f curvature the car can make. August In the diagram belw, a car is mving suth at a cnstant speed alng a circular path. In which directin is the centripetal frce directed? (A) east (B) nrth (C) suth (D) west 13. The diagram belw shws a 3.0 kg ball, suspended by a string, underging unifrm circular mtin. If the speed f the ball is 3.1 m/s and the radius f the circle is 1.2 m, what is the tensin in the string? (A) 31 N (B) 38 N (C) 62 N (D) 76 N 14. By which factr des the centripetal frce change if a car ges arund a curve at 1/3 f its riginal speed? (A) 1/3 (C) 3 (B) 1/9 (D) 9 9

10 15. Tires n a mving bicycle make tw cmplete rtatins in 0.18 s. If the radius f the tires is 0.42 m, hw fast is the bicycle travelling? (A) 0.47 m/s (C) 15 m/s (B) 2.3 m/s (D) 29 m/s 16. If the vehicle belw cmpletes the lp, at which pint is the nrmal frce lwest? (A) A (B) B (C) C (D) D 17. As the radius f a merry-g-rund dubles, by what factr des the magnitude f the centripetal frce acting n a passenger change? (A) duble (C) triple (B) half (D) quadruple 3% 51. (d) What is the maximum speed a car can travel arund a curve n a flat rad if the radius f the 2 curve is m and the cefficient f static frictin between the tires and rad is 0.25? June If a car, travelling at 25.0 m/s, mves arund a banked frictinless curve angled at 7.32, what is the radius f the curve? (A) 19.9 m (C) 63.8 m (B) 37.7 m (D) 496 m 10

11 13. What is true f the velcity f an bject experiencing unifrm circular mtin? 14. Which best represents the acceleratin, a, and frce, F, fr an bject travelling alng a circular path? 15. The diagram belw shws a 3.0 kg ball, suspended by a string, travelling in a hrizntal circular path. If the tensin in the string is 37.8 N and the radius f the circle is 1.2 m, what is the speed f the ball? (A) 3.1 m/s (B) 3.4 m/s (C) 3.9 m/s (D) 9.5 m/s 51. (d) A pail f water n the end f a string revlves at a unifrm rate in a vertical circle f radius 85.0 cm. Its speed is 4.15 m/s and the mass f the pail and water tgether is 1.00 kg. 2% (i) Calculate the magnitude f the tensin in the string when the pail is at the tp f its path. 11

12 2% (ii) At what minimum speed must the pail be travelling when upside dwn at the tp f the circle s that the water des nt fall ut? 2% 51.(e) During a rller caster ride the riders mve thrugh tw lps, the secnd being ne half the radius f the first. The riders travel at the same speed at the tp f each f these tw lps. Using principles f physics, explain why riders wuld experience a greater nrmal frce at the tp f the secnd, smaller lp than at the tp f the first, larger lp. August A car ges arund a curve with a radius f 84 m at a speed f 22 m/s. What is the centripetal acceleratin f the car? 2 2 (A) 0.17 m/s (C) 3.8 m/s 2 2 (B) 0.26 m/s (D) 5.8 m/s 14. If an bject is n a 27 frictinless incline, what will be the acceleratin f the bject n the incline? 2 (A) 0.45 m/s 2 (C) 4.4 m/s 2 (B) 0.55 m/s 2 (D) 8.7 m/s 15. If a student swings a ball, attached by a string, in a hrizntal circle, in which directin wuld the ball travel if the string breaks? (A) in the circular path (C) tangent t the circular path (B) twards the student s hand (D) tangent t the student s hand 12

13 16. What is true f the velcity f an bject experiencing unifrm circular mtin? 17. A runner cmpletes ne lap f a circular track in 37s at a speed f 9.0 m/s. What is the radius f the track? (A) 26 m (C) 330 m (B) 53 m (D) 490 m 18. An 85 kg persn swings n an 8.0 m vine. What is the tensin frce in the vine as the persn passes the lwest pint f the circular path, traveling at 12.5 m/s? (A) 830 N (C) 2500 N (B) 1700 N (D) 6700 N 2% 51.(e) A car mves at 25 m/s arund a level curve with a 50.0 m radius. The centripetal frce prvided by 4 the frictin between the tires and the rad is 1.8 x 10 N. What is the mass f the car? June In the diagram belw, a car is mving suth at a cnstant speed alng a circular path. In which directin is the acceleratin directed? (A) East (B) Nrth (C) Suth (D) West 13

14 12. A pilt executes a vertical dive and fllws thrugh a semi-circular arc as shwn in the diagram belw. When the plane is at the bttm f the arc (pint X), what is true f the nrmal frce n the pilt? (A) greater than Fg, and pinting dwn (B) greater than Fg, and pinting up (C) less than Fg, and pinting dwn (D) less than Fg, and pinting up 13. The rller caster cart shwn belw, passes the pint at the very tp f a lp, which has a radius f 7.00 m. If the nrmal frce is equal t ne half the weight f the cart, what is the speed f the rller caster at this pint? (A) 4.14 m/s (C) 10.1 m/s (B) 8.28 m/s (D) 14.3 m/s 14. A car travels at 21 m/s arund a banked curve. If the radius f the curve is 75 m and assuming frictin is negligible, what is the banking angle? (A) 0.54 (C) 31 (B) 1.6 (D) 81 2% 51. (d) What is the maximum speed at which a 1200 kg car can rund a flat, curved rad, withut slipping, if the radius f the curve is 88.0 m and the cefficient f static frictin is 0.50? 14

15 August The tires n a mving bicycle make ne cmplete rtatin in 0.18 s. If the radius f the tires is 0.42 m, hw fast is the bicycle travelling? (A) 2.3 m/s (C) 4.7 m/s (B) 3.1 m/s (D) 15 m/s 12. What is the centripetal acceleratin f a car as it travels at 36.0 m/s arund a circle with radius m? 2 2 (A) 0.11 m/s (C) 3.8 m/s 2 2 (B) 0.26 m/s (D) 9.4 m/s 13. As the speed f a merry-g-rund dubles, hw des the magnitude f the centripetal frce acting n a passenger change? (A) halves (C) triples (B) dubles (D) quadruples What is the speed f a satellite that rbits Earth km abve the surface? 3 (A) m/s 3 (C) m/s 3 (B) m/s 4 (D) m/s 2% 51.(b) What happens t the mtin f an bject underging unifrm circular mtin if the net frce n the bject becmes zer? 15

16 June Which best describes the directin f the centripetal acceleratin f an bject in unifrm circular mtin? (A) in the directin f mtin (C) ppsite the directin f mtin (B) inward twards the centre f the circle (D) utward frm the centre f the circle 13. What is the perid f a satellite in a gesynchrnus rbit abve Earth? (A) 12 hurs (C) 1 mnth (B) 24 hurs (D) 12 mnths 14. By what factr des the centripetal frce change if a car ges arund a curve at half its riginal speed? (A) decreases by a factr f 2 (C) increases by a factr f 2 (B) decreases by a factr f 4 (D) increases by a factr f A car, travelling at 25.0 m/s, successfully mves arund a banked, frictinless turn angled at What is the radius f this banked curve? (A) 19.9 m (C) 63.8 m (B) 37.7 m (D) 496 m 16. A kg car runds a 50.0 m hrizntal curve with a speed f 15 m/s. If it is travelling with a speed such that it just barely avids slipping n the rad, what is the frce f static frictin between the tires and the rad? 2 3 (A) N (C) N 2 3 (B) N (D) N 3% 51.(c) A car is mving arund a hrizntal curve with a radius f 50.0 m. If the cefficient f static frictin is 0.75, what is the maximum speed fr the car t travel safely arund the curve withut skidding? 16

17 3% 51.(d) The diagram belw represents the lp f a rller caster. If the radius f the lp is 12.0 m, what is the minimum speed, at the tp f the lp, required t prevent passengers frm falling ut? 17

### 14. Which shows the direction of the centripetal force acting on a mass spun in a vertical circle?

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