SECTION B Circular Motion

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1 SECTION B Circulr Motion 1. When person stnds on rotting merry-go-round, the frictionl force exerted on the person by the merry-go-round is (A) greter in mgnitude thn the frictionl force exerted on the person by the merry-go-round (B) opposite in direction to the frictionl force exerted on the merry-go-round by the person (C) directed wy from the center of the merry-go-round (D) zero if the rte of rottion is constnt (E) independent of the person's mss 2. A bll ttched to string is whirled round in horizontl circle hing rdius r. If the rdius of the circle is chnged to 4r nd the sme centripetl force is pplied by the string, the new speed of the bll is which of the following? (A) One-qurter the originl speed (B) One-hlf the originl speed (C) The sme s the originl speed (D) Twice the originl speed (E) Four times the originl speed 3. A rcing cr is moing round the circulr trck of rdius 300 meters shown boe. At the instnt when the cr's elocity is directed due est, its ccelertion is directed due south nd hs mgnitude of 3 meters per second squred. When iewed from boe, the cr is moing (A) clockwise t 30 m/s ( B) clockwise t 10 m/s (C) counterclockwise t 30 m/s (D) counterclockwise t 10 m/s (E) with constnt elocity 4. The horizontl turntble shown boe rottes t constnt rte. As iewed from boe, coin on the turntble moes counterclockwise in circle s shown. Which of the following ectors best represents the direction of the frictionl force exerted on the coin by the turntble when the coin is in the position shown? (A) (B) (C) (D) (E) 5. In which of the following situtions would n object be ccelerted? I. It moes in stright line t constnt speed. II. It moes with uniform circulr motion. III. It trels s projectile in grittionl field with negligible ir resistnce. (A) I only (B) III only (C) I nd II only (D) II nd III only (E) I, II, nd III. 73

2 6. An utomobile moes t constnt speed down one hill nd up nother hill long the smoothly cured surfce shown boe. Which of the following digrms best represents the directions of the elocity nd the ccelertion of the utomobile t the instnt tht it is t the lowest position. s shown? (A) (B) (C) (D) (E) 7. A cr initilly trels north nd then turns to the left long circulr cure. This cuses pckge on the set of the cr to slide towrd the right side of the cr. Which of the following is true of the net force on the pckge while it is sliding? (A) The force is directed wy from the center of the circle. (B) The force is directed north. (C) There is not enough force directed north to keep the pckge from sliding. (D) There is not enough force tngentil to the cr's pth to keep the pckge from sliding. (E) There is not enough force directed towrd the center of the circle to keep the pckge from sliding. 8. A child hs toy tied to the end of string nd whirls the toy t constnt speed in horizontl circulr pth of rdius R. The toy completes ech reolution of its motion in time period T. Wht is the mgnitude of the ccelertion of the toy? (A) Zero (B) 2 4 R T 2 (C) R 2 T (D) g (E) 9. A compressed spring mounted on disk cn project smll bll. When the disk is not rotting, s shown in the top iew boe, the bll moes rdilly outwrd. The disk then rottes in counterclockwise direction s seen from boe, nd the bll is projected outwrd t the instnt the disk is in the position shown boe. Which of the following best shows the subsequent pth of the bll reltie to the ground? 74

3 10. A steel bll supported by stick rottes in circle of rdius r, s shown boe. The direction of the net force cting on the bll when it is in the position shown is indicted by which of the following? (E) 11. Inside wshing mchine, the rdius of the cylinder where the clothes sit is 0.50 m. In one of its settings the mchine spins the cylinder t 2.0 reolutions per second. Wht is the ccelertion of n item of clothing? (A) m/s 2 (B) 1.6 m/s 2 (C) 8.0 m/s 2 (D) 79 m/s 2 (E) 25 m/s A bll of mss m is ttched to the end of string of length Q s shown boe. The bll is relesed from rest from position P. where the string is horizontl. It swings through position Q. where the string is erticl, nd then to position R. where the string is gin horizontl. Wht re the directions of the ccelertion ectors of the bll t positions Q nd R? Position Q Position R (A) Downwrd Downwrd (B) Downwrd To the right (C) Upwrd Downwrd (D) Upwrd To the left (E) To the right To the left 13. A mss m moes on cured pth from point X to point Y. Which of the following digrms indictes possible combintion of the net force F on the mss, nd the elocity nd ccelertion of the mss t the loction shown? 75

4 *14. A spring hs force constnt of 100 N/m nd n unstretched length of 0.07 m. One end is ttched to post tht is free to rotte in the center of smooth tble, s shown in the top iew boe. The other end is ttched to 1 kg disc moing in uniform circulr motion on the tble, which stretches the spring by 0.03 m. Friction is negligible. Wht is the centripetl force on the disc? (A) 0.3 N (B) 3N (C) 10 N (D) 300 N (E) 1,000 N 15. A figure of dncer on music box moes counterclockwise t constnt speed round the pth shown boe. The pth is such tht the lengths of its segments, PQ, QR, RS, nd SP, re equl. Arcs QR nd SP re semicircles. Which of the following best represents the mgnitude of the dncer's ccelertion s function of time t during one trip round the pth, beginning t point P? 16. A cr trels forwrd with constnt elocity. It goes oer smll stone, which gets stuck in the grooe of tire. The initil ccelertion of the stone, s it lees the surfce of the rod, is (A) erticlly upwrd (B) horizontlly forwrd (C) horizontlly bckwrd (D) zero (E) upwrd nd forwrd, t pproximtely 45 to the horizontl 17. A cr is treling on rod in hilly terrin, see figure to the right. Assume the cr hs speed nd the tops nd bottoms of the hills he rdius of curture R. The drier of the cr is most likely to feel weightless: (A) t the top of hill when > (B) t the bottom of hill when > (C) going down hill when = (D) t the top of hill when < (E) t the bottom of hill when < 76

5 18. An object shown in the ccompnying figure moes in uniform circulr motion. Which rrow best depicts the net force cting on the object t the instnt shown? (A) A (B) B (C) C (D) D (E) E 19. A child whirls bll t the end of rope, in uniform circulr motion. Which of the following sttements is NOT true? (A) The speed of the bll is constnt (B) The elocity is of the bll is constnt (C) The rdius is constnt (D) The mgnitude of the bll's ccelertion is constnt (E) The ccelertion of the bll is directed rdilly inwrds towrds the center 20. An stronut in n orbiting spce crft ttches mss m to string nd whirls it round in uniform circulr motion. The rdius of the circle is r, the speed of the mss is, nd the tension in the string is F. If the mss, rdius, nd speed were ll to double the tension required to mintin uniform circulr motion would be (A) F/2 (B) F (C) 2F (D) 4F (E) 8F 21. Assume the roller coster crt rolls frictionlessly long the cured trck from point A to point C under the influence of grity. Wht would be the direction of the crt's ccelertion t point B? (A) upwrd (B) downwrd (C) forwrd (D) bckwrd (E) no ccelertion Questions The digrm below is snpshot of three crs ll moing counterclockwise during one lp rce on n ellipticl trck. 22. Which cr hs hd the lowest erge speed during the rce so fr? (A) cr A (D) ll three crs he hd the sme erge speed (B) cr B (E) cnnot be determined with informtion proided (C) cr C 23. Which cr t the moment of the snpshot MUST he net force cting on it? (A) cr A (D) ll three crs he net forces cting on them (B) cr B (E) cnnot be determined with informtion proided (C) cr C 77

6 24. A centripetl force of 5.0 newtons is pplied to rubber stopper moing t constnt speed in horizontl circle. If the sme force is pplied, but the rdius is mde smller, wht hppens to the speed,, nd the frequency, f, of the stopper? (A) increses & f increses (D) decreses & f increses (B) decreses & f decreses (E) neither chnges (C) increses & f decreses 25. Wht is the centripetl ccelertion of n object (mss = 50 g) on the end of n 80-cm string rotting t constnt rte of 4 times second? (A) 25 m/s 2 (B) 32 m/s 2 (C) 100 m/s 2 (D) 500 m/s 2 (E) 2500 m/s Wht net force is necessry to keep 1.0 kg puck moing in circle of rdius 0.5 m on horizontl frictionless surfce with speed of 2.0 m/s? (A) 0 N (B) 2.0 N (C) 4.0 N (D) 8.0 N (E) 16 N 27. Astronuts on the Moon perform n experiment with simple pendulum tht is relesed from the horizontl position t rest. At the moment shown in the digrm with 0 90, the totl ccelertion of the mss my be directed in which of the following wys? (A) stright to the right (B) stright to the left (C) stright upwrd (D) stright downwrd (E) stright long the connecting string towrd point P (the piot) 28. A 4.0 kg mss is ttched to one end of rope 2 m long. If the mss is swung in erticl circle from the free end of the rope, wht is the tension in the rope when the mss is t its highest point if it is moing with speed of 5 m/s? (A) 5.4 N (B) 10.8 N (C) 21.6 N (D) 50 N (E) 65.4 N 29. A bll of mss m is fstened to string. The bll swings t constnt speed in erticl circle of rdius R with the other end of the string held fixed. Neglecting ir resistnce, wht is the difference between the string's tension t the bottom of the circle nd t the top of the circle? (A) 1 mg (B) 2 mg (C) 4 mg (D) 6 mg (E) 8 mg 30. An object weighing 4 newtons swings on the end of string s simple pendulum. At the bottom of the swing, the tension in the string is 6 newtons. Wht is the mgnitude of the centripetl ccelertion of the object t the bottom of the swing? (A) 0 (B) 0.5 g (C) g (D) 1.5 g (E) 2.5 g 31. Riders in crnil ride stnd with their bcks ginst the wll of circulr room of dimeter 8.0 m. The room is spinning horizontlly bout n xis through its center t rte of 45 re/min when the floor drops so tht it no longer proides ny support for the riders. Wht is the minimum coefficient of sttic friction between the wll nd the rider required so tht the rider does not slide down the wll? (A) (B) (C) 0.11 (D) 0.53 (E)

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