2010 F = m Exm 1 AAPT UNITED STATES PHYSICS TEAM AIP 2010 Enti non multiplicnd sunt preter necessittem 2010 F = m Contest 25 QUESTIONS - 75 MINUTES INSTRUCTIONS DO NOT OPEN THIS TEST UNTIL YOU ARE TOLD TO BEGIN Use g = 10 N/kg throughout this contest. You my write in this booklet of questions. However, you will not receive ny credit for nything written in this booklet. Your nswer to ech question must be mrked on the opticl mrk nswer sheet. Select the single nswer tht provides the best response to ech question. Plese be sure to use No. 2 pencil nd completely fill the box corresponding to your choice. If you chnge n nswer, the previous mrk must be completely ersed. Correct nswers will be wrded one point; incorrect nswers will result in deduction of 1 4 no penlty for leving n nswer blnk. point. There is A hnd-held clcultor my be used. Its memory must be clered of dt nd progrms. You my use only the bsic functions found on simple scientific clcultor. Clcultors my not be shred. Cell phones my not be used during the exm or while the exm ppers re present. You my not use ny tbles, books, or collections of formuls. This test contins 25 multiple choice questions. Your nswer to ech question must be mrked on the opticl mrk nswer sheet tht ccompnies the test. Only the boxes preceded by numbers 1 through 25 re to be used on the nswer sheet. All questions re eqully weighted, but re not necessrily the sme level of difficulty. In order to mintin exm security, do not communicte ny informtion bout the questions (or their nswers or solutions) on this contest until fter Februry 8, 2010. The question booklet nd nswer sheet will be collected t the end of this exm. You my not use scrtch pper. DO NOT OPEN THIS TEST UNTIL YOU ARE TOLD TO BEGIN
2010 F = m Exm 2 Questions 1 to 3 refer to the figure below which shows representtion of the motion of squirrel s it runs in stright-line long telephone wire. The letters A through E refer to the indicted times. time A B C D E 1. If the grph is grph of POSITION vs. TIME, then the squirrel hs the gretest speed t wht time(s) or during wht time intervl(s)? (A) From A to B (B) From B to C only (C) From B to D (D) From C to D only (E) From D to E 2. If, insted, the grph is grph of VELOCITY vs. TIME, then the squirrel hs the gretest speed t wht time(s) or during wht time intervl(s)? (A) t B (B) t C (C) t D (D) t both B nd D (E) From C to D 3. If, insted, the grph is grph of ACCELERATION vs. TIME nd the squirrel strts from rest, then the squirrel hs the gretest speed t wht time(s) or during wht time intervl? (A) t B (B) t C (C) t D (D) t both B nd D (E) From C to D 4. Two tems of movers re lowering pino from the window of 10 floor prtment building. The rope breks when the pino is 30 meters bove the ground. The movers on the ground, lerted by the shouts of the movers bove, first notice the pino when it is 14 meters bove the ground. How long do they hve to get out of the wy before the pino hits the ground? (A) 0.66 sec (B) 0.78 sec (C) 1.67 sec (D) 1.79 sec (E) 2.45 sec
2010 F = m Exm 3 5. Two projectiles re lunched from 35 meter ledge s shown in the digrm. One is lunched from 37 degree ngle bove the horizontl nd the other is lunched from 37 degrees below the horizontl. Both of the lunches re given the sme initil speed of v 0 = 50 m/s. Projectile 1 35 m Projectile 2 The difference in the times of flight for these two projectiles, t 1 t 2, is closest to (A) 3 s (B) 5 s (C) 6 s (D) 8 s (E) 10 s 6. A projectile is lunched cross flt ground t n ngle θ to the horizontl nd trvels in the bsence of ir resistnce. It rises to mximum height H nd lnds horizontl distnce R wy. Wht is the rtio H/R? (A) tn θ (B) 2 tn θ (C) 2 tn θ (D) 1 2 tn θ (E) 1 4 tn θ 7. Hrry Potter is sitting 2.0 meters from the center of merry-go-round when Drco Mlfoy csts spell tht glues Hrry in plce nd then mkes the merry-go-round strt spinning on its xis. Hrry hs mss of 50.0 kg nd cn withstnd 5.0 g s of ccelertion before pssing out. Wht is the mgnitude of Hrry s ngulr momentum when he psses out? (A) 200 kg m 2 /s (B) 330 kg m 2 /s (C) 660 kg m 2 /s (D) 1000 kg m 2 /s (E) 2200 kg m 2 /s 8. A cr ttempts to ccelerte up hill t n ngle θ to the horizontl. The coefficient of sttic friction between the tires nd the hill is µ > tn θ. Wht is the mximum ccelertion the cr cn chieve (in the direction upwrds long the hill)? Neglect the rottionl inerti of the wheels. (A) g tn θ (B) g(µ cos θ sin θ) (C) g(µ sin θ) (D) gµ cos θ (E) g(µ sin θ cos θ)
2010 F = m Exm 4 9. A point object of mss M hngs from the ceiling of cr from mssless string of length L. It is observed to mke n ngle θ from the verticl s the cr ccelertes uniformly from rest. Find the ccelertion of the cr in terms of θ, M, L, nd g. L θ (A) Mg sin θ (B) MgL tn θ (C) g tn θ (D) g cot θ (E) Mg tn θ 10. A block of mss m 1 is on top of block of mss m 2. The lower block is on horizontl surfce, nd rope cn pull horizontlly on the lower block. The coefficient of kinetic friction for ll surfces is µ. Wht is the resulting ccelertion of the lower block if force F is pplied to the rope? Assume tht F is sufficiently lrge so tht the top block slips on the lower block. 1 2 F (A) 2 = (F µg(2m 1 + m 2 ))/m 2 (B) 2 = (F µg(m 1 + m 2 ))/m 2 (C) 2 = (F µg(m 1 + 2m 2 ))/m 2 (D) 2 = (F + µg(m 1 + m 2 ))/m 2 (E) 2 = (F µg(m 2 m 1 ))/m 2 11. The three msses shown in the ccompnying digrm re equl. The pulleys re smll, the string is lightweight, nd friction is negligible. Assuming the system is in equilibrium, wht is the rtio /b? The figure is not drwn to scle! b (A) 1/2 (B) 1 (C) 3 (D) 2 (E) 2 3
2010 F = m Exm 5 12. A bll with mss m projected horizontlly off the end of tble with n initil kinetic energy K. At time t fter it leves the end of the tble it hs kinetic energy 3K. Wht is t? Neglect ir resistnce. (A) (3/g) K/m (B) (2/g) K/m (C) (1/g) 8K/m (D) (K/g) 6/m (E) (2K/g) 1/m 13. A bll of mss M nd rdius R hs moment of inerti of I = 2 5 MR2. The bll is relesed from rest nd rolls down the rmp with no frictionl loss of energy. The bll is projected verticlly upwrd off rmp s shown in the digrm, reching mximum height y mx bove the point where it leves the rmp. Determine the mximum height of the projectile y mx in terms of h. h (A) h (B) 25 49 h (C) 2 5 h (D) 5 7 h (E) 7 5 h 14. A 5.0 kg block with speed of 8.0 m/s trvels 2.0 m long horizontl surfce where it mkes hed-on, perfectly elstic collision with 15.0 kg block which is t rest. The coefficient of kinetic friction between both blocks nd the surfce is 0.35. How fr does the 15.0 kg block trvel before coming to rest? (A) 0.76 m (B) 1.79 m (C) 2.29 m (D) 3.04 m (E) 9.14 m
2010 F = m Exm 6 The following figure is used for questions 15 nd 16. m v0 M A smll block of mss m is moving on horizontl tble surfce t initil speed v 0. It then moves smoothly onto sloped big block of mss M. The big block cn lso move on the tble surfce. Assume tht everything moves without friction. 15. A smll block moving with initil speed v 0 moves smoothly onto sloped big block of mss M. After the smll block reches the height h on the slope, it slides down. Find the height h. (A) h = v2 0 2g (B) h = 1 g (C) h = 1 2g (D) h = 1 2g (E) h = v2 0 g Mv 2 0 m+m Mv 2 0 m+m mv 2 0 m+m 16. Following the previous set up, find the speed v of the smll block fter it leves the slope. (A) v = v 0 (B) v = (C) v = m m+m v 0 M m+m v 0 (D) v = M m m v 0 (E) v = M m m+m v 0 17. Four msses m re rrnged t the vertices of tetrhedron of side length. Wht is the grvittionl potentil energy of this rrngement? (A) 2 Gm2 (B) 3 Gm2 (C) 4 Gm2 (D) 6 Gm2 (E) 12 Gm2
2010 F = m Exm 7 The following grph of potentil energy is used for questions 18 through 20. 18. Which of the following represents the force corresponding to the given potentil? (A) (B) (C) (D) (E)
2010 F = m Exm 8 19. Consider the following grphs of position vs. time. I. II. III. Which of the grphs could be the motion of prticle in the given potentil? (A) I (B) III (C) I nd II (D) I nd III (E) I, II, nd III 20. Consider the following grph of position vs. time, which represents the motion of certin prticle in the given potentil. Wht is the totl energy of the prticle? (A) -5 J (B) 0 J (C) 5 J (D) 10 J (E) 15 J
2010 F = m Exm 9 21. The grvittionl self potentil energy of solid bll of mss density ρ nd rdius R is E. Wht is the grvittionl self potentil energy of bll of mss density ρ nd rdius 2R? (A) 2E (B) 4E (C) 8E (D) 16E (E) 32E 22. A blloon filled with helium gs is tied by light string to the floor of cr; the cr is seled so tht the motion of the cr does not cuse ir from outside to ffect the blloon. If the cr is trveling with constnt speed long circulr pth, in wht direction will the blloon on the string len towrds? A B D C (A) A (B) B (C) C (D) D (E) Remins verticl 23. Two strems of wter flow through the U-shped tubes shown. The tube on the left hs cross-sectionl re A, nd the speed of the wter flowing through it is v; the tube on the right hs cross-sectionl re A = 1/2A. If the net force on the tube ssembly is zero, wht must be the speed v of the wter flowing through the tube on the right? Neglect grvity, nd ssume tht the speed of the wter in ech tube is the sme upon entry nd exit. (A) 1/2v (B) v (C) 2v (D) 2v (E) 4v
2010 F = m Exm 10 24. A uniform circulr disk of rdius R begins with mss M; bout n xis through the center of the disk nd perpendiculr to the plne of the disk the moment of inerti is I 0 = 1 2 MR2. A hole is cut in the disk s shown in the digrm. In terms of the rdius R nd the mss M of the originl disk, wht is the moment of inerti of the resulting object bout the xis shown? R R R/2 xis of rottion (A) (15/32)MR 2 (B) (13/32)MR 2 (C) (3/8)MR 2 (D) (9/32)MR 2 (E) (15/16)MR 2 25. Spcemn Fred s spceship (which hs negligible mss) is in n ellipticl orbit bout Plnet Bob. The minimum distnce between the spceship nd the plnet is R; the mximum distnce between the spceship nd the plnet is 2R. At the point of mximum distnce, Spcemn Fred is trveling t speed v 0. He then fires his thrusters so tht he enters circulr orbit of rdius 2R. Wht is his new speed? R 2R (A) 3/2v 0 (B) 5v 0 (C) 3/5v 0 (D) 2v 0 (E) 2v 0