Ph_CanadaNPhO_93-02 - PHYSICS OLYMPIAD 1993 MULTIPLE CHOICE SCREENING TEST 30 QUESTIONS40 MINUTES DO NOT OPEN THIS TEST UNTIL YOU ARE TOLD TO BEGIN This

Ph_CanadaNPhO_93-02 - PHYSICS OLYMPIAD 1993 MULTIPLE CHOICE...

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Unformatted text preview: PHYSICS OLYMPIAD (ΠΗΨΣΙΧΣ ΟΛΨΜΠΙΑ∆) 1993 MULTIPLE CHOICE SCREENING TEST 30 QUESTIONS—40 MINUTES DO NOT OPEN THIS TEST UNTIL YOU ARE TOLD TO BEGIN This test contains 30 multiple choice questions. Your answer to each question must be marked on the optical mark answer sheet that accompanies the test. Only the boxes Select the single answer that provides the best response to each question. Please be sure to an answer, the previous mark must be completely erased. programs. Calculators may not be shared. Your grade on this multiple choice test will equal your number of correct answers. There is no penalty for guessing. It is to your advantage to answer every question. The values of some possibly useful constants are given below: mass of electron me = 9.1 x 10-31 kg mass of proton mp = 1.7 x 10-27 kg electronic charge e = 1.6 x 10-19 C speed of light c = 3.0 x 108 m/s Coulomb's constant k = 9.0 x 109 Nm2/C2 permittivity constant ε0 = 8.9 x 10-12 C2/Nm2 permeability constant µ0 = gravitational constant G = 6.7 x 10-11 Nm2/kg2 acceleration due to gravity g = 10 m/s2 speed of sound (20 oC) vs = 340 m/s 4π x 10-7 Tm/A DO NOT OPEN THIS TEST UNTIL YOU ARE INSTRUCTED TO BEGIN Copyright © 1993, AAPT 1. A ball of mass m is thrown vertically upward. Air resistance is not negligible. Assume the force of air resistance has magnitude proportional to the velocity, and direction opposite to the velocity's. At the highest point, the ball's acceleration is: (A) 0 (B) less than g (C) g (D) greater than g (E) upward 2. A train is moving forward at a velocity of 2.0 m/s. At the instant the train begins to accelerate at 0.80 m/s2, a passenger drops a quarter which takes 0.50 s to fall to the floor. Relative to a spot on the floor directly under the quarter at release, it lands: (A) 1.1 m toward the rear of the train. (B) 1.0 m toward the rear of the train. (C) 0.10 m toward the rear of the train. (D) directly on the spot. (E) 0.90 m toward the front of the train. 3. The dropped quarter in the preceding question (#2) is viewed by an observer standing next to the tracks. Relative to this observer, the quarter moves before landing. (A) forward 1.1 m (B) forward 1.0 m (C) forward 0.10 m (D) straight down (E) backward 0.10 m x 4. The accompanying graph of position x versus time t represents the motion of a particle. If b and c are both positive constants, which of the following expressions best describes the acceleration a of the particle? (A) a = 0 t (B) a = +b (C) a = -c (D) a = b + ct (E) a = b - ct 5. In the system shown to the right, a force F pushes on block A, giving the system an acceleration a. The coefficient of static friction between the blocks is µ. The correct equation for block B not to slip is: (A) a > µg (B) a < µg (C) a > g (D) a > g/µ Page 1 of 7 F (E) a < g/µ A B 6. A block of mass m starts at rest at height h on a frictionless inclined plane. The block slides down the plane, travels a total distance d across a rough surface h with coefficient of kinetic friction µ, and compresses a spring with force constant k a distance x before momentarily coming to rest. Then the spring extends and the block travels back across the rough surface, sliding up the plane. The correct expression for the maximum height h' that the block reaches on its return is: (A) mgh' = mgh - 2µmgd (B) mgh' = mgh + 2µmgd (C) mgh' = mgh + 2µmgd + kx2 (D) mgh' = mgh - 2µmgd- kx2 (E) mgh' = mgh - 2µmgd- kx2 - 1/2 mv2 7. Air track car A has mass m and velocity v. Air track car B has mass 2m and velocity 3v. The same constant force F is applied to each car until it stops. Car A is brought to rest in time t. The time required to stop car B is: (A) 2t (B) 3t (C) 6t (D) 9t (E) 18t 8. In the preceding question (#7), car A travels a distance d before coming to rest. The distance traveled by car B before coming to rest is: (A) 2d (B) 3d (C) 6d (D) 9d (E) 18d 9. Three air track cars are initially placed as shown in the A accompanying figure. Car A has mass m and initial velocity v to the right. Car B with mass m and car C with mass 4m are both m initially at rest. Car A collides elastically with car B, which in turn collides elastically with car C. After the collision, car C has a velocity of 0.4v to the right. The final velocities of cars A and B are: (A) Car A: 0.6v to the left Car B: at rest (B) Car A: 1.4v to the left Car B: at rest (C) Car A: v to the left Car B: 0.6v to the left (D) Car A: 0.4v to the left Car B: v to the left (E) Car A: 1.6v to the left Car B: v to the right Page 2 of 7 v B C m 4m 10. Three cylinders, all of mass M, roll without slipping down an inclined plane of height H. The cylinders are described as follows: I. hollow of radius R II. solid of radius R/2 III. solid of radius R If all cylinders are released simultaneously from the same height, the cylinder (or cylinders) reaching the bottom first is (are): (A) I (B) II (C) III (D) I & II (E) II & III 11. The system shown to the right is free to rotate about a frictionless axis through its center and perpendicular to the page. All three forces are exerted tangent to their respective rims. The magnitude of the net torque acting on the system is: 37 R/2 F R (A) 1.5 FR 2F (B) 1.9 FR (C) 2.3 FR (D) 2.5 FR (E) 3.5 FR 12. Two identical disks are positioned on a vertical axis. The bottom disk is rotating at angular velocity ω0 and has rotational kinetic energy K0. The top disk is initially at rest. It is allowed to fall, and sticks to the bottom disk. What is the rotational kinetic energy of the system after the collision? (A) 1/4 K0 F O (B) 1/2 K0 (C) K0 (D) 2 K0 (E) 4 K0 13. If the sun were suddenly replaced by a black hole of one solar mass, what would happen to the earth's orbit immediately after the replacement? (A) The earth would spiral into the black hole. (B) The earth would spiral out away from the black hole. (C) The radius of the earth's orbit would be unchanged, but the period of the earth's motion would increase. (D) Neither the radius of the orbit nor the period would change. (E) The radius of the earth's orbit would be unchanged, but the period of the earth's motion would decrease. Page 3 of 7 14. A hypothetical planet has density ρ, radius R, and surface gravitational acceleration g. If the radius of the planet were doubled, but the planetary density stayed the same, the acceleration due to gravity at the planet's surface would be: (A) 4g (B) 2g (C) g (D) g/2 (E) g/4 15. An ideal organ pipe resonates at frequencies of 50 Hz, 150 Hz, 250 Hz,.... The pipe is: (A) open at both ends and of length 1.7 m. (B) open at both ends and of length 3.4 m. (C) open at both ends and of length 6.8 m. (D) closed at one end, open at the other, and of length 1.7 m. (E) closed at one end, open at the other, and of length 3.4 m. 16. A porpoise, whistle-clicking at a frequency f0, swims toward an underwater vertical cliff at a velocity that is 1.0% of the velocity of sound in sea water. The reflected frequency experienced by the swimming porpoise is: (A) 0.98 f0 (B) 0.99 f0 (C) f0 (D) 1.01 f0 17. Three processes compose a thermodynamic cycle shown in the accompanying pV diagram. Process 1→2 takes place at constant temperature. Process 2→3 takes place at constant volume, and process 3→1 is adiabatic. During the complete cycle, the total amount of work done is 10 J. During process 2→3, the internal energy decreases by 20 J; and during process 3→1, 20 J of work is done on the system. How much heat is added to the system during process 1→2? (E) 1.02 f0 1 p 2 3 V (A) 0 Q (B) 10 J 1¨ 2 2¨ 3 3¨ 1 cycle (C) 20 J (D) 30 J (E) 40 J W -20J -20J +10J 18. The root mean square velocity of oxygen gas is v at room temperature. What is the root mean square velocity of hydrogen gas at the same temperature? (A) 16 v (B) 4 v (C) v (D) v/4 Page 4 of 7 (E) v/16 ∆U 19. Monochromatic light of wavelength λ is shone on a grating consisting of six equally spaced slits. The first order interference maximum occurs at an angle of 0.00100 radians. If the outer two slits are covered, the first order maximum will occur at ______ radians. (A) 0.00025 (B) 0.00067 (C) 0.00100 (D) 0.00150 (E) 0.00400 20. You are given two lenses, a converging lens with focal length +10 cm and a diverging lens with focal length -20 cm. Which of the following would produce a virtual image that is larger than the object? (A) Placing the object 5 cm from the converging lens. (B) Placing the object 15 cm from the converging lens. (C) Placing the object 25 cm from the converging lens. (D) Placing the object 15 cm from the diverging lens. (E) Placing the object 25 cm from the diverging lens. 21. Two small identical conducting spheres are separated by a distance much larger than their diameter. They are initially given charges of -2.00 x 10-6 C and +4.00 x 10-6 C, and found to exert a force on each other of magnitude 1.000 N. Without changing their position, they are connected by a conducting wire. When the wire is removed, what is the magnitude of the force between them? (A) 0 (B) 0.125 N (C) 0.250 N (D) 1.000 N (E) 1.125 N 22. Charges of ±Q, with Q = 2.0 x 10-7 C, are placed at three corners of a square whose sides are 0.10 m. The magnitude of the total field at the center of the square is: +Q (B) 2.5 x 104 V/m (C) 7.5 x 104 (D) 3.6 x -Q V/m 105 X 0.10m (A) 5.1 x 103 V/m +Q V/m 0.10m (E) 1.08 x 106 V/m 23. Three 60 W light bulbs are mistakenly wired in series and connected to a 120 V power supply. Assume the light bulbs are rated for single connection to 120 V. With the mistaken connection, the power dissipated by each bulb is: (A) 6.7 W (B) 13.3 W (C) 20 W (D) 40 W Page 5 of 7 (E) 60 W 24. Two thin spherical conducting shells are centered on the same point. The inner sphere has radius b and total charge q. The outer sphere has radius B and total charge Q. At a point a distance R from the common center, where b< R<B, and assuming the electric potential is zero an infinite distance away, the total potential due to the two spheres is: (A) kq/b + kQ/B (B) kq/b + kQ/R (C) kq/R (D) kq/R + kQ/B (E) kq/R + kQ/R 25. What is the magnitude of the total electric field for the two spheres at the point described in the preceding question (#24)? (A) kq/b2 + kQ/B2 (B) kq/b2 + kQ/R2 (C) kq/R2 (D) kq/R2+ kQ/B2 (E) kq/R2 + kQ/R2 26. A current of 0.10 A flows through the 25 ½ resistor represented in the diagram to the right. The current through the 80 ½ resistor is: 80 Ω 0.1 A 25 Ω V 20 Ω (A) 0.10 A (B) 0.20 A 20 Ω (C) 0.30 A 60 Ω (D) 0.40 A (E) 0.60 A 27. The circuit shown in the accompanying figure has been connected for a very long time. The voltage across the capacitor is: (A) 1.2 V (B) 2.0 V (C) 2.4 V (D) 4.0 V (E) 6.0 V Page 6 of 7 100 Ω 6V 200 Ω 100 Ω 4 µF 28. The accompanying sketch represents a bubble chamber photograph. field is directed out of the plane of the sketch. All particles have the same velocity initially from left to ... right. The one that is most likely an electron is: .A . . ... (A) A ... (B) B ... ... (C) C E. . . (D) D The magnetic . . . . . . . . .B . . . .D . . . . .C . . . (E) E 29. What is the correct expression for the magnetic field at point X in the diagram to the right? HINT: The magnitude of the magnetic field at the center of a circular current loop of radius R is µ 0i/(2R). (A) (µ 0i/4)(1/a + 1/b) into the page (B) (µ 0i/4)(1/a - 1/b) out of the page (C) (µ 0i/4)(1/a - 1/b) - µ 0i/(2πa) out of the page (E) (µ 0i/2)(1/a + 1/b) + µ 0i/(2πa) i out of the page (D) (µ 0i/2)(1/a - 1/b) b into the page a X 30. You are given a bar magnet and a looped coil of wire. Which of the following would induce an emf in the coil? I. Moving the magnet away from the coil. II. Moving the coil toward the magnet. III. Turning the coil about a vertical axis. (A) I only (B) II only (C) I & II (D) I & III Page 7 of 7 (E) I, II, III . . . . . . . . . . . . . . 1993 MULTIPLE CHOICE SCREENING TEST ANSWER KEY 1. C 16. E 2. C 17. D 3. B 18. B 4. E 19. C 5. D 20. A 6. A 21. B 7. C 22. D 8. E 23. A 9. A 24. D 10. E 25. C 11. A 26. C 12. B 27. D 13. D 28. A 14. B 29. B 15. D 30. E Physics Olympiad Entia non multiplicanda sunt praeter necessitatem 1996 MULTIPLE CHOICE SCREENING TEST 30 QUESTIONS—40 MINUTES INSTRUCTIONS DO NOT OPEN THIS TEST UNTIL YOU ARE TOLD TO BEGIN This test contains 30 multiple choice questions. Your answer to each question must be marked on the optical mark answer sheet that accompanies the test. Only the boxes preceded by numbers 1 through 30 are to be used on the answer sheet. Select the single answer that provides the best response to each question. Please be sure to use a No. 2 pencil and completely fill the box corresponding to your choice. If you change an answer, the previous mark must be completely erased. A hand-held calculator may be used. However, any memory must be cleared of data and programs. Calculators may not be shared. Your grade on this multiple choice test will be your number of correct answers. There is no penalty for guessing. It is to your advantage to answer every question. The values of some possibly useful constants are given below: mass of electron me = 9.1 x 10-31 kg mass of proton mp = 1.7 x 10-27 kg electronic charge e = 1.6 x 10-19 C speed of light c = 3.0 x 108 m/s Coulomb's constant k = 9.0 x 109 N·m2/C2 permittivity constant ε0 = 8.9 x 10-12 C2/N·m2 permeability constant µ0 = gravitational constant G = 6.7 x 10-11 N·m2/kg2 acceleration due to gravity g = 10 m/s2 speed of sound (20 oC) vs = 340 m/s 4π x 10-7 T·m/A DO NOT OPEN THIS TEST UNTIL YOU ARE INSTRUCTED TO BEGIN Copyright © 1996, AAPT 1. An object is projected straight upward from ground level with a velocity of 50 m/s. Ignoring air resistance, it will return to ground level in approximately: A. 2.5 s B. 5.0 s C. 7.5 s D. 10 s E. 15 s 2. A jogger runs with constant speed v through a forest of pine trees. A pine cone starts to fall from a height h when the jogger is directly below it. How far behind the jogger will the pine cone land? 2 hv2 g A. B. hv2 2g gh 2 C. 2v2 v2 E. 2g 2 gh2 D. v2 3. A ball is thrown downward with speed 15 m/s from the roof of a 30 m building. At the same instant a ball is thrown upward with speed 15 m/s from ground level. Relative to ground level, the two balls pass each other at a height of: A. 0 B. 5.0 m C. 10 m D. 15 m E. 20 m 4. A swimmer can swim with a velocity of 1.0 m/s in still water. The swimmer wishes to swim directly across a river with a current of 0.50 m/s directed from upstream to downstream. To end up directly across the river the swimmer must head at an angle of: A. B. C. D. E. tan-1(1/2) upstream. sin-1(1/2) upstream. directly across the river. sin-1(1/2) downstream tan-1(1/2) downstream 5. What is the tension T in the rope if the 10-N weight is moving upward with constant velocity? A. 3.5 N B. 5.0 N C. 7.1 N D. 10 N E. 14 N 1996 Physics Olympiad T 45o 10 N page 1 6. As shown to the right, two Case I Case II blocks with masses m and M F (M > m) are pushed by a force F F M M m m in both Case I and Case II. The surface is horizontal and frictionless. Let RI be the force that m exerts on M in case I and RII be the force that m exerts on M in case II. Which of the following statements is true? A. B. C. D. E. RI = RII = 0 RI = RII and is not equal to zero or F. RI = RII = F RI < RII RI > RII 7. Two blocks, with masses 17 kg and 15 kg, are connected by a light string that passes over a frictionless pulley of negligible mass as shown to the right. The surfaces of the planes are frictionless. The blocks are released from rest. T1 and T2 are the tensions in the strings. Which of the following statements is correct? A. B. C. D. E. T2 T1 17 kg 15 kg 45o 60o The 15-kg block accelerates down the plane. The 17-kg block accelerates down the plane. Both blocks remain at rest. T 1 > T2 T 1 < T2 8. A small block of mass m starts from rest at the top of a globe of radius R. At what angle θ does it slide off the surface of the globe? Assume the system is frictionless. A. θ = 0o B. θ = cos-1(1/3) C. θ = cos-1(2/3) D. θ = 60o E. θ = 90o R θ 9. An object with mass m and initial velocity v is brought to rest by a constant force F acting for a time t and through a distance d. Possible expressions for the magnitude of the force F are: I. (mv2)/(2d) II. (2md)/t2 III. (mv)/t Which of these give(s) the correct expression for the magnitude of the force F? A. II only B. III only 1996 Physics Olympiad C. I and II only D. II and III only E. I, II, and III page 2 10. A small sphere is moving at a constant speed in a vertical circle. Below is a list of quantities that could be used to describe some aspect of the motion of the sphere. I – kinetic energy II – potential energy III – momentum Which of these quantities will change as this sphere moves around the circle? A. I and II only B. I and III only C. II only D. III only E. II and III only 11. A roller coaster travels with speed vA at point A. Point B is a height H above point A. Assuming no frictional losses and no work done by a motor, what is the speed at point B? vA 2 − 2gH A. B. v A − 2gH C. v A − 2gH D. v A + 2gH E. vA 2 + 2gH 12. Three air track cars are initially placed as shown in the A B C accompanying figure. Car A has mass m and initial velocity v to v the right. Car B with mass m and car C with mass 4m are both m m 4m initially at rest. Car A collides elastically with car B, which in turn collides elastically with car C. After the collision, car B is at rest. The final velocities of cars A and C are: A. B. C. D. E. Car A: 0.6v to the left Car A: 2.6v to the left Car A: at rest Car A: at rest Car A: at rest Car C: 0.4v to the right Car C: 0.4v to the right Car C: 0.5v to the right Car C: 0.25v to the right Car C: v to the right 13. A child with mass m is standing at the edge of a playground merry-goround with moment of inertia I, radius R, and initial angular velocity ω . See figure to the right. The child jumps off the edge of the merry-go-round with tangential velocity v with respect to the ground. The new angular velocity of the merry-go-round is: v ω A. ω Iω 2 − mv 2 I B. C. (I + mR 2 )ω 2 − mv2 I Iω − mvR D. I I + mR 2 ω − mvR E. I ( ) 1996 Physics Olympiad page 3 14. As shown in the figure to the right, a spool has outer radius R and axle radius r. A string is wrapped around the axle of the spool and can be pulled in any of the directions labeled by I, II, or III. The spool will slide to the right without rolling on the horizontal surface if it is pulled in direction(s): A. I only B. II only C. III only D. I and II only E. II and III only I II III r R 15. A uniform flag pole of length L and mass M is pivoted on the ground with a frictionless hinge. The flag pole makes an angle θ with the horizontal. The moment of inertia of the flag pole about one end is (1/3)ML2. If it starts falling from the position shown in the accompanying figure, the linear acceleration of the free end of the flag pole – labeled P – would be: A. Β. C. D. E. P L θ (2/3) g cos θ (2/3) g g (3/2) g cos θ (3/2) g 16. The root mean square velocity of oxygen gas (atomic mass 16) is v at room temperature. What is the root mean square velocity of helium (atomic mass 4) at the same temperature? A. 4 v B. 2 v C. v D. v/2 E. v/4 17. Which of the accompanying PV diagrams best represents an adiabatic process (process where no heat enters or leaves the system)? A. P C. P B. P V V E. P D. P V V V 18. String A and String B have the same mass and length. String A is under tension T and string B is under tension 2T. The speed of waves in B is _____ times the speed of waves in A. A. 0.50 B. 0.71 C. 1.00 D. 1.4 E. 2.0 1996 Physics Olympiad page 4 19. On a day when the velocity of sound in air is v, a whistle moves with velocity u toward a stationary wall. The whistle emits sound with frequency f. What frequency of reflected sound will be heard by an observer traveling along with the whistle? v -u A. f v + u B. f v v u + C. f v D. f v- u u E. f v + u v -u 20. You are given two lenses, a converging lens with focal length + 10 cm and a diverging le...
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