AAPT UNITED STATES PHYSICS TEAM AIP 2009

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2 2009 F = ma Exam 2 1. A 0. k apple falls from rest throuh a heiht of 40 cm onto a flat surface. Upon impact, the apple comes to rest in 0.1 s, and 4 cm 2 of the apple comes into contact with the surface durin the impact. What is the averae pressure exerted on the apple durin the impact? Inore air resistance. (A) 67,000 Pa (B) 21,000 Pa CORRECT (C) 6,700 Pa (D) 210 Pa (E) 67 Pa The followin information is used for questions 2 and. Three blocks of identical mass are placed on a frictionless table as shown. The center block is at rest, whereas the other two blocks are movin directly towards it at identical speeds v. The center block is initially closer to the left block than the riht one. All motion takes place alon a sinle horizontal line. 2. Suppose that all collisions are instantaneous and perfectly elastic. After a lon time, which of the followin is true? (A) The center block is movin to the left. (B) The center block is movin to the riht. (C) The center block is at rest somewhere to the left of its initial position. (D) The center block is at rest at its initial position. CORRECT (E) The center block is at rest somewhere to the riht of its initial position.. Suppose, instead, that all collisions are instantaneous and perfectly inelastic. After a lon time, which of the followin is true? (A) The center block is movin to the left. (B) The center block is movin to the riht. (C) The center block is at rest somewhere to the left of its initial position. (D) The center block is at rest at its initial position. (E) The center block is at rest somewhere to the riht of its initial position. CORRECT 4. A spaceman of mass 80 k is sittin in a spacecraft near the surface of the Earth. The spacecraft is acceleratin upward at five times the acceleration due to ravity. What is the force of the spaceman on the spacecraft? (A) 4800 N CORRECT (B) 4000 N (C) 200 N (D) 800 N (E) 400 N

3 2009 F = ma Exam 5. Three equal mass satellites A, B, and C are in coplanar orbits around a planet as shown in the fiure. The manitudes of the anular momenta of the satellites as measured about the planet are A, B, and C. Which of the followin statements is correct? A B C (A) A > B > C CORRECT (B) C > B > A (C) B > C > A (D) B > A > C (E) The relationship between the manitudes is different at various instants in time. 6. An object is thrown with a fixed initial speed v 0 at various anles α relative to the horizon. At some constant heiht h above the launch point the speed v of the object is measured as a function of the initial anle α. Which of the followin best describes the dependence of v on α? (Assume that the heiht h is achieved, and assume that there is no air resistance.) (A) v will increase monotonically with α. (B) v will increase to some critical value v max and then decrease. (C) v will remain constant, independent of α. CORRECT (D) v will decrease to some critical value v min and then increase. (E) None of the above. 7. A bird is flyin in a straiht line initially at 10 m/s. It uniformly increases its speed to 15 m/s while coverin a distance of 25 m. What is the manitude of the acceleration of the bird? (A) 5.0 m/s 2 (B) 2.5 m/s 2 CORRECT (C) 2.0 m/s 2 (D) 0.5 m/s 2 (E) 0.2 m/s 2

5 2009 F = ma Exam A 2.25k mass underoes an acceleration as shown below. How much work is done on the mass? 4 Acceleration (m/s/s) Position (m) (A) 6 J CORRECT (B) 22 J (C) 5 J (D) -17 J (E) -6 J 12. Batman, who has a mass of M = 100 k, climbs to the roof of a 0 m buildin and then lowers one end of a massless rope to his sidekick Robin. Batman then pulls Robin, who has a mass of m = 75 k, up the roof of the buildin. Approximately how much total work has Batman done after Robin is on the roof? (A) 60 J (B) 7 10 J (C) J CORRECT (D) 600 J (E) 10 4 J 1. ucy (mass.1 k), Henry (mass 6.7 k), and Mary (mass 24. k) sit on a lihtweiht seesaw at evenly spaced 2.74 m intervals (in the order in which they are listed; Henry is between ucy and Mary) so that the seesaw balances. Who exerts the most torque (in terms of manitude) on the seesaw? Inore the mass of the seesaw. (A) Henry (B) ucy CORRECT (C) Mary (D) They all exert the same torque. (E) There is not enouh information to answer the question.

6 2009 F = ma Exam A wooden block (mass M) is hun from a pe by a massless rope. A speedin bullet (with mass m and initial speed v 0 ) collides with the block at time t = 0 and embeds in it. et S be the system consistin of the block and bullet. Which quantities are conserved between t = 10 s and t = +10 s? (A) The total linear momentum of S. (B) The horizontal component of the linear momentum of S. (C) The mechanical enery of S. (D) The anular momentum of S as measured about a perpendicular axis throuh the pe. (E) None of the above are conserved. CORRECT 15. A 22.0 k suitcase is draed in a straiht line at a constant speed of 1.10 m/s across a level airport floor by a student on the way to the 40th IPhO in Merida, Mexico. The individual pulls with a 1.00 x 10 2 N force alon a handle with makes an upward anle of 0.0 derees with respect to the horizontal. What is the coefficient of kinetic friction between the suitcase and the floor? (A) µ k = 0.01 (B) µ k = 0.94 (C) µ k = CORRECT (D) µ k = (E) µ k = Two identical objects of mass m are placed at either end of a sprin of sprin constant k and the whole system is placed on a horizontal frictionless surface. At what anular frequency ω does the system oscillate? (A) k/m (B) 2k/m CORRECT (C) k/2m (D) 2 k/m (E) k/m/2 17. You are iven a standard kiloram mass and a tunin fork that is calibrated in Hz. You are also provided with a complete collection of laboratory equipment, but none of it is calibrated in SI units. You do not know the values of any fundamental constants. Which of the followin quantities could you measure in SI units? (A) The acceleration due to ravity. (B) The speed of liht in a vacuum. (C) The density of room temperature water. (D) The sprin constant of a iven sprin. CORRECT (E) The air pressure in the room.

7 2009 F = ma Exam A simple pendulum of lenth is constructed from a point object of mass m suspended by a massless strin attached to a fixed pivot point. A small pe is placed a distance 2/ directly below the fixed pivot point so that the pendulum would swin as shown in the fiure below. The mass is displaced 5 derees from the vertical and released. How lon does it take to return to its startin position? Fixed Pivot Point Small Pe (A) π (B) π ( ) ( ) (C) π (D) π (E) π ( ) ( ) 1 + ( ) CORRECT Point Object of mass m 19. A certain football quarterback can throw a football a maximum rane of 80 meters on level round. What is the hihest point reached by the football if thrown this maximum rane? Inore air friction. (A) 10 m (B) 20 m CORRECT (C) 0 m (D) 40 m (E) 50 m 20. Consider a completely inelastic collision between two lumps of space oo. ump 1 has mass m and oriinally moves directly north with a speed v 0. ump 2 has mass m and oriinally moves directly east with speed v 0 /2. What is the final speed of the masses after the collision? Inore ravity, and assume the two lumps stick toether after the collision. (A) 7/16 v 0 (B) 5/8 v 0 (C) 1/8 v 0 CORRECT (D) 5/8 v 0 (E) 1/8 v 0

8 2009 F = ma Exam 8 The followin information is used for questions 21 and 22. Two stars orbit their common center of mass as shown in the diaram below. The masses of the two stars are M and M. The distance between the stars is d. 21. What is the value of the ravitational potential enery of the two star system? (A) GM2 d (B) GM2 d (C) GM2 d 2 (D) GM2 d CORRECT (E) GM2 d Determine the period of orbit for the star of mass M. d (A) π GM CORRECT (B) π 4 (C) π (D) 2π (E) π 4 d GM d GM d GM d GM 2. A mass is attached to an ideal sprin. At time t = 0 the sprin is at its natural lenth and the mass is iven an initial velocity; the period of the ensuin (one-dimensional) simple harmonic motion is T. At what time is the power delivered to the mass by the sprin first a maximum? (A) t = 0 (B) t = T/8 (C) t = T/4 (D) t = T/8 CORRECT (E) t = T/2

9 2009 F = ma Exam A uniform rectanular wood block of mass M, with lenth b and heiht a, rests on an incline as shown. The incline and the wood block have a coefficient of static friction, µ s. The incline is moved upwards from an anle of zero throuh an anle θ. At some critical anle the block will either tip over or slip down the plane. Determine the relationship between a, b, and µ s such that the block will tip over (and not slip) at the critical anle. The box is rectanular, and a b. b a θ (A) µ s > a/b (B) µ s > 1 a/b (C) µ s > b/a CORRECT (D) µ s < a/b (E) µ s < b/a Two discs are mounted on thin, lihtweiht rods oriented throuh their centers and normal to the discs. These axles are constrained to be vertical at all times, and the discs can pivot frictionlessly on the rods. The discs have identical thickness and are made of the same material, but have differin radii r 1 and r 2. The discs are iven anular velocities of manitudes ω 1 and ω 2, respectively, and brouht into contact at their edes. After the discs interact via friction it is found that both discs come exactly to a halt. Which of the followin must hold? Inore effects associated with the vertical rods. r1 r2 (A) ω 2 1 r 1 = ω 2 2 r 2 (B) ω 1 r 1 = ω 2 r 2 (C) ω 1 r = ω 2 r 2 (D) ω 1 r 1 = ω 2 r 2 CORRECT (E) ω 1 r = ω 2 r 2

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