1988 Physics C - Mechanics Multiple-Choice

1988 Physics C - Mechanics Multiple-Choice - 1988 Physics...

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Unformatted text preview: 1988 Physics C: Mechanics PHYSICS C SECTION I, MECHANICS Time—45 minutes 35 Questions Directions: Each of the questions or incomplete statements below is followed by five suggested answers or comple- tions. Select the one that is best in each case and then fill in the corresponding oval on the answer sheet. 1. Which of the following pairs of graphs shows the Questions 2—3 distance traveled versus time and the speed versus time for an object uniformly accelerated from rest attime t= 0? (A) Distance W W 0 (B) Distance W t— (C) Distance W (D) Distance T W (E) Distance K N Speed Speed Sp ed F Speed Speed am a m A 4-kilogram mass has a speed of 6 meters per second on a horizontal frictionless surface, as shown above. The mass collides head-on and elastically with an identical 4-kilogram mass initially at rest. The second 4-kilogram mass then collides head-on and sticks to a third 4-kilogram mass initially at rest. 2. The final speed of the first 4-kilogram mass is (A) 0 m/s (B) 2 m/s (C) 3 m/s (D) 4 m/s (E) 6m/s 3. The final speed of the two 4-kilogram masses that stick together is (A) 0 m/s (B) 2 m/s (C) 3 m/s (D) 4 m/s (E) (Sm/s I 4. A particle of mass m moves along a straight path with a speed 9 defined by the function u = in2 + c, where b and c areconstants and r is time. What is the magnitude F of the net force on the particle at time t = t1 ? (A) Mi2 + c (B) 3mbt1 + 2c mbtl (D) mbrl + c (E) Zmbti Physics c: Mechanics 5. An object released from rest at time t = 0 slides down a frictionless incline a distance of 1 meter during the first second. The distance traveled by the object during the time interval from t = I second to r = 2 seconds is (A) 1m (B) 2m (C) 3m (D)4m (E) 5m . Two people are in a boat that is capable of a maximum speed of 5 kilometers per hour in still water, and wish to cross a river I kilometer wide to a point directly across from their starting point. If the speed of the water in the river is 5 kilometers per hour, how much time is required for the crossing? (A) Zl-ohr (B) 110-1“ (C) [in (D) IO hr . (E) The point directly across from the starting point cannot be reached under these conditions. N N V v1 2 W E W E S S Time tl Time 12 7. Vectors V, and V2 shown above have equal magnitudes. The vectors represent the velocities of an object at times t. and 11, respectively. The average acceleration of the object between time t. and t; was (A) zero (B) directed north (C) directed west (D) directed north of east (E) directed north of west 8. A projectile of mass M1 is fired horizontally from a spring gun that is initially at rest on a frictionless surface. The combined mass of the gun and projec- tile is Mz. If the kinetic energy of the projectile after firing is K, the gun will recoil with a kinetic energy equal to (A) K M (8) fix M12 M22 K M1 (D) —“—M2 _ M] K MI (E) WK 9. 10. _..\‘: 61 ‘__’x | I A piece of wire of uniform cross section is bent in the shape shown above. What are the coordinates (It, i) of the center of mass? 3" _.V_ (A) 15/14 6/7 (B) 6/7 6/7 (C) 15/14 3/7 (D) 1 1 (E) 1 6/7 A projectile is fired from the surface of the Earth with a speed of 200 meters per second at an angle of 30' above the horizontal. If the ground is level, what is the maximum height reached by the projectile? (A) 5 m (B) 10 m (C) 500 m (D) 1,000 m (E) 2,000 m 11. 12. Physics c: Mechanlca A particle moves along the x-axis with a non- constant acceleration described by a = 12!, where a is in meters per second squared and t is in seconds. If the particle starts from rest so that its speed 0 and position x are zero when r = 0, where is it located when t = 2 seconds? (A) x = 12m (B) x = 16m (C) x = 24m (D) x = 32 m (E) x = 48 m A figure skater is spinning on frictionless ice with her arms fully extended horizontally. She then drops her arms to her sides. Which of the following correctly describes her rotational kinetic energy and angular momentum as her arms fall? Rotational Kinetic Angular Energy Momentum (A) Remains constant Remains constant (B) Decreases Increases (C) Decreases Decreases (D) Increases Decreases (E) Increases Remains constant Phyclcc c: Meet-names l3. A ball is dropped from a height of 10 meters onto a hard surface so that the collision at the surface may be assumed elastic. Under such conditions the motion of the ball is (A) simple harmonic with a period of about L4 5 (B) simple harmonic with a period of about 2.8 s (C) simple harmonic with an amplitude of 5 in (D) periodic with a period of about 2.8 s but not simple harmonic (E) motion with constant momentum Questions 14- l 5 An object moving in a straight line has a velocity v in meters per second that varies with time t in seconds according to the following function. v=4+0.5!2 14. The instantaneous acceleration of the object 15. at t = 2 sec0nds is (A) 2 m/s2 (B) 4 m/s2 (C) 5 m/sz (D) 6 m/s2 (E) 3 m/s2 The displacement of the object between t = 0 and r = 6 seconds is (A) 22 m (B) 28 m (C) 40 m (D) 42 m (E) 60 m 16. 17. A pendulum consists of a ball of mass m suspended at the end of a massless cord of length L as shewn above. The pendulum is drawn aside through an angle of 60' with the vertical and released. At the low point of its swing, the speed of the pendulum ball is A rock is lifted for a certain time by a force F that is greater in magnitude than the rock's weight W. The change in kinetic energy of the rock during this time is equal to the (A) work done by the net force (F — W) (B) work done by F alone (C) work done by W alone (D) difference in the momentum of the rock before and after this time (B) difference in the potential energy of the rock before and after this time Physics c: Mechanlcs Questions 18—19 refer to the graph below of the displaoe- 19. Which of the following graphs shows the kinetic ‘ment x versus time I for a particle in simple harmonic energy K of the particle as a function of its motion. displacement x ? x (A) K (B) K 0 T r ' x 0 x 18. Which of the following graphs shows the kinetic ¥x 0 energy K of the particle as a function of time t for one cycle of motion? (C) K (D) K (MK (B) K 0M1 OPAL-LT! 0 x o x (C) K (D) K T (E) K 0 t 0 I T E ( _) K Physics C: Moehanlcs 20. A satellite travels around the Sun in an elliptical 21. orbit as shown above. As the satellite travels from point X to point Y, which of the following is true about its speed and angular momentum? M Anfllar Momentum (A) Remains constant Remains constant (B) Increases Increases (C) Decreases Decreases Remains constant Remains constant (D) Increases (E) Decreases A newly discovered planet, “Cosmo,” has a mass that is 4 times the mass of the Earth‘ The radius of the Earth is Re. The gravitational field strength at the surface of Cosmo is equal to that at the surface of the Earth if the radius of Cosmo is equal to w%& (ma ©2m (mJE (E) R92 22. Two artificial satellites, l and 2, orbit the Earth in circular orbits having radii R1 and R2, respec- tively, as shown above. If R; = 2R. , the accelera- tions 0: and a, of the two satellites are related by which of the following? (A) a2 = 4a: (B) a2 = 2m (C) 02 = a] (D) a2 = % (E) a2 = 5’41 Phyelea c: Moehanlee 23. A bowling ball of mass M and radius R, whose Pm Q o . ————— - —f R . . . . 2 2 l I l moment of inertia about its center 15 3 MR , rolls \\ : ; I / without slipping along a level surface at speed 0. ' \\ x : I// s. _._. ’ Q The maximum vertical height to which it can roll if 24. A ball of mass m is attached to the end of a string of length ll as shown above. The ball is released (A) % i from rest from position P, where the string is hori- it ascends an incline is g zontal. It swings through positiOn Q, where the 2 01 string is vertical, and then to position R, where the (B) 5 E string is again horizontal. What are the directions of the acceleration vectors of the ball at positions Q (C) % 2;. and R ? (D) l 0—2 Position Q Position R 10 g (A) Downward Downward [,2 (B) Downward To the right (E) :2— (C) Upward Downward (D) Upward To the left (E) To the right To the left Physics c: Mechanics 25. A mass m moves on a curved path from point X to point Y. Which of the following diagrams indicates a possible combination of the net force F on the mass, and the velocity v and acceleration a of' the mass at the loca- tion shown? (A) Y (B) y Questions 26-27 A particle moves in a circle in such a way that the x- and y-coordinates of its motion are given in meters as functions of time t in seconds by: x = 5 cos (3:) y = 5 sin (3:) 26. What is the period of revolution of the particle? 1 , (A) g s (B) 38 27. Which of the following is true of the speed of the particle? (A) It is always equal to 5 m/s. (B) It is always equal to 15 m/s. (C) It oscillates between 0 and 5 m/s. (D) It oscillates between 0 and 15 m/s. (E) It oscillates between 5 and 15 m/s. 28. The radius of the Earth is approximawa 6,000 kilo— meters. The acceleration of an astronaut in a perfectly circular orbit 300 kilometers above the Earth would be most nearly (A) Dm/s2 (B) 0.05 111152 (C) 5m/Sz (D) 9 m/s2 (E) 1] t'n/s2 Phyelel c: Mechanics 20N _ 29. Two blocks are pushed along a horizontal friction- 30. less surface by a force of 20 newtons to the right, as shown above. The force that the 2-kilogram block exerts on the 3-kilogram block is (A) 8 newtons to the left (B) 8 newtons to the right (C) 10 newtons to the left (D) 12 newtons to the right (E) 20 newtons to the left When a mass m is hung on a certain ideal spring, the spring stretches a distance d. If ' the mass is then set oscillating on the spring, the period of oscillation is proportional to (A) ff (B) g (C) ",4; (D) $ (E) § Physics c: Meehanlcs x—fiF—QAF 3]. In which of the following diagrams is the torque about point 0 equal in magnitude to the torque about point X in the diagram above? (All forces lie in the plane of the paper.) (A) 7 (B) t le—Q—i Irrl o-———>2F 0~——;—-—F (C)0'__Q__I (D)0|‘_Q'__i D6032!" HE!" ‘ 30°I (E) None of the above 32. A 10-kilogram body is constrained to move along the x—axis. The potential energy U of the body in joules is given as a function of its position x in meters by ‘U(x) = 6x2 — 4x + 3 The force on the particle at x = 3 meters is (A) 32N in +x direction (B) 32N in -x direction (C) 45 N in +x direction (D) 45 N in -x direction (E) 98 N in +x direction 33. 34. 35. A rock is dropped from the top of a 45-meter tower, and at the same time a ball is thrown from the top of the tower in a horizontal direction. Air resistance is negligible. The ball and the rock hit the level ground a distance of 30 meters apart. The horizontal velocity of the ball thrown was most nearly (A) Sin/s (B) 10 m/s (C) 14.1m/s (D) 20 m/s (E) 28.3 m/s Two objects of equal mass hang from independent springs of unequal spring constant and oscillate up and down. The spring of greater spring constant must have the (A) smaller amplitude of oscillation (B) larger amplitude of oscillation (C) shorter period of oscillation (D) longer period of oscillation (E) lower frequency of oscillation A satellite moves in a stable circular orbit with speed :20 at a distance R from the center of a planet. For this satellite to move in a stable circular orbit a distance 2R from the center of the planet, the speed of the satellite must be t} (A) 7° (13) ole (C) 00 (D) 290 w (E) 290 END OF SECTION I, MECHANICS IF YOU FINISH BEFORE TIME IS CALLED, YOU MAY CHECK YOUR WORK ON SECTION I, MECHANICS, ONLY. DO NOT TURN TO ANY OTHER TEST MATERIALS. ...
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