Note: To simplify calculations, you may use g = 10 m/s in all problems.V =7.5 m/s Questions 2-4 refer to the following figure: B C - NWAVAN D velocity (m/s) 1. An object is thrown horizontally to the right off a high cliff with an initial speed of 7.5 m/s. Which arrow best represents the direction of the object's velocity after A + 2 seconds? (Assume air resistance is negligible.) 5 6 9 F (A) . time (s) (B) 2. Rank the change in momentum for each segment from least (most negative) to greatest (most positive). Assume (D) that the mass of the object remains constant. (A) BC, EF, DE, AB, CD (B) AB, CD, DE, EF, BC (C) BC, EF, DE, CD, AB (D) CD, DE, EF, BC, AB 3. During which segment is the magnitude of average acceleration greatest? (A) AB (B) BC (C) CD (D) DE4. What is the total distance traveled by the object? N (A) 32 m (B) 34 m (C) 36 m (D) 38 m F 7. A person standing on a horizontal floor is acted upon by A two forces: the downward pull of gravity and the upward normal force of the floor. These two forces (A) have equal magnitudes and form an action/reaction 5. A ball is thrown with an initial velocity v at an angle 0 pair above the ground. If the acceleration due to gravity is -g, (B) have equal magnitudes and do not form an action/ which of the following is the correct expression of the reaction pair time it takes for the ball to reach its highest point, y, from (C) have unequal magnitudes and form an action/ the ground? reaction pair (A) v sin 0/g (D) have unequal magnitudes and do not form an action/ (B) -v cos @/g reaction pair (C) v sin @/g (D) v cos O/g8. Which of the following graphs best represents the force of friction on an object starting at rest that eventually starts sliding across a level surface due to a gradually increasing horizontal force? F (A) F app F 6. A bubble in a glass of water releases from rest at the bot- (B) tom of the glass and rises at acceleration a to the surface in t seconds. How much farther does the bubble travel in its last second than in its first second? Assume that the F app journey takes longer than 2 seconds. (A) a(t + 1 s)? F (B) a(t - 1 s)(1 s) (C) (C) at (D) a(t + 1 s)(1 s) Fapp (D) F F app9. Two objects have a mass 1 kg and carry a charge of magnitude 1 C each. Which statement correctly identi- fies the relationship between the magnitude of the force 3m of gravity, F , and the magnitude of the electric force, F. between the objects? 2m (A) F>FE (B) FFE C) F=F (D) Cannot be determined without knowing the sign of the charges 12. In the figure above, two blocks of mass 3m and 2m are attached together. The plane is frictionless and the pulley is frictionless and massless. The inclined portion of the plane creates an angle o with the horizontal floor. What is the acceleration of the block 2m if both blocks are released from rest (gravity = g)? (A) 2mg (B) (2) 8 sin 0 10. Consider the above configuration of masses attached via a massless rope and pulley over a frictionless inclined plane. What is the acceleration of the masses? (D) Gesine (A) (m, - m,) g/(m, + m,) (B) (m, - m, sin 0) g/(m, + m,) (C) (m, - m, cos 0) g/(m, + m,) (D) 8 1 1. A person is pulling a block of mass m with a force equal to its weight directed 30 above the horizontal plane across a rough surface, generating a friction f, on the block. If the person is now pushing downward on the block with the same force 30 below the horizontal plane 13. If a roller coaster cart of mass m was not attached to across the same rough surface, what is the friction on the the track, it would still remain in contact with a track block? (H, is the coefficient of kinetic friction across the throughout a loop of radius r as long as surface.) (A) ve V(rg) (A) f (B) 1.5f (B) v2 V(rg) (C) 26 C) vey(rgim) (D) 3f (D) v2 (rg/m)16. A sphere starts from rest atop a hill with a constant angle of inclination and is allowed to roll without slipping down the hill. What force provides the torque that causes the sphere to rotate? (A) Static friction (B) Kinetic friction (C) The normal force of the hill on the sphere (D) Gravity 14. The diagram above shows a top view of an object of mass M on a circular platform of mass 2M that is rotating counterclockwise. Assume the platform rotates without friction. Which of the following best describes an action by the object that will increase the angular speed of the entire system? (A) The object moves toward the center of the platform, increasing the total angular momentum of the system. 17. Which of the following correctly describes the motion of B) The object moves toward the center of the platform, a real object in free fall? Assume that the object experi- decreasing the rotational inertia of the system. ences drag force proportional to speed and that it strikes C) The object moves away from the center of the the ground before reaching terminal speed. platform, increasing the total angular momentum (A) It will fall with increasing speed and increasing of the system. acceleration. (D) The object moves away from the center of the (B) It will fall with increasing speed and decreasing platform, decreasing the rotational inertia of the acceleration. system. (C) It will fall with decreasing speed and increasing acceleration. (D) It will fall with decreasing speed and decreasing Moon acceleration. Planet 18. Which of the following concerning uniform circular motion is true? (A) The centrifugal force is the action/reaction pair of the centripetal force. (B) The centripetal acceleration and velocity point in the 15. A moon has an elliptical orbit about the planet as same direction. shown above. The moon's mass is much smaller than (C) The velocity of the object in motion changes, the planet's. Which of the following quantities is/are whereas the acceleration of the object is constant. (approximately) conserved as the moon moves from (D) A satellite undergoing uniform circular motion is point A to point B ? falling toward the center even though its path is circular. I. The moon's mechanical energy II. The moon's angular momentum III. The moon's (linear) momentum (A) I and II only B) I and III only C) II and III only (D) I, II, and III2 21 19. A girl of mass m and a boy of mass 2m are sitting on opposite sides of a lightweight seesaw with its fulcrum 21. A wooden block experiences a frictional force, F, as in the center. Right now, the boy and girl are equally far it slides across a table. If a block of the same material from the fulcrum, and it tilts in favor of the boy. Which with half the height and twice the length were to slide of the following would NOT be a possible method to bal- across the table in the same direction. what would be the ance the seesaw? frictional force it experienced? (A) Move the boy to half his original distance from the (A) (1/2)F fulcrum. (B) F (B) Move the girl to double her original distance from (C) 2F the fulcrum. (D) 4F (C) Allow a second girl of mass in to join the first. D) Move the fulcrum to half its original distance from the boy. Sun 22. Two objects, a sphere and a block of the same mass, are released from rest at the top of an inclined plane. The sphere rolls down the inclined plane without slipping. The block slides down the plane without friction. Which object reaches the bottom of the ramp first? (A) The sphere, because it gains rotational kinetic energy, but the block does not B) The sphere, because it gains mechanical energy due to the torque exerted on it, but the block does not 20. Earth's orbit around the Sun can be approximated as a (C) The block, because it does not lose mechanical circle. Given that the Earth's mass is m, its tangential energy due to friction, but the sphere does speed as it revolves around the Sun is v, and the distance (D) The block, because it does not gain rotational from the Sun to the Earth is r, which of the following cor- kinetic energy, but the sphere does rectly describes the work done by the centripetal force, W , in one year's time? (A) W > 2n(mv/r) (B) W. = 21(mv /r) (C) W Fradial collision will be B) FZF (A) double the magnitude and in the same direction (C) F, = F radial B) double the magnitude and in the opposite direction (D) FF did C) half the magnitude and in the same direction (D) half the magnitude and in the opposite direction34. The Gravitron is a carnival ride that looks like a large 37. A flute supports standing waves with pressure nodes at cylinder. People stand inside the cylinder against the wall each end. The lowest note a flute can play is 261.63 Hz. as it begins to spin. Eventually, it is rotating fast enough What is the approximate length of the flute? (speed of that the floor can be removed without anyone falling. sound in air = 343 m/s) Given that the coefficient of friction between a person's (A) 32.8 cm clothing and the wall is , the tangential speed is v, and (B) 65.6 cm the radius of the ride is r, what is greatest mass that a (C) 76.3 cm person can be to safely go on this ride? D) 131 cm (A) w/(rg) (B) rv/(ug) 38. You are standing on a railroad track as a train approaches (C) rel(uva) at a constant velocity. Suddenly the engineer sees you, (D) None of the above applies the brakes, and sounds the whistle. Which of the following describes the sound of the whistle while the 35. In a spring-block oscillator, the maximum speed of the train is slowing down, as you hear it? block is (A) Loudness increasing, pitch increasing B) Loudness increasing, pitch constant (A) proportional to amplitude C) Loudness decreasing, pitch increasing (B) proportional to the square of amplitude D) Loudness increasing, pitch decreasing C) proportional to the square root of amplitude (D) inversely proportional to the square root of amplitude 36. A student is experimenting with a simple spring-block oscillator of spring constant & and amplitude A. The block attached to the spring has a mass of M. If the student places a small block of mass m on top of the original block, which of the following is true? (A) The small block is most likely to slide off when the original block is at maximum displacement from the equilibrium position, but will not slide off as long as the coefficient of static friction between the blocks is greater than kA/[(M+m)g]. (B) The small block is most likely to slide off when the original block is at the equilibrium position, but will not slide off as long as the coefficient of static friction between the blocks is greater than KA/[(M+m)g]. (C) The small block is most likely to slide off when the original block is at maximum displacement from the equilibrium position, but will not slide off as long as the coefficient of static friction between the blocks is greater than (M+m)g/(kA). D) The small block is most likely to slide off when the original block is at the equilibrium position, but will not slide off as long as the coefficient of static friction between the blocks is greater than (M+m)g/(kA).Questions 39-41 refer to the following figure: Voltage (V) R, MA + + Time (s) 42. A circuit consists of a 500 ? resistor connected to a vari- able voltage source. The voltage is increased linearly from 0 V to 5 V over a period of 20 s, as shown in the graph 39. Determine the total power dissipated through the circuit above. Which of the following graphs corresponds to the shown above in terms of V, R,, R, and R. power dissipated by the resistor as a function of time? Power (W) V/2 (A) 0.01+ R + R, + R, (A) (B) R + R, + R; 1/2 R (R, + R, ) + + Time (s) (C) 20 V' ( R, + R, + R, ) (D) V ( R, + R, + R, ) Power (W) R, ( R, + R, ) 0.05 40. If V = 100 V, R, = 50 0. R, = 80 0, and R, = 120 0. (B) determine the voltage across R- (A) 100 V B) 60 V C) 40 V + + Time (s) 0 20 (D) 20 V Power (W] 41. If R, were to burn out, the current coming out from the 0.01 battery would (C) (A) increase B) decrease stay the same D) There is no current, because the circuit is now OL + + Time (s) incomplete. 0 20 Power (W) 0.05- (D) 20 + Time (s)10 0 --- 20 0 50 + 9 43. A Wheatstone bridge (diagram above) is a configuration of resistors and a sensitive current meter, called a gal- 45. In the figure above, four charges are arranged. If the vanometer, that is used to determine the resistance of an unknown resistor. In the Wheatstone bridge shown here, magnitudes of all the charges q are all the same and the find the value of R, such that the current through galva- distance / between them is as shown above, what is the nometer G is zero. (A) 25 0 magnitude of the net force on the bottom right charge in (B) 150 terms of q, r, and k (where k = - (C) 10 0 (D) 2.50 (A) * =(1 + 2V2) 44. What happens to the electric force between two point charges if the magnitude of both charges is doubled, and the distance between them is halved? (1 + 2V2) (A) The force is halved (B) The force remains the same. C) The force is quadrupled. (D) The force increases by a factor of 16. (D) *2 Directions: For each of the questions 46-50, two of the sug- gested answers will be correct. Select the two answers that are best in each case, and then fill in both of the corresponding circles on the answer sheet. 46. An object traveling at x m/s can stop at a distance d m with a maximum negative acceleration. If the car is traveling at 2x m/s, which of the following statements are true? Select two answers. (A) The stopping time is doubled. (B) The stopping time is quadrupled. The stopping distance is doubled. (D) The stopping distance is quadrupled.10 = 50 2 R 49. Which of the following will decrease the current through R in the circuit above? Select two answers. 47. A 2 kg mass is attached to a massless, 0.5 m string and is used as a simple pendulum by extending it to an (A) A decrease in R, angle 0 = 50 and allowing it to oscillate. Which of the (B) An increase in R, following changes will change the period of the pendu- (C) An increase in R2 lum? Select two answers. (D) An increase in R, (A) Replacing the mass with a l kg mass (B) Changing the initial extension of the pendulum to a 50. A sound wave travels through a metal rod with wave- 10 angle length ) and frequency f. Which of the following are (C) Replacing the string with a 0.25 m string true? Select two answers. (D) Moving the pendulum to the surface of the Moon (A) When this sound wave passes into air, the frequency will change. 48. N resistors (N > 2) are connected in parallel with a battery (B) When this sound wave passes into air, the of voltage V . If one of the resistors is removed from the wavelength will change. circuit, which of the following quantities will decrease? (C) While in the metal rod, the A and frequency f have a Select two answers. direct relationship. (D) While in the metal rod, the A and frequency f have (A) The voltage across any of the remaining resistors an inverse relationship. (B) The current output by the battery (C) The total power dissipated in the circuit (D) The voltage supplied by the battery