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Physics 221 – Spring 2007 – Final Exam PHYSICS 221 Spring 2007 FINAL EXAM: May 1st 2007 4:30pm—6:30pm Name (printed): ____________________________________________ ID Number: ______________________________________________ Section Number: __________________________________________ INSTRUCTIONS: Each question is of equal weight, answer all questions. All questions are multiple choice. Choose the best answer to each question. Before turning over this page, put away all materials except for pens, pencils, erasers, rulers, your calculator and “aid sheet”. An “aid sheet” is one two sided 8½×11 page of notes prepared by the student. There is also a list of possibly useful equations at the end of the exam. "In general, any calculator, including calculators that perform graphing numerical analysis functions, is permitted. Electronic devices that can store large amounts of text, data or equations are NOT permitted." If you are unsure whether or not your calculator is allowed for the exam ask your TA. Examples of allowed calculators: Texas Instruments TI-30XII/83/83+/89, 92+ Casio FX115/250HCS/260/7400G/FX7400GPlus/FX9750 Sharp EL9900C. Examples of electronic devices that are not permitted: Any laptop, palmtop, pocket computer, PDA or e-book reader. In marking the multiple-choice bubble sheet use a number 2 pencil. Do NOT use ink. If you did not bring a pencil, ask for one. Fill in your last name, middle initial, and first name. Your ID is the middle 9 digits on your ISU card. Special codes K to L are your recitation section; for the Honors sections please encode your section number as follows: H1⇒02; H2⇒13 and H3⇒25. If you need to change any entry, you must completely erase your previous entry. Also, circle your answers on this exam. Before handing in your exam, be sure that your answers on your bubble sheet are what you intend them to be. It is strongly suggested that you circle your choices on the question sheet. You may also copy down your answers on a piece of paper to take with you and compare with the posted answers. You may use the table at the end of the exam for this. When you are finished with the exam, place all exam materials, including the bubble sheet, and the exam itself, in your folder and return the folder to your recitation instructor. No cell phone calls allowed. Either turn off your cell phone or leave it at home. Anyone answering a cell phone must hand in their work; their exam is over. Total number of questions is 28 but score will be out of 27 (so one question is “extra credit”). Questions are numbered 56-83. Best of luck, David Atwood and Paula Herrera-Siklody Physics 221 – Spring 2007 – Final Exam Neglect air resistance in all problems. 56. The acceleration of a particle constrained to move along the x-axis is ax = 4.0 m/s 4 t 2 . At t = 0, the particle is at x = 0 and its velocity is −3.0 m/s. ( ) Where is the particle at t = 3.0 s? (A) (B) (C) (D) (E) x = 18 m x = 30 m x = 96 m x = 150 m x = 320 m 57. You want to kick a ball into your neighbor’s yard, over the 2.0-m high fence. The ball leaves the ground at 8.0 m/s and just barely clears the fence when it is at the top of its trajectory. At what angle was the ball moving relative to the horizontal right after the kick? (A) (B) (C) (D) (E) 22° 38° 44° 52° 63° Physics 221 – Spring 2007 – Final Exam 58. A coin is placed near the edge of a turntable with radius 30 cm. The turntable makes 20 turns in one minute. What is the minimum coefficient of static friction needed to ensure that the coin moves along with the turntable? (A) (B) (C) (D) (E) 0.13 0.42 0.51 0.70 0.82 59. Two blocks 1 and 2 (m1 = 4m2) on an incline are connected through an ideal, massless string that goes through an ideal, massless pulley as shown in the figure. The incline makes an angle of 30° with the horizontal. The blocks are released from rest and there is no friction between the blocks or between block 1 and the incline. 2 1 30° Find the acceleration of block 1 right after it is released. (A) (B) (C) (D) (E) 0 2.9 m/s2 5.9 m/s2 7.4 m/s2 9.8 m/s2 Physics 221 – Spring 2007 – Final Exam 60. A 100g ball is launched vertically using a spring as shown below. The spring is compressed by 10cm from its relaxed length so that the ball is at ground level. The ball rises to a maximum height of 1m. What is the force constant, k, of the spring? 1m 100g (A) 49 N/m (B) 98N/m (C) 196 N/m (D) 392 N/m (E) 588 N/m 10 cm Physics 221 – Spring 2007 – Final Exam 61. Consider the two situations depicted below where a block is attached to an ideal string which winds around the given pulley without slipping. In both cases the mass of the pulley is m, but the blocks have different masses m and M (see figure). The blocks accelerate downwards at the same rate in both cases. What is the ratio M:m? Solid uniform disk of Hoop of mass m (all mass mass m concentrated on rim) (A) 3:1 (B) 2:1 (C) 1:1 (D) 1:2 (E) 1:3 m M 62. Two particles of masses m1 and m2 = 4m1 head toward each other along the x axis with velocities v1x = 30 m/s and v2x = –10 m/s. The particles collide elastically. What is the speed of particle 1 right after the collision? (A) 0 (B) 6.0 m/s (C) 10 m/s (D) 25 m/s (E) 34 m/s Physics 221 – Spring 2007 – Final Exam 63. John wants to ride a jet ski across a river that is 1.0-km wide and flows from north to south at a rate of 5.0 km/h. Starting at point A on the west bank he would like to drive his jet ski in a straight line to point B due east of point A. If the jet ski can move at a speed of 10 km/h with respect to the water, how long does it take to cross the river? (A) (B) (C) (D) (E) 0.013 hours 0.089 hours 0.10 hours 0.12 hours 0.20 hours 5.0 km/h A John's trajectory B 64. A uniform sphere of mass 5M and radius R is glued to a uniform rod of mass 3M and length 2R. The rod is perpendicular to the surface of the sphere. The system rotates about axis P, which is perpendicular to the page through a point in the surface of the sphere (see figure). What is the moment of inertia of this rigid body for this axis? (A) 3MR 2 (B) 6MR 2 (C) 8MR 2 (D) 11MR 2 (E) 35MR 2 P R 5M 2R 3M Physics 221 – Spring 2007 – Final Exam 65. The graph below shows a position-dependent net force acting on a 1.0-kg block moving along the x-axis. Initially the block is at x = 0 m, moving in the +x direction. When it reaches 8.0 m, it has a kinetic energy of 30 J. What was the initial kinetic energy of the block? (A) 12 J (B) 18 J (C) 24 J (D) 36 J (E) 48 J Net Force 3N 2N 1N 1m 2m 3m 4m 5m 6m 7m 8m x Physics 221 – Spring 2007 – Final Exam 66. A uniform plank of length 4.0 m and mass 4.0 kg is placed on the edge of a table with 75% of its length on the table. We want to place a 6.0 kg cube of side 1.0 m on the free end of the plank without tipping over the system. What is the maximum allowed value of d? 1.0 m d? 6.0 kg 4.0 kg 4.0 m (A) (B) (C) (D) (E) 1.0 m 0.052 m 0.17 0.33 0.67 The system tips over for any (positive) value of d. 67. A 1.0-kg particle attached to a spring with k = 400 N/m oscillates with simple harmonic motion along the x axis. As it passes the equilibrium position, the velocity of the particle is vx = 2.0 m/s. What is the position of the particle 2.0 s after? (A) (B) (C) (D) (E) x = –6.7 cm x = –3.2 cm x = +1.2 cm x = +7.5 cm x = +10 cm Physics 221 – Spring 2007 – Final Exam 68. The solar system of the Ugly Star (mass 1030 kg) has two planets, 1 and 2, that have circular orbits of radii r1 = 1011 m and r2 = 2 r1. A 1000-kg spacecraft is to be sent from planet 1 to planet 2. The spacecraft leaves planet 1 when this is in the position shown in the figure, and reaches planet 2 on the other side of the star, traveling along the trajectory shown in the figure below. Note that the velocity vector of the spacecraft is parallel to the velocity vector of planet 1 at launch and parallel to the velocity vector of planet 2 on arrival. Planet 1 (position upon launching) Ugly Star spacecraft How long will the spacecraft trip take? (A) (B) (C) (D) (E) 700 hours 2650 hours 6200 hours 11200 hours 23900 hours Planet 2 (position upon spacecraft arrival) Physics 221 – Spring 2007 – Final Exam The situation below refers to the next two questions: Two charges are fixed at the positions shown below. y Q1 = 3.0μC Q2 = −3.0μC Q1 Q2 x x = 3.0 cm 69. Find the force on Q1 by Q2. (A) (B) (C) (D) (E) 3.0 ×107 i N −3.0 × 107 i N 90i N −90i N None of the above 70. Determine the y-component of the total electric field at point (x, y) = (0, 3.0 cm). (A) (B) (C) (D) (E) Ey = 0 Ey = 1.2 × 107 N/C Ey = 1.5 × 107 N/C Ey = 1.7 × 107 N/C Ey = 1.9 × 107 N/C Physics 221 – Spring 2007 – Final Exam 71. Shown below are four conducting spheres, each with a total charge Q. Point P is in each case at the same distance from the center of the sphere. In cases 1 and 2, point P is outside the spheres. In cases 3 and 4, it is inside the spheres. (Each sphere is to be considered an isolated system, very far from any other charged object) 4 3 2 1 P P P P Rank the magnitude of the electric field at point P in each case. (A) (B) (C) (D) (E) E1 = E2 = E3 = E4 E1 < E2 = E3 = E4 E1 < E2 < E3 < E4 E1 = E2 > E4 > E3 E1 = E2 > E3 = E4 72. A sphere of radius R has a charge Q uniformly distributed throughout its volume. Consider an imaginary sphere of radius R/2 with center located at distance R/2 from the real sphere (see figure). What is the electric flux through the imaginary sphere? (A) 0 Q (B) ε0 Q 2ε 0 Q (D) 4ε 0 Q (E) 8ε 0 (C) R/2 R R/2 Physics 221 – Spring 2007 – Final Exam 73. Two very thin surfaces with equal uniform charge density σ = +8.85 nC/m2 are placed parallel to the yz axes, at x1 = 0 and at x2 = 2.0 cm, respectively. If we take the electric potential to be zero at x = 0, what is the electric potential at x = 6.0 cm? (A) (B) (C) (D) (E) 0V −60 V 60 V −40 V 40 V 74. The figure below shows the electric field lines produced by an electric dipole. Compare the electric potential at points A, B and C. B A (A) (B) (C) (D) (E) VB < VA < VC VA = VB < VC VB < VC < VA VA > VB = VC VA < VB = VC C Physics 221 – Spring 2007 – Final Exam 75. Three capacitors are connected to an ideal battery as shown below. When the capacitors are all fully charged, a dielectric with κ > 1 is inserted between the plates of capacitor C2. Due to this, and compared with the values before the dielectric was inserted, the charge in C1 __________________ and the charge in C3 __________________ . C2 V0 C1 C3 (A) decreases, decreases (B) decreases, remains the same (C) increases, remains the same (D) remains the same, increases (E) remains the same, decreases 76. An electric dipole made of two charges ± 3.0 ×10−18 C separated a distance 1.0 ×10−6 m is placed between the plates of a parallel plate capacitor that is connected to a 9.0-V battery. The plates of the capacitor have an area of 400 m2 and are separated by an air-filled gap 0.10 mm wide. The dipole moment makes an angle of 60° with the plates of the capacitor. Determine the magnitude of the torque on the dipole. (A) 0 (B) 4.1×10−20 Nm (C) 8.2×10−20 Nm (D) 1.4×10−19 Nm (E) 2.7×10−19 Nm Physics 221 – Spring 2007 – Final Exam The situation below refers to the next two questions: An ideal battery and four resistors are connected as shown below. All wires are ideal. The ideal ammeter reads 0.40 A. R1 = 10 Ω R2 = 20 Ω R3 = 30 Ω R4 = 40 Ω R2 R1 R3 A R4 V0 77. Find the equivalent resistance of the circuit. (A) (B) (C) (D) (E) 6.7 Ω 17 Ω 26 Ω 55 Ω 100 Ω 78. Determine the power dissipated in resistor R3. (A) (B) (C) (D) (E) 1.2 W 3.1 W 4.8 W 8.8 W 16 W Physics 221 – Spring 2007 – Final Exam 79. In the circuit below, all resistors are 10 Ω and all batteries are 10 V. The wires and the battery are ideal. Determine the current through the central wire. (A) (B) (C) (D) (E) 0.33 A 0.67 A 1.0 A 1.3 A 2.0 A Physics 221 – Spring 2007 – Final Exam Laboratory Final 80. Consider the motion of a cart like the one you used in lab, and which is adjusted to have significant frictional drag. Assume that the friction is well described by the "laws" of (dry) friction that you studied this semester. Also assume that the cart is given an initial velocity toward the left on the horizontal track and then released. (Assume the sensor gives positions relative to the X axis illustrated in the figure). X 0 Which of the following best illustrates the acceleration, aX, versus time of the cart during the same time interval? ax ax ax t 0 A ax t B ax t C t D 81. Consider a hollow metal sphere mounted on a thin insulating rod. Using standard apparatus (e.g., an electrophorus), the largest possible electric charge is placed on the sphere. Where is the electric field largest, and for a sphere of a given size, what factor determines the magnitude of the maximum charge? location where electric field is largest A B C D E center of sphere surface of sphere surface of sphere center of sphere none of the above factor that determines the magnitude of the maximum charge dielectric strength of air type of metal dielectric strength of air type of metal t E Physics 221 – Spring 2007 – Final Exam 82. Using the rotating wheel apparatus such as you used in lab, a disk (which is not spinning) is dropped concentrically upon the wheel as it is rotating freely. Assume that the disk has a moment of inertia of 0.5I0 , where I0 is the moment of inertia of the rotating wheel. Which of the following graphs best represents the angular velocity, ω, as a function of time before, during, and after the disk is dropped? ω A ω t B ω C t ω D t ω E t 83. Consider two air pucks (made of some unknown material) which can slide upon a smooth horizontal surface with little friction, leaving trails of spark marks, with marks produced at a fixed frequency. The pucks are of equal mass, and are pushed (and released) toward one another, and then collide. Assume that the pucks rotate little before and after the collision. For the record shown above, select the comment listed below which is most appropriate. (A) The data looks O.K., although the collision clearly is not elastic. (B) The data must be invalid since clearly momentum is not conserved. (C) The data must be invalid since the collision clearly is not elastic. (D) The data looks O.K.; both momentum and mechanical energy appear to be conserved. (E) One must know the time between sparks to make a definitive statement. NOTE: By the data being invalid is meant that, for the situation described, such data is impossible. To obtain such data, then some large extraneous factor must be at work (such as hidden magnets, angels, etc.) t Physics 221 – Spring 2007 – Final Exam You may record your answers on this page and take it with you after the exam to compare to the posted solutions. Solutions posted on WebCT about one hour after exam. 61 71 81 62 72 82 63 73 83 64 74 65 75 56 66 76 57 67 77 58 68 78 59 69 79 60 70 80