ࡱ> TG ,bjbjَ 'D]NNNNF t ND2r J(8D:D:D:D:D:D:D$EG^D-"^Dr R8DNN8DQ"?8Xb8D> 4XrNN C\Exam #2 Physics I Spring 2007 If you would like to get credit for having taken this exam, we need your name (printed clearly) at the top and section number below. Your name should be at the top of every page. Section # QuestionsValueScorePart A 40Part B 24Part C 36Total 100_____ 1 M/R 8-10 (Bedrosian) _____ 2 M/R 10-12 (Wilke) _____ 4 M/R 12-2 (Yamaguchi) _____ 5 M/R 2-4 (Yamaguchi) _____ 7 M/R 4-6 (Wilke) _____ 9 T/F 10-12 (Wetzel) _____ 10 T/F 10-12 (Washington) _____ 11 T/F 12-2 (Eah) _____ 12 T/F 2-4 (Eah) _____ 14 M/R 12-2 (Zhang) _____ 15 M/R 2-4 (Bedrosian) You may not unstaple this exam. Only work written on the same page as the question will be graded. Cheating on this exam will result in an F in the course. On this exam, please neglect any relativistic and/or quantum mechanical effects. If you dont know what those are, dont worry, we are neglecting them! On all multiple-choice questions, choose the best answers in the context of what we have learned in Physics I. On graphing and numerical questions, show all work to receive credit. Part A Multiple Choice 40 Points Total (10 at 4 Points Each) Write your choice(s) on the line to the left of the question number. ______ 1. Equation 26 on the Formula Sheet expresses Conservation of Mechanical Energy if and only if Non-conservative forces do no work. The net external force is zero. The change of kinetic energy equals the net work done. Objects collide and bounce off each other without sticking together. ______ 2. Comparing Equations 20 and 23 on the Formula Sheet, why was the subscript "cons" added to the force vector in Equation 23? Potential energy can only be defined for conservative forces. Potential energy can only be defined when the force is constant. Potential energy can only be defined when momentum is conserved. Adding subscripts to equations makes them look more impressive. ______ 3. Consider a coin glued to the outer edge of a rotating disk. We define the angle of rotation of the coin about the center of the disk, q, so that q = 0 at time t = 0 s. In order to use Equation 31 correctly to predict the rotation angle of the coin at a later time, it is necessary that The angular speed of the coin is constant. The linear speed of the coin is constant. The centripetal acceleration of the coin is constant. The tangential acceleration of the coin is constant. ______ 4. Consider a system consisting of two objects that collide. We define an origin of coordinates to measure their locations. In order for the angular momentum of the system about the origin to be conserved, it is necessary that The collision is elastic. The net external force on the system is zero. The net external torque on the system is zero. The total work done on the system by all non-conservative forces equals zero. Questions 5-10 refer to Tarzan swinging from a vine as shown in the figure to the right. In the initial position, A, Tarzan is beginning the swing to Jane (shown on the right) from rest at a height h above the lowest point of the swing. Point B is the lowest point of the swing. Assume the vine has a constant length, d, and negligible mass. Ignore air resistance.  The attachment point of the vine is the coordinate origin for calculating angular momentum and torque. ______ 5. During Tarzan's swing between A and B, which quantities below are conserved? Select all that apply or put "0" for none. Kinetic Energy of Tarzan. Potential Energy of Tarzan in gravity. Total Mechanical Energy of Tarzan. Angular Momentum of Tarzan. For questions 6-10, select from the following directions. To the right on the page. To the left on the page. Up on the page. Down on the page. Right and down on the page. Out of the page. Into the page. No direction; quantity = 0. ______ 6. When Tarzan is at point A (just starting from rest with his feet off the rock), what is the direction of his angular momentum? ______ 7. When Tarzan is at point A (just starting from rest with his feet off the rock), what is the direction of the total torque on him? ______ 8. When Tarzan is at point B (the lowest point), what is the direction of his angular momentum? ______ 9. When Tarzan is at point B (the lowest point), what is the direction of the total torque on him? ______ 10. Suppose Tarzan let go of the vine after reaching point B. In the instant after letting go, what would be the direction of Tarzan's angular momentum? B Graphing 24 Points An object of unknown mass starting with 1.0 J of kinetic energy moving in the +X direction moves in one dimension and is acted on by a net conservative force, from x = 0 to x = 10 cm. The graph of total potential energy (U) is shown below. Note that the curved portions of the potential energy graph are parabolas. Graph the kinetic energy (K) and net force acting on the object as functions of displacement (x). Make sure your plots clearly show: A. Any minimum or maximum points. B. Whether the graph segments are curved or straight. C. The values of K and net force (Fnet) at x = 0, 2, 4, 5, 6, 8, and 10 cm. Show all work, including what equations and/or principles of physics you are using. Note: You may not assume an arbitrary value for the objects mass to do this problem.  EMBED Zoner.Draw.Document  Problem C (36 Points) Ball on a Stick Please note that this is a multi-step problem leading to the final answer. While each step will be graded individually, you will want to double-check the earlier steps carefully. The final numerical answer to the problem has been provided so that you can check your work. We will be grading primarily on whether you are using correct equations and/or principles of physics. A ball on a stick begins at rest in position A, with the stick horizontal. The stick is free to rotate about a frictionless pivot at its center. In position B, the ball has moved to its lowest position vertically below the pivot. We want to find the angular momentum of the ball and stick in position B. The pivot point is the origin for calculating all angular quantities.  EMBED Zoner.Draw.Document  The mass of the stick is 3.75 kg and its total length is L = 4.0 m. Use I = 1/12 M L2 for the stick. The mass of the ball is 5.0 kg. Treat it as a point mass on the end of the stick. The system is the stick and the ball. Neglect air resistance and use g = 9.8 N/kg. C-1: Can you correctly use Conservation of Angular Momentum to solve this problem? Explain why or why not in one or a few complete sentences. (5 Points) C-2: Can you correctly use Conservation of Mechanical Energy to solve this problem? Explain why or why not in one or a few complete sentences. (5 Points) C-3: Calculate the rotational inertia of the system about the pivot point. (3 Points) C-4: Calculate the angular acceleration of the system in Position A. (5 Points) C-5: Calculate the angular acceleration of the system in Position B. (4 Points) C-6: Calculate the change in potential energy from Position A to Position B. (4 Points) C-7: Calculate the change in kinetic energy from Position A to Position B. (4 Points) C-8: Calculate the angular momentum of the system at Position B. (6 Points) Answer: 70 kg m2/s in Z direction. Important: Did you clearly show what equation(s) and/or principle(s) of physics you used? Did you include units for all of your numerical answers? For vector quantities, did you indicate both the magnitude and direction? Formula Sheet for Homework and Exams Page 1 of 2 1.  EMBED Equation.3  2.  EMBED Equation.3  3.  EMBED Equation.3  4.  EMBED Equation.3  5.  EMBED Equation.3  6.  EMBED Equation.3  7.  EMBED Equation.3  8.  EMBED Equation.3  9.  EMBED Equation.3  10.  EMBED Equation.3  11.  EMBED Equation.3  12.  EMBED Equation.3  13.  EMBED Equation.3  14.  EMBED Equation.3  15.  EMBED Equation.3  16.  EMBED Equation.3   EMBED Equation.3  17.  EMBED Equation.3  18.  EMBED Equation.3  19.  EMBED Equation.3  20.  EMBED Equation.3  21.  EMBED Equation.3  22.  EMBED Equation.3  23.  EMBED Equation.3  24.  EMBED Equation.3  25.  EMBED Equation.3  26.  EMBED Equation.3  27.  EMBED Equation.3  28.  EMBED Equation.3  29.  EMBED Equation.3  30.  EMBED Equation.3  31.  EMBED Equation.3  32.  EMBED Equation.3  33.  EMBED Equation.3  34.  EMBED Equation.3  35a.  EMBED Equation.3  35b.  EMBED Equation.3  36.  EMBED Equation.3  37.  EMBED Equation.3  38.  EMBED Equation.3  39.  EMBED Equation.3  40.  EMBED Equation.3  41.  EMBED Equation.3  42.  EMBED Equation.3  43.  EMBED Equation.3  44x.  EMBED Equation.3  44y.  EMBED Equation.3  44z.  EMBED Equation.3  45a.  EMBED Equation.3  45b.  EMBED Equation.3  Formula Sheet for Homework and Exams Page 2 of 2 46a.  EMBED Equation.3  46b.  EMBED Equation.3  47a.  EMBED Equation.3  47b.  EMBED Equation.3  48a.  EMBED Equation.3  48b.  EMBED Equation.3  49.  EMBED Equation.3  50.  EMBED Equation.3  51.  EMBED Equation.3  52.  EMBED Equation.3  53x.  EMBED Equation.3  53y.  EMBED Equation.3  53z.  EMBED Equation.3  54.  EMBED Equation.3  55.  EMBED Equation.3  Useful Constants (You can use the approximate values on exams.) 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