洋桃课堂【AP物理C】【真题】解答题C2004

2004 AP® PHYSICS C: MECHANICS FREE-RESPONSE QUESTIONS AP® Physics C 2004 Free Response Questions The materials included in these files are intended for noncommercial use by AP teachers for course and exam preparation; permission for any other use must be sought from the Advanced Placement Program®. Teachers may reproduce them, in whole or in part, in limited quantities, for face-to-face teaching purposes but may not mass distribute the materials, electronically or otherwise. This permission does not apply to any third-party copyrights contained herein. These materials and any copies made of them may not be resold, and the copyright notices must be retained as they appear here. The College Board is a nonprofit membership association whose mission is to connect students to college success and opportunity. Founded in 1900, the association is composed of more than 4,500 schools, colleges, universities, and other educational organizations. Each year, the College Board serves over three million students and their parents, 23,000 high schools, and 3,500 colleges, through major programs and services in college admissions, guidance, assessment, financial aid, enrollment, and teaching and learning. Among its best-known programs are the SAT®, the PSAT/NMSQT®, and the Advanced Placement Program® (AP®). The College Board is committed to the principles of equity and excellence, and that commitment is embodied in all of its programs, services, activities, and concerns. For further information, visit www.collegeboard.com College Board, Advanced Placement Program, AP, SAT, and the acorn logo are registered trademarks of the College Entrance Examination Board. 2004M1. A rope of length L is attached to a support at point C. A person of mass m1 sits on a ledge at position A holding the other end of the rope so that it is horizontal and taut, as shown above. The person then drops off the ledge and swings down on the rope toward position B on a lower ledge where an object of mass m2 is at rest. At position B the person grabs hold of the object and simultaneously lets go of the rope. The person and object then land together in the lake at point D, which is a vertical distance L below position B. Air resistance and the mass of the rope are negligible. Derive expressions for each of the following in terms of m1, m2, L, and g. a. The speed of the person just before the collision with the object b. The tension in the rope just before the collision with the object c. The speed of the person and object just after the collision d. The ratio of the kinetic energy of the person‑object system before the collision to the kinetic energy after the collision e. The total horizontal displacement x of the person from position A until the person and object land in the water at point D. 2004M2. A solid disk of unknown mass and known radius R is used as a pulley in a lab experiment, as shown above. A small block of mass m is attached to a string, the other end of which is attached to the pulley and wrapped around it several times. The block of mass m is released from rest and takes a time t to fall the distance D to the floor. a. Calculate the linear acceleration a of the falling block in terms of the given quantities. b. The time t is measured for various heights D and the data are recorded in the following table. i. What quantities should be graphed in order to best determine the acceleration of the block? Explain your reasoning. ii. On the grid below, plot the quantities determined in (b) i., label the axes, and draw the best‑fit line to the data. iii. Use your graph to calculate the magnitude of the acceleration. c. Calculate the rotational inertia of the pulley in terms of m, R, a, and fundamental constants. d. The value of acceleration found in (b)iii, along with numerical values for the given quantities and your answer to (c), can be used to determine the rotational inertia of the pulley. The pulley is removed from its support and its rotational inertia is found to be greater than this value. Give one explanation for this discrepancy. 2004M3. A uniform rod of mass M and length L is attached to a pivot of negligible friction as shown above. The pivot is located at a distance L/3 from the left end of the rod. Express all answers in terms of the given quantities and fundamental constants. a. Calculate the rotational inertia of the rod about the pivot. b. The rod is then released from rest from the horizontal position shown above. Calculate the linear speed of the bottom end of the rod when the rod passes through the vertical. c. The rod is brought to rest in the vertical position shown above and hangs freely. It is then displaced slightly from this position. Calculate the period of oscillation as it swings. 2004E1. The figure above left shows a hollow, infinite, cylindrical, uncharged conducting shell of inner radius r1 and outer radius r2. An infinite line charge of linear charge density +λ is parallel to its axis but off center. An enlarged cross section of the cylindrical shell is shown above right. a. On the cross section above right, i. sketch the electric field lines, if any, in each of regions I, II, and III and ii. use + and ‑ signs to indicate any charge induced on the conductor. b. In the spaces below, rank the electric potentials at points a, b, c, d, and e from highest to lowest (1 = highest potential). If two points are at the same potential, give them the same number. ____Va ____Vb ____Vc‑ ____Vd ____Ve c. The shell is replaced by another cylindrical shell that has the same dimensions but is nonconducting and carries a uniform volume charge density +ρ. The infinite line charge, still of charge density +λ, is located at the center of the shell as shown above. Using Gauss's law, calculate the magnitude of the electric field as a function of the distance r from the center of the shell for each of the following regions. Express your answers in terms of the given quantities and fundamental constants. i. r < rl ii. rl ≤ r ≤ r2 iii. r > r2 2004E2. In the circuit shown above left, the switch S is initially in the open position and the capacitor C is initially uncharged. A voltage probe and a computer (not shown) are used to measure the potential difference across the capacitor as a function of time after the switch is closed. The graph produced by the computer is shown above right. The battery has an emf of 20 V and negligible internal resistance. Resistor R1 has a resistance of 15 kΩ and the capacitor C has a capacitance of 20 μF. a. Determine the voltage across resistor R2 immediately after the switch is closed. b. Determine the voltage across resistor R2 a long time after the switch is closed. c. Calculate the value of the resistor R2. d. Calculate the energy stored in the capacitor a long time after the switch is closed. e. On the axes below, graph the current in R2 as a function of time from 0 to 15 s. Label the vertical axis with appropriate values. Resistor R2 is removed and replaced with another resistor of lesser resistance. Switch S remains closed for a long time. (f) Indicate below whether the energy stored in the capacitor is greater than, less than, or the same as it was with resistor R2 in the circuit. _____Greater than _____Less than _____The same as Explain your reasoning. 2004E3. A rectangular loop of dimensions 3 ℓ and 4 ℓ lies in the plane of the page as shown above. A long straight wire also in the plane of the page carries a current I. a. Calculate the magnetic flux through the rectangular loop in terms of I, ℓ , and fundamental constants. Starting at time t = 0, the current in the long straight wire is given as a function of time t by I (t) = I0e‑kt , where I0 and k are constants. b. The current induced in the loop is in which direction? ____Clockwise ____Counterclockwise Justify your answer. The loop has a resistance R. Calculate each of the following in terms of R, I0 , k, ℓ , and fundamental constants. c. The current in the loop as a function of time t d. The total energy dissipated in the loop from t = 0 to t =∞