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MECH + E&M - 1990 - 1990 The College Board Advanced...

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Unformatted text preview: 1990 The College Board Advanced Placement Examination l atomic mass unit, Rest mass of the proton, Rest mass of the neutron, Rest mass of the electron. Magnitude of the electron charge, Avogadro’s number, Universal gas constant, Boltzmann‘s constant. Speed- of light. Planck‘s constant, 1 electron volt, Vacuum permittivity, Coulomb's law constant, Vacuum permeability, Magnetic constant, Acceleration due to gravity at the Earth's surface, Universal gravitational constant. 1 atmosphere pressure. I angstrom, ' l tesla. PHYSICS C SECTION [I TABLE OF INFORMATION 1 u = 1.66 x 10‘27 kilogram 1.67 x 10—27 kilogram m" = 1.67 x 10‘27 kilogram me = 9.11 X 10‘3l kilogram 1.60 X 10‘19 coulomb e g N9 = 6.02 x 1023 per mole R = 8.32 joules/(mole - K) k, = 1.38 X lO‘njoule/K c = 3.00 x It)“ meters/second h = 6.63 x l0'3‘joulevsecond = 4.14 x 10"5eV-second he = l.99 x l0‘25jouleometer = 1.24 X 10‘ eV-angstrom leV = 1.60 x l0"9joule so = 8.85 x 10’l2 coulome/(newton - meterz) k = 1/41re0 = 9.0 x 109 newtons-rneterzicoulornla2 p0 = 41: x 10'7 weber,‘(ampere - meter) k' = Me: = Ito/4r: = 10'7weber/(ampere - meter) 3 = 9.8 meters/second2 G = 6.67 X 10'” meter’Kkilog'ram -second2) 1 atm 1.0 X 105 newtons/meter2 = 1.0 x 105 pascals (Pa) IA = l X 10“" meter l T = l weber/meter2 The following conventions are used in this examination. 1. Unless otherwise stated, the frame of reference of any problem is assumed to be inertial. II. The direction of any electric current is the direction of flow of positive charge (conventional current). "I. For any isolated electric charge, the electric potential is defined as zero at an infinite distance from the charge. Copyright © 1990 by Educational Testing Service. All rights reserved. Princeton, NJ. 08541 PHYSICS C SECTION II, MECHANICS Timei45 minutes 3 Questions ANSWER ALL OF THE QUESTIONS. EACH OF THE THREE QUESTIONS HAS EQUAL WEIGHT, BUT THE PARTS WITHIN A QUESTION MAY NOT HAVE EQUAL WEIGHT. SHOW YOUR WORK. CREDIT FOR YOUR ANSWERS DEPENDS ON THE QUALITY OF YOUR EXPLANATIONS. V0 x=0 Mech. 1. An object of mass m moving along the x-axis with velocity v is slowed by a force F = —kv, where k is a constant. At time t = 0, the object has velocity v0 at position x = 0, as shown above. (a) What is the initial acceleration (magnitude and direction) produced by the resistance force?' (b) Derive an equation for the object’s velocity as a function of time t, and sketch this function on the axes below. Let a velocity directed to the right be considered positive. 1; “0 — [)0 (c) Derive an equation for the distance the object travels as a function of time t and sketch this function on the axes below. (d) Determine the distance the object travels from t = 0 to t = co. GU 8N Ill THE NEXT PAGE Mech. 2. A block of mass m slides up the incline shown above with an initial speed on in the position shown. (a) If the incline is frictionless, determine the maximum height H to which the block will rise, in terms of the given quantities and appropriate constants. (b) If the incline is rough with coefficient of sliding friction u, determine the maximum height to which the block will rise in terms of H and the given quantities. A thin hoop of mass m and radius R moves up the incline shown above with an initial speed no in the position shown. (c) If the incline is rough and the hoop rolls up the incline without slipping, determine the maximum height to which the hoop will rise in terms of H and the given quantities. (d) If the incline is frictionless, determine the maximum height to which the hoop will rise in terms of H and the given quantities. GD UN Tl] THE NEXT PAGE Mech. 3. A S-kilogram block is fastened to a vertical spring that has a spring constant of 1,000 newtons per meter. A 3-kilogram block rests on top of the S-kilogram block, as shown ab0ve. (a) When the blocks are at rest, how much is the spring compressed from its original length? The blocks are now pushed down and released so that they oscillate. (b) Determine the frequency of this oscillation. (c) Determine the magnitude of the maximum acceleration that the blocks can attain and still remain in contact at all times. (d) How far can the spring be compressed beyond the compression in part (a) without causing the blocks to exceed the acceleration value in part (c) ‘2 (e) Determine the maximum speed of the blocks if the spring is compressed the distance found in part (d): END OF SECTION II. MECHANICS PHYSICS C SECTION II, ELECTRICITY AND MAGNETISM Time—45 minutes 3 Questions ANSWER ALL OF THE QUESTIONS. EACH OF THE THREE QUESTIONS HAS EQUAL WEIGHT, BUT THE PARTS WITHIN A QUESTION MAY NOT HAVE EQUAL WEIGHT. SHOW YOUR WORK. CREDIT FOR YOUR ANSWERS DEPENDS ON THE QUALITY OF YOUR EXPLANATIONS. E & M 1. A sphere of radius R is surrounded by a concentric spherical shell of inner radius 2R and outer radius 3R, as shown above. The inner sphere is an insulator containing a net charge + Q distributed uniformly throughout its volume. The spherical shell is a conductor containing a net charge + (1, different from + Q. Use Gauss‘s law to determine the electric field for the following values for 'r, the distance from the center of the insulator. (a)0<r<R (b)R<r<2R (c) 2R<r<3R Determine the surface charge density (charge per unit area) on (d) the inside surface of the conducting shell; (e) the outside surface of the conducting shell. Gil UN If] IHE NEXT PAGE IBI I Regain in E & M 2. In the mass Spectrometer shown above, particles having a net charge + Q are accelerated from rest through a potential difference in Region I. They then move in a straight line through Region II, which contains a magnetic field B and an electric field E. Finally, the particles enter Region III, which contains only a magnetic field B, and move in a semicircular path of radius R before striking the detector. The magnetic fields in Regions II and III are uniform, have the same magnitude B, and are directed out of the page as shown. (a) In the figure above, indicate the direction of the electric field necessary for the particles to move in a straight line through Region II. In terms of any or all the quantities Q, B , E , and R, determine expressions for (b) the speed 1: of the charged particles as they enter Region III; (e) the mass m of the charged particles; ((1) the accelerating potential V in Region I; (e) the acceleration a of the particles in Region III; (f) the time I required for the particles to move along the semicircular path in Region III. 80 DN Ill THE NEXT PAGE XXXXX Battery Loop Box Mg E & M 3. A uniform magnetic field of magnitude B is horizontal and directed into the page in a rectangular region of space, as shown above. A light, rigid wire loop, with one side of width 92, has current I. The loop is supported by the magnetic field, and hangs vertically, as shown. The wire has resistance R and supports a box that holds a battery to which the wire loop is connected. The total mass of the box and its contents is M. (a) On the following diagram that represents the rigid wire loop, indicate the direction of the current I. The loop remains at rest. In terms of any or all of the quantities B, 9., M , R, and appropriate constants, determine expressions for (b) the current I in the loop; (6) the emf of the battery, assuming it has negligible internal resistance. An amount of mass Am is removed from the box and the loop then moves upward, reaching a terminal speed 0 in a very short time, before the box reaches the field region. In terms of v and any or all of the original variables, determine expressions for (d) the magnitude of the induced emf; (e) the current 1’ in the loop under these new conditions; (f) the amount of mass Am removed. END OF SECTION II, ELECTRICITY AND MAGNETISM ...
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