MECH + E&M - 1983

MECH + E&M - 1983 - The College Board Advanced...

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Unformatted text preview: The College Board Advanced Placement Examination PHYSICS C SECTION II, MECHANICS Mech. l. A particle moves along the parabola with equation y = %x2 shown below. .1" 0 (a) Suppose the particle moves so that the x—component of its velocity has the constant value vx = C; that is, x = Ct. i. On the diagram above, indicate the directions of the particle‘s velocity vector v and acceleration vector at at point R, and label each vector. ii. Determine the y—component of the particle’s velocity as a function of x. iii. Determine the y-eomponent of the particle’s acceleration. (b) Suppose, instead, that the particle moves along the same parabola with a velocity whose x—component C W ' i. Show that the particle's speed is constant in this case. ii. On the diagram below, indicate the directions of the particle’s velocity vector v and acceleration vector in at point S, and label each vector. State the reasons for your choices. is given by v).r = J’ [ill UN ll] iHE NEXT PAGE Copyright © 1983 by Educational Testing Service. All rights reserved. Princeton, NJ. 0854! Mech. 2. A uniform solid cylinder of mass m1 and radius R is mounted on frictionless bearings about a fixed axis through 0. The moment of inertia ofthe cylinder about the axis is I: %m1R2. A block of mass m2, suspended by a cord wrapped around the cylinder as shown above, is released at time t = 0. (a) On the diagram below draw and identify all of the forces acting on the cylinder and on the block. D (b) In terms of m1, m2, R, and g, determine each of the following. i. The acceleration of the block ii. The tension in the cord iii. The angular momentum of the disk as a function of time t Mech. 3. A particle of mass m slides down a fixed, frictionless sphere of radius R, Starting from rest at the top. (a) In terms of m, g, R, and 0, determine each of the following for the particle while it is sliding on the sphere. i. The kinetic energy of the particle ii. The centripetal acceleration of the mass iii. The tangential acceleration of the mass (b) Determine the value of 6 at which the particle leaves the sphere. END OF SECTION II, MECHANICS PHYSICS C SECTION II, ELECTRICITY AND MAGNETISM Time *45 minutes ‘ B E&M 1. Two concentric, conducting spherical shells, A and B, have radii a and b, respectively, (a<b). Shell 3 is grounded, whereas shell A is maintained at a positive potential V0. (a) Using Gauss‘s law, develop an expression for the magnitude E of the electric field at a distance r from the center of the shells in the region between the shells. Express your answer in terms of the charge Q on the inner shell. (b) By evaluating an appropriate integral, develop an expression for the potential ViJ in terms of Q. a. and b. (c) Develop an expression for the capacitance of the system in terms of a and b. C it!) 2 x1060 O—H E E&M 2. The series circuit shown above contains a resistance R = 2 X [0‘5 ohms, a capacitor of unknown capacitance C, and a battery of unknown emf E and negligible internal resistance. Initially the capacitor is uncharged and the switch S is open. At time I: 0 the switch S is closed. For t> 0 the current in the circuit is described by the equation: in) = 1'09"”, where in = [0 microamperes and t is in seconds. (a) Determine the emf of the battery. (b) By evaluating an appropriate integral, develop an expression for the charge on the right-hand plate of the capacitor as a function of time for t> 0. (c) On the axes below sketch a graph of the charge Q on the capacitor as a function of time i. Q Qmax GU UN Tl] THE NEXT PAGE (d) Determine the capacitance C. E&M 3. (a) A long straight wire carries current 1 into the plane of the page as shown above. Using Ampere’s law, develop an expression for the magnetic field intensity at a point M that is a distance R from the center of the wire. On the diagram above indicate your path of integration and indicate the direction of the field at point M. (b) Two long parallel wires that are a distance 20 apart carry equal currents 1 into the plane of the page as shown above. i. Determine the resultant magnetic field intensity at the point 0 midway between the wires. ii. Develop an expression for the resultant magnetic field intensity at the point N, which is a vertical distance of y above point 0. On the diagram above indicate the direction of the resultant magnetic field at point N. END OF SECTION II, ELECTRICITY AND MAGNETISM ...
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This note was uploaded on 02/19/2011 for the course PHYS 102 taught by Professor Allen during the Spring '11 term at Northwestern IA.

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MECH + E&M - 1983 - The College Board Advanced...

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