AP物理C解答题 C1988

AP? Physics C

1988 Free response Questions

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1988M1. A highway curve that has a radius of curvature of 100 meters is banked at an angle of 15° as shown above.

a. Determine the vehicle speed for which this curve is appropriate if there is no friction between the road

and the tires of the vehicle.

On a dry day when friction is present, an automobile successfully negotiates the curve at a speed of 25 m/s.

b. On the diagram below, in which the block represents the automobile, draw and label all of the forces on

the automobile.

c. Determine the minimum value of the coefficient of friction necessary to keep this automobile from

sliding as it goes around the curve.

Copyright ? 1988 by College Entrance Examination Board. All rights reserved.

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1988M2. A 5-kilogram object initially slides with speed vo in a hollow frictionless pipe. The end of the pipe contains two springs. one nested inside the other, as shown above. The object makes contact with the inner spring at point A, moves 0.1 meter to make contact with the outer spring at point B, and then moves an additional 0.05 meter before coming to rest at point C. The graph shows the magnitude of the force exerted on the object by the springs as a function of the objects distance from point A. a. Calculate the spring constant for the inner spring.

b. Calculate the decrease in kinetic energy of the object as it moves from point A to point B.

c. Calculate the additional decrease in kinetic energy of the object as it moves from point B to point C. d. Calculate the initial speed vo of the object.

e. Calculate the spring constant of the outer spring.

1988M3. The two uniform disks shown above have equal mass, and each can rotate on frictionless bearings about a fixed axis through its center. The smaller disk has a radius R and moment of inertia I about its axis. The larger disk has a radius 2R

a. Determine the moment of inertia of the larger disk about its axis in terms of I.

The two disks are then linked as shown below by a light chain that cannot slip. They are at rest when, at time t = 0, a student applies a torque to the smaller disk, and it rotates counterclockwise with constant

angular acceleration ?. Assume that the mass of the chain and the tension in the lower part of the chain, are negligible. In terms of I, R, ?, and t, determine each of the following:

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b. c. d. e.

The angular acceleration of the larger disk The tension in the upper part of the chain

The torque that the student applied to the smaller disk

The rotational kinetic energy of the smaller disk as a function of time

1988E1. The isolated conducting solid sphere of radius a shown above is charged to a potential V. a. Determine the charge on the sphere.

Two conducting hemispherical shells of inner radius b are then brought up and, without contacting the solid sphere are connected to form a spherical shell surrounding and concentric with the solid sphere as shown below The outer shell is then grounded.

b. By means of Gauss's law, determine the electric field in the space between the solid sphere and the

shell at a distance r from the center.

c. Determine the potential of the solid sphere relative to ground.

d. Determine the capacitance of the system in terms of the given quantities and fundamental

constants.

P

1988E2. In the circuit shown above. the battery has been connected for a long time so that the currents have steady values. Given these conditions, calculate each of the following a. The current in the 9-ohm resistor. b. The current in the 8-ohm resistor.

c. The potential difference across the 30-microfarad capacitor. d. The energy stored in the 30-microfarad capacitor.

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At some instant, the connection at point P fails, and the current in the 9-ohm resistor becomes zero. e. Calculate the total amount of energy dissipated in the 8-ohm resistor after the connection fails.

1988E3. The long solenoid shown in the left-hand figure above has radius r1 and n turns of wire per unit length, and it carries a current i. The magnetic field outside the solenoid is negligible.

a. Apply Ampere's law using the path abcda indicated in the cross section shown in the righthand

figure above to derive an expression for the magnitude of the magnetic field B near the center of the solenoid

A loop of radius r2 is then placed at the center of the solenoid, so that the plane of the loop is perpendicular to the axis of the solenoid, as shown above. The current in the solenoid is decreased at a steady rate from i to zero in time t. In terms of the given quantities and fundamental constants, determine: b. The emf induced in the loop.

c. The magnitude of the induced electric field at a point in the loop.

The loop is now removed and another loop of radius r3 is placed outside the solenoid, so that the plane of the loop is perpendicular to the axis of the solenoid, as shown above. The current in the solenoid is again decreased at a steady rate from i to zero in time t. In terms of the given quantities and fundamental constants, determine:

d. The emf induced in the loop. e.

The magnitude of the i

Copyright ? 1988 by College Entrance Examination Board. All rights reserved.

College Board, Advanced Placement Program, AP, SAT, and the acorn logo are registered trademarks of the College Entrance Examination Board.

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