ap-2013物理b真题-physics-b-free-response-questions

AP? Physics B

2013 Free-Response Questions

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TABLE OF INFORMATION DEVELOPED FOR 2012

meter, m mole, mol watt, W farad, F kilogram, kg hertz, Hz coulomb, C tesla, T

second, s newton, N volt, V degree Celsius, C

ampere, A pascal, Pa ohm, W

electron-volt, eV UNIT

SYMBOLS

kelvin, K joule, J henry, H

PREFIXES

Factor Prefix Symbol 910

giga G 610 mega M 310 kilo k

210 centi c 310 milli m 610 micro m

910

nano n 1210

pico p

The following conventions are used in this exam.

I. 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).

III. For any isolated electric charge, the electric potential is defined as zero at

an infinite distance from the charge. IV. For mechanics and thermodynamics equations, W represents the work done on a system.

ADVANCED PLACEMENT PHYSICS B EQUATIONS DEVELOPED FOR 2012

ADVANCED PLACEMENT PHYSICS B EQUATIONS DEVELOPED FOR 2012

PHYSICS B

SECTION II Time—90 minutes

7 Questions

Directions: Answer all seven questions, which are weighted according to the points indicated. The suggested times are about 11 minutes for answering each of Questions 1, 3-5 and 7 and about 17 minutes for answering each of

Questions 2 and 6. The parts within a question may not have equal weight. Show all your work in this booklet in the spaces provided after each part.

1. (10 points)

A sailboat at rest on a calm lake has its anchor dropped a distance of 4.0 m below the surface of the water. The

anchor is suspended by a rope of negligible mass and volume. The mass of the anchor is 50 kg, and its volume is

336.2510 m . The density of water is 31000 kg m .

(a) On the dot below that represents the anchor, draw and label the forces (not components) that act on the

anchor.

(b) Calculate the magnitude of the buoyant force acting on the anchor. If you need to draw anything other than

what you have shown in part (a) to assist in your solution, use the space below. DO NOT add anything to the figure in part (a).

(c) Calculate the tension in the rope. If you need to draw anything other than what you have shown in part (a) to

assist in your solution, use the space below. DO NOT add anything to the figure in part (a).

(d) The bottom of the boat is at a depth d below the surface of the water. Suppose the anchor is lifted back into

the boat so that the bottom of the boat is at a new depth d below the surface of the water. How does d compare to d ? ____ d d ____ d d ____ d d ! Justify your answer.

2. (15 points)

A 20 kg box on a horizontal frictionless surface is moving to the right at a speed of 4.0 m. The box hits and

remains attached to one end of a spring of negligible mass whose other end is attached to a wall. As a result, the spring compresses a maximum distance of 0.50 m, and the box then oscillates back and forth.

(a)

i. The spring does work on the box from the moment the box first hits the spring to the moment the

spring first reaches its maximum compression. Indicate whether the work done by the spring is

positive, negative, or zero.

____ Positive ____ Negative ____ Zero

Justify your answer.

ii. Calculate the magnitude of the work described in part i.

(b) Calculate the spring constant of the spring.

(c) Calculate the magnitude of the maximum acceleration of the box.

(d) Calculate the frequency of the oscillation of the box.

(e) Let x = 0 be the point where the box makes contact with the spring, with positive x directed toward the right.

i. On the axes below, sketch the kinetic energy K of the oscillating box as a function of position x for the

range 0.50 m x to 0.50 m x .

ii. On the axes below, sketch the acceleration a of the oscillating box as a function of position x for the

range 0.50 m x to 0.50 m x .

3. (10 points)

A student is asked to experimentally determine the index of refraction of the semicircular block of transparent

l at the center of plastic shown in the figure above. The student aims a red laser beam of wavelength 632 nm

the flat side of the block, as shown. The ray is refracted from air into the plastic and strikes the semicircular side of the block perpendicularly. The student uses a protractor to aim the laser at several different angles of

incidence i q between 0 and 90 and to measure the angles of refraction r q. The student’s data are given in the table below.

q0 15 30 45 60 75

i

q0 10 21 30 37 44

r

sin i q0 0.260.500.710.870.97

sin r q0 0.170.360.500.600.70

(a) On the grid below, plot data that will allow the index of refraction of the plastic to be calculated from a

straight line that represents the data. Clearly label the axes, including the scales.

(b) On your graph, draw a straight line that best represents the data. Use the slope of the line to determine the

index of refraction of the plastic.

(c) The student now wants to confirm the result obtained in part (b) by using the critical angle for the plastic.

Describe one experimental method the student can use to measure the critical angle. Indicate how the index of refraction can be determined from this measurement.

4. (10 points)

A 0.30 kg ball is in a cup of negligible mass attached to a block of mass M that is on a table. A string passing

over a light pulley connects the block to a 2.5 kg object, as shown above. The system is released from rest, the block accelerates to the right, and after moving 0.95 m the block collides with a bumper near the end of the table.

The ball continues to move and lands on the floor at a position 2.4 m below and 1.8 m horizontally from where it leaves the cup. Assume all friction is negligible.

(a) Calculate the speed of the ball just after the block hits the bumper and the ball leaves the cup.

(b) Calculate the magnitude of the acceleration of the block as it moves across the table.

(c) Calculate the mass M of the block.

(d) If the mass of the ball is increased, the horizontal distance it travels before hitting the floor will decrease.

Explain why this will happen.

5. (10 points)

In a certain process, 3200 J of energy is added to an ideal gas by heating. During the same process, 2100 J of work is done on the gas.

(a) Determine the change in the internal energy of the gas.

(b) Indicate whether each of the following properties of the gas increases, decreases, or remains the same during

the process.

i. Volume

____ Increases ____ Decreases ____ Remains the same

Justify your answer.

ii. Temperature

____ Increases ____ Decreases ____ Remains the same

Justify your answer.

iii. Pressure

____ Increases ____ Decreases ____ Remains the same

Justify your answer.

Suppose that in a different process 1800 joules of work is done on the ideal gas at a constant temperature.

(c) Determine the change in internal energy of the gas during the process.

(d) Which of the following correctly describes the energy transfer by heating, if any, between the gas and its

surroundings?

____ Energy is transferred into the gas. ____ Energy is transferred out of the gas.

____ There is no energy transfer by heating.

Justify your answer.

6. (15 points)

Two long, straight horizontal wires are near each other and parallel, with one directly above the other as shown

in the figure. Wire X is fixed in place and connected to a battery (not shown) so that it carries a current of 65 A. Wire Y , which is part of a second circuit, is free to move vertically and is suspended at rest by the magnetic force

between the wires. The mass per length of wire Y is 35.610 kg m . Neglect effects from the parts of the circuits that are not shown.

(a) Calculate the magnitude of the magnetic field produced by wire X at the position of wire Y . (b)

i. Calculate the magnitude of the current in wire Y . ii. Indicate the direction of the current in wire Y .

____ To the left ____ To the right ____ Neither left nor right, since there is no current

(c) Now wire Y is moved to a new position that is closer to wire X , but wire Y is still below wire X and is still

carrying the same current as determined in part (b). Wire Y is released from rest. Describe the initial motion of wire Y . Justify your answer.

(d) Suppose wire Y is moved to a position 0.025 m above wire X . What changes in current, if any, must occur to

maintain equilibrium?

(e) With wire

Y still above wire X , the circuit connected to wire Y is removed. Wire Y , which is 1.2 m long, is then moved vertically up and away from wire X at a constant speed of 3.0 m/s.

i. Calculate the magnitude of the induced emf in wire Y when the wires are 0.050 m apart.

ii. Indicate which end of wire Y is at a higher electric potential.

____ The left end ____ The right end

____ Neither end, since they are at the same electric potential Justify your answer.

7. (10 points)

The energy-level diagram for an isolated hypothetical atom is shown above.

n state undergo transitions in which the atoms only

(a) A collection of such atoms with electrons in the 3

n state. On the diagram above, draw arrows to emit photons, and the electrons eventually end in the 1

indicate all possible transitions, given the starting and ending states for the electrons.

(b) Calculate the longest wavelength of photons that the atom can emit during the transitions identified in

part (a).

(c) What is the ionization energy of an atom in the ground state?

(d) Photons of energy 11.0 eV are incident on the atom. What effect can this have on an electron in the

n state? Justify your answer.

1

(e) Photons of energy 14.0 eV are incident on the atom. What effect can this have on an electron in the

n state? Justify your answer.

1

STOP

END OF EXAM