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AP? Physics B 2004 Free-Response Questions

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TABLE OF INFORMATION FOR 2004 and 2005 CONSTANTS AND CONVERSION FACTORS 1 unified atomic mass unit,

1u

UNITS Name meter kilogram second ampere kelvin

?1

PREFIXES Factor

10 9 10 10 10

6 3 ?2

= 1.66 ? 10 -27 kg = 931 MeV/c 2

Symbol m kg s A K mol Hz N Pa J W C V

?

Prefix giga mega kilo centi milli micro nano pico

Symbol G M k c m

?

Proton mass, Neutron mass, Electron mass, Magnitude of the electron charge, Avogadro’s number, Universal gas constant, Boltzmann’s constant, Speed of light, Planck’s constant,

m p = 1.67 × 10 ?27 kg mn = 1.67 × 10 ?27 kg me = 9.11 × 10 ?31 kg

e = 1.60 × 10 ?19 C N0 = 6.02 × 10 mol

23

10 ?3 10

?6

R

= 8.31 J / ( mol ? K )

mole hertz newton pascal joule watt coulomb

2

k B = 1.38 × 10 ?23 J / K c = 3.00 × 10 8 m / s h = 6.63 × 10 = 4.14 × 10

?34 ?15

10 ?9 10 ?12

n p

eV ? s

J ?s

VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES

hc = 1.99 × 10 ?25 J ? m = 1.24 × 10 3 eV ? nm C / N?m

2

θ

0

sin θ 0 1/2 3/5

2 /2

cos θ 1

3 /2

tan θ 0

3 /3

Vacuum permittivity, Coulomb’s law constant, Vacuum permeability, Magnetic constant, Universal gravitational constant, Acceleration due to gravity at the Earth’s surface, 1 atmosphere pressure, 1 electron volt,

? 0 = 8.85 × 10

9

?12

volt ohm henry farad

k = 1 / 4π ? 0 = 9.0 × 10 N ? m 2 / C 2 k ' = ? 0 / 4π = 10 (T ? m) / A

?7

30

37 45 53 60 90

? 0 = 4π × 10 ?7 (T ? m) / A

H F T

C

4/5

2 /2

3/4 1 4/3

3

G

= 6.67

?

10

-11

m / kg ? s

3

2

tesla degree Celsius electronvolt

g = 9.8 m / s 2

4/5

3 /2

3/5 1/2 0

1 atm = 1.0 × 10 5 N / m 2 = 1.0 × 10 5 Pa 1 eV = 1.60 × 10 ?19 J

eV

1

∞

The following conventions are used in this examination. 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.

2

ADVANCED PLACEMENT PHYSICS B EQUATIONS FOR 2004 and 2005

NEWTONIAN MECHANICS

u

ELECTRICITY AND MAGNETISM

F= E= q1 q 2 4 p? 0 r 2 1 F q q1 q 2 4 p? 0 r 1

=

u0

+ at

1 2 at 2

x = x0 + u0 t +

u

2

=

u0 2

+ 2a a x - x 0 f

a F f h J K k

? F = Fnet = ma

F fric ? mN ac =

t u

2

r

= rF sin q

p = mv J = FDt = K = 1 mu 2 2

Dp

= = = = = = = = m = N = P = p = r = r = T = t = U = u = W= x = m = q = t =

acceleration force frequency height impulse kinetic energy spring constant length mass normal force power momentum radius or distance position vector period time potential energy velocity or speed work done on a system position coefficient of friction angle torque

A B C d E

UE = qV = E avg = ? V= C= C= 1 4 p? 0 Q V V d

∑ qr

i

i

i

?0 A

d 1 1 Uc = QV = CV 2 2 2 I avg = R=

area magnetic field capacitance distance electric field e emf F force I current length P power Q charge q point charge R resistance r distance t time U potential (stored) energy V electric potential or potential difference u = velocity or speed r = resistivity fm = magnetic flux

= = = = = = = = = = = = = = = = =

DUg = mgh

W = F ? Dr = FDr cos q Pavg = W Dt

DQ Dt

ρ

A V = IR P = IV Cp = Ci ∑ i

P = F ? v = Fu cos q Fs = - k x Us = 1 2 kx 2

1 1 = Cs C i i Rs =

∑

i

∑ Ri

i

m Ts = 2 p k Tp = 2 p T = 1 f Gm1m2 r2 g

1 = Rp

1 ∑R

i

FB = qu B sin θ FB = BI sin θ B=

m0 I

2p r

FG = UG

fm = B ? A = BA cos θ

Gm1m2 = r

eavg = ? e= B

u

Df Dt

m

3

ADVANCED PLACEMENT PHYSICS B EQUATIONS FOR 2004 and 2005 FLUID MECHANICS AND THERMAL PHYSICS

P = P0 + r gh Fbuoy = rVg A1u1 = A2u2 1 P + r gy + ru 2 = const. 2 D = a 0 DT P= F A

ATOMIC AND NUCLEAR PHYSICS

E = hf = pc Kmax = hf ? f

l =

PV = nRT K avg =

urms

3 k T 2 B 3RT = M 3k B T

m

=

W = - P DV

DU = Q + W

e= ec = W QH TH - TC TH

A = area e = efficiency F = force h = depth Kavg = average molecular kinetic energy = length M = molar mass n = number of moles P = pressure Q = heat transferred to a system T = temperature U = internal energy V = volume u = velocity or speed urms = root-mean-square velocity W = work done on a system y = height a = coefficient of linear expansion m = mass of molecule r = density

h p

DE = ( Dm) c 2

E= f = K= m= p = l= f=

energy frequency kinetic energy mass momentum wavelength work function

GEOMETRY AND TRIGONOMETRY

Rectangle A = bh Triangle 1 A = bh 2 Circle A = pr 2 C = 2 pr Parallelepiped V = wh Cylinder V = pr 2 S = 2 pr + 2 pr 2 Sphere 4 V = pr 3 3 S = 4 pr 2 Right Triangle a 2 + b2 = c2 a sin q = c b cos q = c a tan q = b

WAVES AND OPTICS

u = fl c n = u n 1 sin q1 = n 2 sin q 2

sin q c = n2 n1

A= C= V= S = b = h = = w= r =

area circumference volume surface area base height length width radius

1 + 1 = 1 si s0 f h s M = i = - i s0 h0 R 2 d sin q = ml f = xm ? ml L d

d = separation f = frequency or focal length h = height L = distance M = magnification m = an integer n = index of refraction R = radius of curvature s = distance u = speed x = position l = wavelength q = angle

c q b 90°

a

4

2004 AP? PHYSICS B FREE-RESPONSE QUESTIONS

PHYSICS B

SECTION II Time—90 minutes 6 Questions Directions: Answer all six questions, which are weighted according to the points indicated. The suggested time is about 17 minutes for answering each of questions 1-4, and about 11 minutes for answering each of questions 5-6. The parts within a question may not have equal weight. Show all your work in the pink booklet in the spaces provided after each part, NOT in this green insert.

1. (15 points) A roller coaster ride at an amusement park lifts a car of mass 700 kg to point A at a height of 90 m above the lowest point on the track, as shown above. The car starts from rest at point A, rolls with negligible friction down the incline and follows the track around a loop of radius 20 m. Point B, the highest point on the loop, is at a height of 50 m above the lowest point on the track. (a) i. Indicate on the figure the point P at which the maximum speed of the car is attained. ii. Calculate the value umax of this maximum speed. (b) Calculate the speed uB of the car at point B. (c) i. On the figure of the car below, draw and label vectors to represent the forces acting on the car when it is upside down at point B. ii. Calculate the magnitude of all the forces identified in (c)i. (d) Now suppose that friction is not negligible. How could the loop be modified to maintain the same speed at the top of the loop as found in (b)? Justify your answer.

Copyright ? 2004 by College Entrance Examination Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for AP students and parents).

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2004 AP? PHYSICS B FREE-RESPONSE QUESTIONS

2. (15 points) While exploring a sunken ocean liner, the principal researcher found the absolute pressure on the robot observation submarine at the level of the ship to be about 413 atmospheres. The density of seawater is 1025 kg m 3 . (a) Calculate the gauge pressure pg on the sunken ocean liner. (b) Calculate the depth D of the sunken ocean liner. (c) Calculate the magnitude F of the force due to the water on a viewing port of the submarine at this depth if the viewing port has a surface area of 0.0100 m 2 . Suppose that the ocean liner came to rest at the surface of the ocean before it started to sink. Due to the resistance of the seawater, the sinking ocean liner then reached a terminal velocity of 10.0 m s after falling for 30.0 s. (d) Determine the magnitude a of the average acceleration of the ocean liner during this period of time. (e) Assuming the acceleration was constant, calculate the distance d below the surface at which the ocean liner reached this terminal velocity. (f) Calculate the time t it took the ocean liner to sink from the surface to the bottom of the ocean.

3. (15 points) A square loop of wire of side 0.20 m has a total resistance of 0.60 W . The loop is positioned in a uniform magnetic field B of 0.030 T. The field is directed into the page, perpendicular to the plane of the loop, as shown above. (a) Calculate the magnetic flux φ through the loop. The field strength now increases uniformly to 0.20 T in 0.50 s. (b) Calculate the emf (c) i. Calculate the magnitude I of the current in the loop during this period. ii. What is the direction of the current in the loop? _____ Clockwise Justify your answer. (d) Describe a method by which you could induce a current in the loop if the magnetic field remained constant.

Copyright ? 2004 by College Entrance Examination Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for AP students and parents).

e induced in the loop during this period.

_____ Counterclockwise

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2004 AP? PHYSICS B FREE-RESPONSE QUESTIONS

4. (15 points) Two small speakers S are positioned a distance of 0.75 m from each other, as shown in the diagram above. The two speakers are each emitting a constant 2500 Hz tone, and the sound waves from the speakers are in phase with each other. A student is standing at point P, which is a distance of 5.0 m from the midpoint between the speakers, and hears a maximum as expected. Assume that reflections from nearby objects are negligible. Use 343 m/s for the speed of sound. (a) Calculate the wavelength of these sound waves. (b) The student moves a distance Y to point Q and notices that the sound intensity has decreased to a minimum. Calculate the shortest distance the student could have moved to hear this minimum. (c) Identify another location on the line that passes through P and Q where the student could stand in order to observe a minimum. Justify your answer. (d) i. How would your answer to (b) change if the two speakers were moved closer together? Justify your answer. ii. How would your answer to (b) change if the frequency emitted by the two speakers was increased? Justify your answer.

Copyright ? 2004 by College Entrance Examination Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for AP students and parents).

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2004 AP? PHYSICS B FREE-RESPONSE QUESTIONS

5. (10 points) The diagram above of pressure P versus volume V shows the expansion of 2.0 moles of a monatomic ideal gas from state A to state B. As shown in the diagram, PA = PB = 600 N m 2 , VA = 3.0 m 3 , and VB = 9.0 m 3 . (a) i. Calculate the work done by the gas as it expands. ii. Calculate the change in internal energy of the gas as it expands. iii. Calculate the heat added to or removed from the gas during this expansion. (b) The pressure is then reduced to 200 N m 2 without changing the volume as the gas is taken from state B to state C. Label state C on the diagram and draw a line or curve to represent the process from state B to state C. (c) The gas is then compressed isothermally back to state A. i. Draw a line or curve on the diagram to represent this process. ii. Is heat added to or removed from the gas during this isothermal compression? ____ added to Justify your answer. ____ removed from

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2004 AP? PHYSICS B FREE-RESPONSE QUESTIONS

6. (10 points) A student performs a photoelectric effect experiment in which light of various frequencies is incident on a photosensitive metal plate. This plate, a second metal plate, and a power supply are connected in a circuit, which also contains two meters, M1 and M2, as shown above. The student shines light of a specific wavelength l onto the plate. The voltage on the power supply is then adjusted until there is no more current in the circuit, and this voltage is recorded as the stopping potential VS . The student then repeats the experiment several more times with different wavelengths of light. The data, along with other values calculated from it, are recorded in the table below.

l (m)

VS (volts) f (Hz) K max (eV)

4.00 ? 10 -7 0.65 7.50 ? 1014 0.65

4.25 ? 10 -7 0.45 7.06 ? 1014 0.45

4.50 ? 10 -7 0.30 6.67 ? 1014 0.30

4.75 ? 10 -7 0.15 6.32 ? 1014 0.15

(a) Indicate which meter is used as an ammeter and which meter is used as a voltmeter by checking the appropriate spaces below. M1 M2 Ammeter Voltmeter _____ _____ _____ _____

(b) Use the data above to plot a graph of K max versus f on the axes below, and sketch a best-fit line through the data.

(c) Use the best-fit line you sketched in part (b) to calculate an experimental value for Planck’s constant. (d) If the student had used a different metal with a larger work function, how would the graph you sketched in part (b) be different? Explain your reasoning. END OF EXAMINATION

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