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Unformatted text preview: AP® Physics B 2010 FreeResponse Questions The College Board
The College Board is a notforprofit membership association whose mission is to connect students to college success and opportunity. Founded in 1900, the College Board is composed of more than 5,700 schools, colleges, universities and other educational organizations. Each year, the College Board serves seven million students and their parents, 23,000 high schools, and 3,800 colleges through major programs and services in college readiness, college admission, guidance, assessment, financial aid and enrollment. Among its widely recognized programs are the SAT®, the PSAT/NMSQT®, the Advanced Placement Program® (AP®), SpringBoard® and ACCUPLACER®. The College Board is committed to the principles of excellence and equity, and that commitment is embodied in all of its programs, services, activities and concerns. © 2010 The College Board. College Board, ACCUPLACER, Advanced Placement Program, AP, AP Central, SAT, SpringBoard and the acorn logo are registered trademarks of the College Board. Admitted Class Evaluation Service is a trademark owned by the College Board. PSAT/NMSQT is a registered trademark of the College Board and National Merit Scholarship Corporation. All other products and services may be trademarks of their respective owners. Permission to use copyrighted College Board materials may be requested online at: www.collegeboard.com/inquiry/cbpermit.html. Visit the College Board on the Web: www.collegeboard.com. AP Central is the official online home for the AP Program: apcentral.collegeboard.com. TABLE OF INFORMATION FOR 2010 and 2011 CONSTANTS AND CONVERSION FACTORS Proton mass, m p = 1.67 ¥ 10 27 kg Neutron mass, mn = 1.67 ¥ 10 27 kg Electron mass, me = 9.11 ¥ 10 31 kg Avogadro’s number, N 0 = 6.02 ¥ 1023 mol1 Universal gas constant, Electron charge magnitude, e = 1.60 ¥ 10 19 C 1 electron volt, 1 eV = 1.60 ¥ 10 19 J Speed of light, Universal gravitational constant, Acceleration due to gravity at Earth’s surface, c = 3.00 ¥ 108 m s G = 6.67 ¥ 10 11 m 3 kgis2 R = 8.31 J (mol iK) g = 9.8 m s2 Boltzmann’s constant, k B = 1.38 ¥ 10 23 J K 1 unified atomic mass unit, Planck’s constant, Vacuum permittivity, Coulomb’s law constant, k = 1 4 p Vacuum permeability, 1 u = 1.66 ¥ 10 27 kg = 931 MeV c 2
h = 6.63 ¥ 10 34 J is = 4.14 ¥ 10 15 eV is hc = 1.99 ¥ 10 25 J im = 1.24 ¥ 103 eV i nm
0 0 = 8.85 ¥ 10 12 C2 N im 2 = 9.0 ¥ 109 N im 2 C2 m0 = 4 p ¥ 10 7 (T im) A Magnetic constant, k ¢ = m0 4 p = 1 ¥ 10 7 (T im) A 1 atmosphere pressure, meter, kilogram, second, ampere, kelvin, m kg s A K mole, hertz, newton, pascal, joule, mol Hz N Pa J 1 atm = 1.0 ¥ 105 N m 2 = 1.0 ¥ 105 Pa
watt, coulomb, volt, ohm, henry, W C V W H farad, tesla, degree Celsius, electronvolt, F T ∞C eV UNIT SYMBOLS PREFIXES Factor
10
9 VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES Symbol G M k c m Prefix giga mega kilo centi milli micro nano pico q sin q
cos q tan q 0 30 37 45 53 60 90 0 1 0 12
32 33 35 45 34 22 22
1 45 35 43 32 1 0 106 103 10 2 10 3 10 6 10 9 10
1 2 12
3 • m
n 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. 2 ADVANCED PLACEMENT PHYSICS B EQUATIONS FOR 2010 and 2011
NEWTONIAN MECHANICS ELECTRICITY AND MAGNETISM u = u0 + at x = x0 + u0 t + 12 at 2 u 2 = u0 2 + 2 a ( x  x0 ) Â F = Fnet = ma
Ffric £ m N ac = a F f h J K k m N P p r T t U u W x m q t u2 r t = rF sin q p = mv
J = FDt = Dp
1 K = mu 2 2 DUg = mgh
W = F Dr cos q Pavg = W Dt = = = = = = = = = = = = = = = = = = = = = = acceleration force frequency height impulse kinetic energy spring constant length mass normal force power momentum radius or distance period time potential energy velocity or speed work done on a system position coefficient of friction angle torque F=
E= 1 q1q2 4p 0 r 2
F q A B C d E F I UE = qV =
Eavg = V= C= C= Uc = V d 1 q1q2 4p 0 r e 1 4p 0 Q V
0A Â
i qi ri d 1 1 QV = CV 2 2 2 P Q q R r t U V = = = = = = = = = = = = = = = = = I avg = DQ Dt R= r A u= r= q= fm = area magnetic field capacitance distance electric field emf force current length power charge point charge resistance distance time potential (stored) energy electric potential or potential difference velocity or speed resistivity angle magnetic flux V = IR P = IV
Cp = P = F u cos q
Fs =  k x Â Ci
i Us = 12 kx 2 1 1 =Â Cs i Ci Rs = Â Ri
i Ts = 2 p
Tp = 2 p m k
g 1 = Rp ÂR
i 1
i FB = qu B sin q FB = BI sin q
B= m0 I 2p r T= 1 f Gm1m2 r2 FG =  fm = BA cos q UG =  Gm1m2 r eavg = Dfm Dt e =Bu 3 ADVANCED PLACEMENT PHYSICS B EQUATIONS FOR 2010 and 2011 FLUID MECHANICS AND THERMAL PHYSICS WAVES AND OPTICS r=mV
P = P0 + rgh Fbuoy = rVg A1u1 = A2 u2
P + rgy +
D =a 12 ru = const. 2 0 DT H=
P= kA DT L
F A PV = nRT = Nk BT
K avg = 3 kT 2B urms = 3 RT = 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 H = rate of heat transfer k = thermal conductivity K avg = average molecular kinetic energy = length L = thickness m = mass M = molar mass n = number of moles N = number of molecules P = pressure Q = heat transferred to a system T = temperature U = internal energy V = volume u = velocity or speed urms = rootmeansquare velocity W = work done on a system y = height a = coefficient of linear expansion m = mass of molecule r = density u = fl
n= c u n 1 sin q1 = n 2 sin q2 sin qc = n2 n1 1 1 1 + = si s0 f h s M= i = i h0 s0
R 2 d sin q = m l f= 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 xm ª m lL d GEOMETRY AND TRIGONOMETRY Rectangle A = bh Triangle 1 A = bh 2 Circle A = pr 2 C = 2pr Parallelepiped V = wh Cylinder V = pr 2 A= C= V= S= b= h= = w= r= area circumference volume surface area base height length width radius ATOMIC AND NUCLEAR PHYSICS S = 2pr + 2pr 2 Sphere 4 V = pr 3 3
S = 4pr 2
Right Triangle a 2 + b2 = c2 a sin q = c b cos q = c a tan q = b E = hf = pc K max = hf  f l= h p
2 D E = ( Dm ) c E = energy f = frequency K = kinetic energy m = mass p = momentum l = wavelength f = work function c q b 90° a 4 2010 AP® PHYSICS B FREERESPONSE QUESTIONS 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 17 minutes for answering each of Questions 12 and about 11 minutes for answering each of Questions 37. 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) Block A of mass 4.0 kg is on a horizontal, frictionless tabletop and is placed against a spring of negligible mass and spring constant 650 N m . The other end of the spring is attached to a wall. The block is pushed toward the wall until the spring has been compressed a distance x, as shown above. The block is released and follows the trajectory shown, falling 0.80 m vertically and striking a target on the floor that is a horizontal distance of 1.2 m from the edge of the table. Air resistance is negligible. (a) Calculate the time elapsed from the instant block A leaves the table to the instant it strikes the floor. (b) Calculate the speed of the block as it leaves the table. (c) Calculate the distance x the spring was compressed. Block B, also of mass 4.0 kg, is now placed at the edge of the table. The spring is again compressed a distance x, and block A is released. As it nears the end of the table, it instantaneously collides with and sticks to block B. The blocks follow the trajectory shown in the figure below and strike the floor at a horizontal distance d from the edge of the table. © 2010 The College Board. Visit the College Board on the Web: www.collegeboard.com. GO ON TO THE NEXT PAGE. 5 2010 AP® PHYSICS B FREERESPONSE QUESTIONS (d) Calculate d if x is equal to the value determined in part (c). (e) Consider the system consisting of the spring, the blocks, and the table. How does the total mechanical energy E2 of the system just before the blocks leave the table compare to the total mechanical energy E1 of the system just before block A is released? ____ E2 < E1 Justify your answer. ____ E2 = E1 ____ E2 > E1 © 2010 The College Board. Visit the College Board on the Web: www.collegeboard.com. GO ON TO THE NEXT PAGE. 6 2010 AP® PHYSICS B FREERESPONSE QUESTIONS 2. (15 points) A large pan is filled to the top with oil of density rO . A plastic cup of mass mC , containing a sample of known mass mS , is placed in the oil so that the cup and sample float, as shown above. The oil that overflows from the pan is collected, and its volume is measured. The procedure is repeated with a variety of samples of different mass, and the pan is refilled each time. (a) On the dot below that represents the cupsample system, draw and label the forces (not components) that act on the system when it is floating on the surface of the oil. ∑
(b) Derive an expression for the overflow volume VO (the volume of oil that overflows due to the floating system) in terms of rO , mS , mC , and fundamental constants. 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). Assume that the following data are obtained for the overflow volume VO for several sample masses mS . Sample mass mS (kg) 0.020 0.030 0.040 0.050 0.060 0.070 Overflow volume VO ( m3 ) 29 ¥ 10 6 38 ¥ 10 6 54 ¥ 10 6 62 ¥ 10 6 76 ¥ 10 6 84 ¥ 10 6 © 2010 The College Board. Visit the College Board on the Web: www.collegeboard.com. GO ON TO THE NEXT PAGE. 7 2010 AP® PHYSICS B FREERESPONSE QUESTIONS
(c) Graph the data on the axes below, plotting the overflow volume as a function of sample mass. Place numbers and units on both axes. Draw a straight line that best represents the data. (d) Use the slope of the bestfit line to calculate the density of the oil. (e) What is the physical significance of the intercept of your line with the vertical axis? © 2010 The College Board. Visit the College Board on the Web: www.collegeboard.com. GO ON TO THE NEXT PAGE. 8 2010 AP® PHYSICS B FREERESPONSE QUESTIONS 3. (10 points) Three particles are fixed in place in a horizontal plane, as shown in the figure above. Particle 3 at the top of the triangle has charge q3 of +1.0 ¥ 10 6 C , and the electrostatic force F on it due to the charge on the two other particles is measured to be entirely in the negative xdirection. The magnitude of the charge q1 on particle 1 is known to be 4.0 ¥ 10 6 C , and the magnitude of the charge q2 on particle 2 is known to be 1.7 ¥ 10 6 C , but their signs are not known. (a) Determine the signs of the charges q1 and q2 and indicate the correct signs below. q1 ____ Negative ____ Positive q2 ____ Negative ____ Positive (b) On the diagram below, draw and label arrows to indicate the direction of the force F1 exerted by particle 1 on particle 3 and the force F2 exerted by particle 2 on particle 3. (c) Calculate the magnitude of F, the electrostatic force on particle 3. (d) Calculate the magnitude of the electric field at the position of particle 3 due to the other two particles. (e) On the figure below, draw a small ¥ in the box that is at a position where another positively charged particle could be fixed in place so that the electrostatic force on particle 3 is zero. Justify your answer. © 2010 The College Board. Visit the College Board on the Web: www.collegeboard.com. GO ON TO THE NEXT PAGE. 9 2010 AP® PHYSICS B FREERESPONSE QUESTIONS
4. (10 points) A locomotive runs on a steam engine with a power output of 4.5 ¥ 106 W and an efficiency of 12 percent. (a) Calculate the rate at which heat is being delivered to the steam engine. (b) Calculate the magnitude of the resistive forces acting on the locomotive when it is moving with a constant speed of 7.0 m s . Suppose the gas in another heat engine follows the simplified path ABCDA in the PV diagram below at a rate of 4 cycles per second. (c) i. What does the area bounded by path ABCDA represent? ii. Calculate the power output of the engine. (d) Indicate below all of the processes during which heat is added to the gas in the heat engine. ____ AB ____BC ____CD ____DA © 2010 The College Board. Visit the College Board on the Web: www.collegeboard.com. GO ON TO THE NEXT PAGE. 10 2010 AP® PHYSICS B FREERESPONSE QUESTIONS 5. (10 points) As shown above, a beam of red light of wavelength 6.65 ¥ 10 7 m in air is incident on a glass prism at an angle q1 with the normal. The glass has index of refraction n = 1.65 for the red light. When q1 = 40∞, the beam emerges on the other side of the prism at an angle q4 = 84∞. (a) Calculate the angle of refraction q2 at the left side of the prism. (b) Using the same prism, describe a change to the setup that would result in total internal reflection of the beam at the right side of the prism. Justify your answer. (c) The incident beam is now perpendicular to the surface. The glass is coated with a thin film that has an index of refraction n f = 1.38 to reduce the partial reflection of the beam at this angle. i. Calculate the wavelength of the red light in the film. ii. Calculate the minimum thickness of the film for which the intensity of the reflected red ray is near zero. © 2010 The College Board. Visit the College Board on the Web: www.collegeboard.com. GO ON TO THE NEXT PAGE. 11 2010 AP® PHYSICS B FREERESPONSE QUESTIONS 6. (10 points) The plastic cart shown in the figure above has mass 2.5 kg and moves with negligible friction on a horizontal surface. Attached to the cart is a rigid rectangular loop of wire that is 0.10 m by 0.20 m, has resistance 4.0 W, and has a mass that is negligible compared to the mass of the cart. The plane of the rectangular loop is parallel to the plane of the page. A uniform magnetic field of 2.0 T, perpendicular to and directed into the plane of the page, starts at x = 0, as shown above. (a) On the figure below, indicate the direction of the induced current in the loop when its front edge is at x = 0.12 m. Justify your answer. (b) When the front edge of the rectangular loop is at x = 0.12 m, its speed is 3.0 m s . Calculate the following for that instant. i. The magnitude of the induced current in the rectangular loop of wire ii. The magnitude of the net force on the loop (c) At a later time, the cart and loop are completely inside the magnetic field. Determine the magnitude of the net force on the loop at that time. Justify your answer. © 2010 The College Board. Visit the College Board on the Web: www.collegeboard.com. GO ON TO THE NEXT PAGE. 12 2010 AP® PHYSICS B FREERESPONSE QUESTIONS 7. (10 points) Light of wavelength 400 nm is incident on a metal surface, as shown above. Electrons are ejected from the metal surface with a maximum kinetic energy of 1.1 ¥ 10 19 J. (a) Calculate the frequency of the incoming light. (b) Calculate the work function of the metal surface. (c) Calculate the stopping potential for the emitted electrons. (d) Calculate the momentum of an electron with the maximum kinetic energy. END OF EXAM © 2010 The College Board. Visit the College Board on the Web: www.collegeboard.com. 13 ...
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 Spring '11
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