AP Physics B 00 Scoring Guidelines Form B The materials included in these files are intended for use by AP teachers for course and exam preparation in the classroom; permission for any other use must be sought from the Advanced Placement Program. Teachers may reproduce them, in whole or in part, in limited quantities, for face-to-face teaching purposes but may not mass distribute the materials, electronically or otherwise. These materials and any copies made of them may not be resold, and the copyright notices must be retained as they appear here. This permission does not apply to any third-party copyrights contained herein. These materials were produced by Educational Testing Service (ETS ), which develops and administers the examinations of the Advanced Placement Program for the College Board. The College Board and Educational Testing Service (ETS) are dedicated to the principle of equal opportunity, and their programs, services, and employment policies are guided by that principle. The College Board is a national nonprofit membership association dedicated to preparing, inspiring, and connecting students to college and opportunity. Founded in 1900, the association is composed of more than 4,00 schools, colleges, universities, and other educational organizations. Each year, the College Board serves over three million students and their parents,,000 high schools, and 3,500 colleges, through major programs and services in college admission, guidance, assessment, financial aid, enrollment, and teaching and learning. Among its best-known programs are the SAT, the PSAT/NMSQT, and the Advanced Placement Program (AP ). The College Board is committed to the principles of equity and excellence, and that commitment is embodied in all of its programs, services, activities, and concerns. Copyright 00 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. APIEL is a trademark owned by the College Entrance Examination Board. PSAT/NMSQT is a registered trademark jointly owned by the College Entrance Examination Board and the National Merit Scholarship Corporation. Educational Testing Service and ETS are registered trademarks of Educational Testing Service.
General Notes About 00 AP Physics Scoring Guidelines 1. The solutions contain the most common method(s) of solving the free-response questions, and the allocation of for these solutions. Other methods of solution also receive appropriate credit for correct work.. Generally, double penalty for errors is avoided. For example, if an incorrect answer to part (a) is correctly substituted into an otherwise correct solution to part (b), full credit will usually be awarded. One exception to this may be cases when the numerical answer to a later part should be easily recognized as wrong, e.g., a speed faster than the speed of light in vacuum. 3. Implicit statements of concepts normally receive credit. For example, if use of the equation expressing a particular concept is worth one point, and a student s solution contains the application of that equation to the problem but the student does not write the basic equation, the point is still awarded. 4. The scoring guidelines typically show numerical results using the approximate value g 10 m s for ease of calculation, but use of 9.8 m s is of course also acceptable. 5. Numerical answers that differ from the published answer due to differences in rounding throughout the question typically receive full credit. The exception is usually when rounding makes a difference in obtaining a reasonable answer. For example, in calculations of mass differences in a nuclear reaction, rounding to too few digits can lose the accuracy required to determine a mass difference. Copyright 00 by College Entrance Examination Board. All rights reserved.
00 FORM B SCORING GUIDELINES Question 1 15 total Distribution of (a) 4 For any statement indicating that impulse equals change in momentum For any statement indicating that impulse can be determined from the area under the graph p Ft area under the curve 3 3 1 p 0.5 10 s 10 10 N 5 N s For recognizing that the impulse on the kg cart is negative, and subtracting it from the initial momentum of the cart p kg after.0 kg3.0 m s 5 N s =1 N s p kg after kgυ kg after 1 N s υ kg after 0.5 m s to the right (b) 3 For any statement of conservation of momentum p kg before p kg after p m after For correct substitutions 6 Ns=1 Ns+ m 1.6 ms m 3.1 kg Alternate solution The average acceleration is the average force divided by the mass a F m For calculating the average acceleration υ 1.6 m s a 1600 m s t 3 110 s For calculating the average force F 1 0 10,000 N=5000 N m 5000 N 1600 m s m 3.1 kg Alternate Note: An alternate solution is to do part (b) first using impulse, in which case the first two noted above for part (a) could be earned. Then conservation of momentum can be used to solve part (a), so the first point noted above for part (b) could be earned. Copyright 00 by College Entrance Examination Board. All rights reserved. 3
00 FORM B SCORING GUIDELINES Question 1 (cont d.) (c) For using the slope of the graph to determine the acceleration b05. 16. g ms a = slope = 3.5 - s a = 073. m s b g Distribution of (d) 3 For using the area under the curve or one of the equations d υt or d υt For calculating a distance for each segment of the graph d1 1.6m s s 3. m 1.6 0.5 m s 1 d 1.5 s or 1.6 m s1.5 s 0.73 m s 1.5 s d 1.6 m d3 0.5 m s1.5 s 0.8 m dtot d1 d ds d 5.5 m tot (e) 3 The acceleration is negative, so the cart must be moving opposite to the force of gravity, which is the only force acting on it. For indicating that the ramp goes up For using conservation of energy 1 mgh m υ υ i f 1 h 10 m s h 0.1 m 1.6 ms 0.5 ms Copyright 00 by College Entrance Examination Board. All rights reserved. 4
00 FORM B SCORING GUIDELINES Question 15 total Distribution of (a) 3 for each correctly drawn and appropriately labeled force For no incorrect forces The horizontal and vertical components of the tension were acceptable if properly labeled (b) 3 For indicating that the sum of the vertical forces is zero Fy 0 For correctly substituting the applicable forces T cosθ mg 0 T cosθ m g Copyright 00 by College Entrance Examination Board. All rights reserved. 5
00 FORM B SCORING GUIDELINES Question (cont d.) (c) 4 Distribution of The centripetal force is supplied by the horizontal component of the tension Fc Tsin θ For using a correct expression for the centripetal force F c mυ T sin θ r For eliminating the tension or the mass using the answer to part (b) mυ sin θ T cos θυ mg mg tan θ OR T sin θ r cosθ gr For using the substitution r sin θ mυ mg tan θ OR sin θ υ g sinθtanθ or T cos θυ sin gsin θ T θ gsin θ cosθ (d) 3 For using a correct expression for period or frequency π r υ T or f υ π r For substituting the velocity from part (c) (unsimplified acceptable) gsinθtanθ 1 g tanθ 1 g f or or πsinθ π sinθ π cosθ (e) For any indication that the initial velocity of the ball is horizontal For any indication that the subsequent trajectory is parabolic Copyright 00 by College Entrance Examination Board. All rights reserved. 6
00 FORM B SCORING GUIDELINES Question 3 15 total Distribution of (a) 6 For the correct expression for the total resistance in the parallel branch 1 1 1 Rp 6 Ω 3 Ω For the correct value for the parallel branch Rp Ω For correctly combining R p in series with the remaining resistance Rt Ω 3 Ω For the correct total resistance Rt 5 Ω For using Ohm s law I V R 9 V 5 Ω I 1.8 A (b) 3 For indicating that bulb A is brightest For a correct justification based on the power expended by each bulb (either quantitative reasoning or direct calculations) For example: P I R P 1.8 A 3 Ω 9.7 W A One third of the current flows through bulb B and two-thirds through bulb C P B 1.8 A 6 Ω. W 3 and P C 1.8 A 3 3 Ω 4.3 W One justification point was awarded for only discussing the relative currents in the bulbs or the relative voltages across them. Copyright 00 by College Entrance Examination Board. All rights reserved. 7
00 FORM B SCORING GUIDELINES Question 3 (cont d.) (c) i. For indicating that the brightness of bulb A decreases For a correct justification For example: The total resistance increases so the current through bulb A decreases, thus decreasing its power output Distribution of ii. For indicating that the brightness of bulb B increases For a correct justification For example: The current through bulb B increases, thus increasing its power output iii. For indicating that the brightness of bulb C decreases For a correct justification For example: The current through bulb C is now zero, so the bulb goes out Copyright 00 by College Entrance Examination Board. All rights reserved. 8
00 FORM B SCORING GUIDELINES Question 4 15 total Distribution of (a) 3 For indicating that the focal length is half the radius of curvature 3 (b) 3 each for any two correct principal rays (the three principal rays are shown above) For a correctly drawn image (c) i. For indicating the image is inverted ii. For indicating the image is real iii. For indicating the image is smaller than the object Copyright 00 by College Entrance Examination Board. All rights reserved. 9
00 FORM B SCORING GUIDELINES Question 4 (cont d.) (d) 3 Distribution of each for any two correct rays (i.e. showing no refraction for normal incidence and refraction away form the normal for non-normal incidence) For a correctly drawn image (e) i. For indicating the image is upright ii. For indicating the image is virtual iii. For indicating the image is smaller than the object Copyright 00 by College Entrance Examination Board. All rights reserved. 10
00 FORM B SCORING GUIDELINES Question 5 10 total Distribution of (a) For indicating the correct polarity, negative on the left and positive on the right (b) Using the expression for the magnitude of the electric field between two parallel plates: E V d For correct substitutions V 5000 N C 0.0 m V 100 V (c) Using the expression for the capacitance of a parallel-plate capacitor: 0 C A d For correct substitutions 8.85 10 1 C N m 0.3 m C 0.0 m 10 C 1.3 10 F (d) Using the expression for the force and substituting: F qe 1.6 10 19 C 5000 N C For the correct magnitude of the force For the correct direction 16 F 8.0 10 N to the right Copyright 00 by College Entrance Examination Board. All rights reserved. 11
00 FORM B SCORING GUIDELINES Question 5 (cont d.) (e) The potential difference between the center and one of the plates is 50 V For correctly equating the work to the kinetic energy, and using 50 V for the potential difference 1 W qv mυ Solving for υ: 19 31 υ qv m 1.610 C 50 V 9.11 10 kg 6 υ 4. 10 m s Alternate solution For determining the acceleration 16 31 14 a F m 810 N 9.1110 kg 8.8 10 m s Using an applicable kinematic equation f 0 υ υ ad 14 f υ 0 8.8 10 m s 0.01 m 6 υ 4. 10 m s Distribution of Alternate Copyright 00 by College Entrance Examination Board. All rights reserved. 1
00 FORM B SCORING GUIDELINES Question 6 10 total Distribution of (a) 3 For using the equation for an ideal gas pv nrt p nrt V For correct substitutions p 4.5 mol 8.31J mol K 300 K 8 10 m 6 p 1.40 10 Pa 3 3 (b) 3 For the correct relationship between pressures and temperatures at constant volume p1 p T1 T Solving for p : p1t p T1 For substituting the value of p1 from part (a) 1.40 10 6 Pa73 K p 300 K 6 p 1.8 10 Pa Alternate solution For using the equation for an ideal gas pv nrt p nrt V For correct substitutions 3 3 4.5 mol8.31j mol K73 K 8 10 m p 6 p 1.8 10 Pa Alternate Copyright 00 by College Entrance Examination Board. All rights reserved. 13
00 FORM B SCORING GUIDELINES Question 6 (cont d.) (c) 4 Distribution of For using the mass of the water times its heat of fusion as the total heat used in melting ice For using the correct expressions for the heat lost by the canister and neon m L nc T m c T w w n s s ncnt mscst mw Lw For using the correct T 4.5 mol1.5 J mol K300 K 73 K1.0 kg448 J kg K300 K 73 K m w 5 3.33 10 J kg m 0.440 kg w Copyright 00 by College Entrance Examination Board. All rights reserved. 14
00 FORM B SCORING GUIDELINES Question 7 10 total Distribution of (a) 5 For using the expression for debroglie wavelength λ h p or hmυ Determining the speed from the kinetic energy K: 1 K mυ υ Km For including the conversion of K from ev to joules For correctly determining the velocity 19 31 6 υ 3.70 ev 1.6 10 J ev 9.1110 kg 1.14 10 m s For correctly substituting this velocity into the equation for the wavelength 6.63 10 34 J s 9.11 10 31 kg 1.14 10 6 m s λ 10 λ 6.38 10 m (b) For using the correct equation relating wavelength to energy, or an equivalent combination of equations λ hc E (or a combination such as E hf and f c λ ) The energy E is equal to the kinetic energy of the electrons. Substituting for hc and E: 1.4 10 3 ev nm 3.70 ev λ or equivalent calculation using joules λ 335 nm Copyright 00 by College Entrance Examination Board. All rights reserved. 15
00 FORM B SCORING GUIDELINES (c) 3 Question 7 (cont d.) 4.9 ev Distribution of 3.7 ev E1 3.7 ev E 4.9 ev E3 1. ev 0 ev For a diagram with correctly labeled levels or some identification of the relative energies For an indication of the additional transition of 1. ev Copyright 00 by College Entrance Examination Board. All rights reserved. 16