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_ap05_sg_physicsb__46638 - AP® Physics B 2005 Scoring...

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Unformatted text preview: AP® Physics B 2005 Scoring Guidelines The College Board: Connecting Students to College Success The College Board is a not-for-profit membership association whose mission is to connect students to college success and opportunity. Founded in 1900, the association is composed of more than 4,700 schools, colleges, universities, and other educational organizations. Each year, the College Board serves over three and a half million students and their parents, 23,000 high schools, and 3,500 colleges through major programs and services in college admissions, 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 excellence and equity, and that commitment is embodied in all of its programs, services, activities, and concerns. Copyright © 2005 by College Board. All rights reserved. College Board, AP Central, APCD, Advanced Placement Program, AP, AP Vertical Teams, Pre-AP, SAT, and the acorn logo are registered trademarks of the College Entrance Examination Board. Admitted Class Evaluation Service, CollegeEd, Connect to college success, MyRoad, SAT Professional Development, SAT Readiness Program, and Setting the Cornerstones are trademarks owned by the College Entrance Examination Board. PSAT/NMSQT is a registered trademark of the College Entrance Examination Board and National Merit Scholarship Corporation. Other products and services may be trademarks of their respective owners. Permission to use copyrighted College Board materials may be requested online at: http://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 and Pre-AP: apcentral.collegeboard.com. AP® PHYSICS B 2005 SCORING GUIDELINES General Notes About 2005 AP Physics Scoring Guidelines 1. The solutions contain the most common method(s) of solving the free-response questions and the allocation of points for these solutions. Other methods of solution also receive appropriate credit for correct work. 2. 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 value g = 9.8 m s 2 , but use of 10 m s 2 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, suppose a solution requires subtracting two numbers that should have five significant figures and that differ starting with the fourth digit (e.g., 20.295 and 20.278). Rounding to three digits will lose the accuracy required to determine the difference in the numbers, and some credit may be lost. Copyright © 2005 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). 2 AP® PHYSICS B 2005 SCORING GUIDELINES Question 1 10 points total (a) Distribution of points 4 points The velocities can be found from the slope of the position graph. For showing a positive velocity of magnitude 1.5 m s (i.e., 12 m 8 s) between 0 s and 8 s inclusive For showing zero velocity between 10 s and 18 s inclusive For showing a negative velocity of magnitude 2.4 m s (i.e., 12 m 5 s) between 20 s and 25 s inclusive For showing two nonvertical transition regions; between t = 8 s and 10 s and between t = 18 s and 20 s 1 point 1 point 1 point 1 point Copyright © 2005 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). 3 AP® PHYSICS B 2005 SCORING GUIDELINES Question 1 (continued) Distribution of points (b) (i) 3 points For a definition or equation for average acceleration aavg = Du Dt OR u = u0 + at 1 point For the correct substitution from part (a) aavg = (0 - 1.5 m s) 2 s 1 point For the correct answer including units and sign aavg = -0.75 m s2 1 point (ii) 1 point For a correctly drawn vector, with or without a label (c) 1 point 2 points The acceleration is zero, so the normal force (apparent weight) is equal to the gravitational force. For a correct relationship leading to a calculation of apparent weight N = W = mg OR N - W = ma ( Wapp = (70 kg ) 9.8 m s2 1 point ) For the correct answer with units 1 point Wapp = 686 N (or 700 N using g = 10 m s ) 2 Copyright © 2005 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). 4 AP® PHYSICS B 2005 SCORING GUIDELINES Question 2 10 points total (a) Distribution of points 2 points For each correctly drawn and labeled tension, with arrowhead in right direction One point was deducted for each of the following until score reached zero: No force of gravity Each extraneous force Any missing labels Drawing all forces along correct lines with labels but no arrowheads received only one point. Components of the tension in the pendulum string could be included in addition to or instead of the net tension, as long as they were clearly labeled as such. (b) 1 point each 4 points For any indication that the net force is zero For an attempt to determine the components of the tension in the pendulum string For correctly determining these components Th = T p sin 30∞ 1 point 1 point 1 point mg = T p cos 30∞ Th sin 30∞ = = tan 30∞ cos 30∞ mg Th = mg tan 30∞ ( ) Th = (1.8 kg ) 9.8 m s2 tan 30∞ For the correct answer with units Th = 10 N 1 point Copyright © 2005 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). 5 AP® PHYSICS B 2005 SCORING GUIDELINES Question 2 (continued) Distribution of points (b) (continued) Alternate solution Alternate points For indicating that the addition of the three force vectors gives a 30-60-90 right triangle 2 points For a correct trigonometric relationship between forces 1 point Th = tan 30∞ mg For the correct answer with units 1 point Th = 10 N If no forces were drawn in part (a), one point could be earned for writing the component equations T = mg sin q and T = mg cos q , and two points for T = mg tan q . (c) 4 points For any indication of conservation of energy For any indication of the need to use a change in height 12 1 mgh0 + mu0 = mgh f + mu 2 f 2 2 For setting u0 = 0 1 point 1 point 1 point 12 mu f = mg Dh 2 u f = 2 g Dh Dh = L - L cos 30∞ u f = 2 gL (1 - cos 30∞) ( ) u f = 2 9.8 m s2 (2.3 m ) (1 - cos 30∞) For the correct answer, with units u f = 2.5 m s 1 point 2 A solution that used the kinematic equation u 2 = u0 + 2as could only receive full credit if f the student explained how the equation is equivalent to conservation of energy. Copyright © 2005 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). 6 AP® PHYSICS B 2005 SCORING GUIDELINES Question 3 15 points total (a) Distribution of points 4 points For use of the correct formula for the electric field E q q 1 E= E=k 2 OR 4p 0 r 2 r For adding the two E vectors from the charges qˆ Ê 2q ˆ Ê EO = Á + k 2 ˜ + Á - k 2 ˜ Ë a¯ Ë a¯ For the correct (positive) expression for the magnitude of the field q EO = k 2 a For any indication that the field is in the +y-direction (b) 1 point 1 point 1 point 1 point 3 points For use of the correct formula for the potential V q 1q V =k V= OR r 4p 0 r For adding the two potentials 2q q VO = k +k a a For the correct (positive) answer 3kq VO = a (c) (i) and (ii) 1 point 1 point 1 point 4 points For determining the distance r between charges in terms of x0 and a in either part (i) or (ii) 1 point 2 r = x0 + a 2 For use of Coulomb’s law in either part (i) or (ii) 1 point F=k q1 q2 r2 For both correct substitution of charges into Coulomb’s law and correct substitution of the previously determined expression for r in either part (i) or (ii) For correct (positive) answer for both part (i) and (ii) For part (i): Fq = k For part (ii): Fq = k (- q ) (q ) 2 x0 + a 2 =k ( - q ) (2 q ) 2 x0 + a 2 1 point 1 point q2 2 x0 + a 2 =k 2q2 2 x0 + a 2 Copyright © 2005 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). 7 AP® PHYSICS B 2005 SCORING GUIDELINES Question 3 (continued) Distribution of points (d) 4 points For having all three vectors on the same side of the x-axis (i.e., recognizing that the vertical components should all be in the same direction) For a single resultant vector from A pointing down and to the right, toward a point below the x-axis and above +2q For a single resultant vector from C pointing down and to the left, toward a point below the x-axis and above +2q For a single resultant vector pointing straight down from B 1 point 1 point 1 point 1 point Magnitudes of the vectors and any components that may have been drawn were not evaluated. Copyright © 2005 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). 8 AP® PHYSICS B 2005 SCORING GUIDELINES Question 4 15 points total (a) Distribution of points 2 points For checking any length-measuring device and not the stopwatch Only one point was awarded for checking any length-measuring device and the stopwatch. No points were awarded if no length-measuring device was checked or all the equipment was checked. (b) 2 points 3 points For a diagram including at least a laser, a slide, and a screen For correctly labeling the equipment For correctly identifying the two distances to be measured, with symbols 1 point 1 point 1 point Example diagram: Copyright © 2005 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). 9 AP® PHYSICS B 2005 SCORING GUIDELINES Question 4 (continued) Distribution of points (c) 3 points Points could only be earned in the following order, with each successive point dependent on earning the previous point. For a central maximum For a continuous graph with approximately equally spaced maxima For nothing else incorrect (e.g., no negative intensity) (d) 1 point 1 point 1 point 4 points For appropriate use of equipment (including all items checked in (a)) For indicating a measurement of the distance from the slits to the screen For indicating appropriate measurements of the maxima (e.g., the distance between adjacent maxima or the distance of successive maxima from the center) For a complete and clear description For example: Set up the laser to shine on the slide, and set the screen far away on the other side of the slide. Measure the distance L from the slide to the screen with the tape measure. Use the ruler to measure the distance x between adjacent maxima. 1 point 1 point 1 point 1 point Copyright © 2005 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). 10 AP® PHYSICS B 2005 SCORING GUIDELINES Question 4 (continued) Distribution of points (e) 3 points Points could only be earned in the following order, with each successive point dependent on earning the previous point. For using appropriate equations For explicitly identifying, in some other part of the question, the symbols used here For correct correlation of symbols in equations to symbols in diagram in part (b) x ml L OR d sin = ml and tan q = m (since sin q ª tan q for small angles), xm ª L d where m is an integer, xm is the distance of a maximum of order m from the central maximum, l is the wavelength, L is the distance between slits and the screen, and d is the slit separation Solving for d lL dª using distances x between adjacent maxima and Dm = 1 x ml L OR d ª using distances from center of pattern xm 1 point 1 point 1 point Copyright © 2005 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). 11 AP® PHYSICS B 2005 SCORING GUIDELINES Question 5 10 points total (a) Distribution of points 3 points For an equation that uses the ratio of densities rr rw to find the fraction of the total volume (or height) submerged 1 point The weight of the raft equals the weight of the displaced water. Wr = Ww mr g = mw g rrVr g = rwVw g Solving for the volume of displaced water, which equals the submerged volume of the raft r Vw = r Vr rw For recognizing that the submerged volume (or height) must be subtracted from the total volume (or height) Vsubmerged = Ah = Vr - Vw Ah = Vr h= Vr A 1 point rr rˆ Ê Vr = Vr Á 1 - r ˜ Ë rw rw ¯ rr ˆ Ê Á1 - r ˜ Ë w¯ 650 kg m3 ˆ 1.8 m 3 Ê 1Ë ¯ 8.2 m 2 Á 1000 kg m3 ˜ For the correct answer h= 1 point h = 0 .07 7 m Some students misinterpreted the statement about the volume of the raft, taking it to mean the volume of the part above the water instead of the total volume. If the solution to part (b) showed work that demonstrated understanding of the concepts needed for part (a), appropriate credit for this part was awarded. Copyright © 2005 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). 12 AP® PHYSICS B 2005 SCORING GUIDELINES Question 5 (continued) Distribution of points (b) 4 points For indicating that the buoyant force is equal to the weight of the raft Fbuoy = Wr For correct substitutions for calculating the buoyant force, either by directly calculating the raft’s weight or calculating the weight of the displaced water ( ) (1.80 m ) (9.8 m s ) OR Fbuoy = rwVw g = (1000 kg m 3 ) (1.17 m 3 ) (9.8 m s2 ) Fbuoy = rrVr g = 650 kg m 3 3 1 point 1 point 2 For the correct answer with units 1 point Fbuoy = 1.15 ¥ 10 N (or 1.17 ¥ 10 N using g = 10 m s ) 4 2 4 For indicating that the direction of the buoyant force is up (c) 1 point 3 points The additional weight that can be carried is equal to the weight of water displaced by the part of the raft now above water. For indicating a correct equation for the net force Waddl = Wextra water OR Waddl = FbuoyNEW - Wraft 1 point The first equation above yields Waddl = rwVtop g = rw Ahg Substituting the algebraic expression for h from part (a) and simplifying yields Waddl = rwVr g - rrVr g = Vr g ( rw - rr ) , which is equivalent to substitution into the second equation above. For correct numerical substitutions to get the weight (or mass) of the top of the raft ( Waddl = 1.80 m 3 ) (9.8 m s ) (1000 kg 2 m - 650 kg m 3 3 ) Waddl = 6200 N (variation due to rounding earlier on was accepted) For dividing the total weight (or mass) by the weight (or mass) of a person and indicating the correct number of people that the raft can carry. (The final answer must indicate a whole number of people.) W 6200 N n = addl = = 8.4 mp g (75 kg ) 9.8 m s2 ( 1 point 1 point ) A maximum of 8 people can be on the raft. Copyright © 2005 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). 13 AP® PHYSICS B 2005 SCORING GUIDELINES Question 6 10 points total (a) Distribution of points 2 points For writing the ideal gas equation of state PV = nRT For an indication that V = AH PAH = nRT nR H= T PA Note: Simply writing PAH = nRT or the equivalent earned both points. If the student tried to rearrange the equation, algebra mistakes were not penalized in this part. (b) 1 point 1 point 4 points For labeling both axes with linear numerical scales For having neither axis labeled with its scale starting at zero (no penalty for showing zero at the end of an axis and a “break” in the axis) For accurately plotting five data points that closely fit a straight line with a positive slope One point was lost if some points were inaccurately plotted. Both points were lost if the data points were not visible, even if a line was drawn. 1 point 1 point 2 points Example answer shown below. The question did not ask for a best-fit line, and it was not required for this part. However, a line is shown in the example, since it could be used in the determination of n. Copyright © 2005 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). 14 AP® PHYSICS B 2005 SCORING GUIDELINES Question 6 (continued) Distribution of points (c) 4 points nR T PA For any clear indication that the student used more than one data point For example: Setting up a slope calculation using subtraction, averaging calculated values for n or the ratio H T , or using a linear regression on the calculator For the correct slope of a best-fit line through the data points (this point not awarded if slope method not used) For correct substitutions into a correct expression containing n using consistent units for the values of P, R, A, and H Example using the line shown above, which happens to go through the first and last data points nR Slope of line = PA (1.47 - 1.11) m 0.36 m Slope = = (405 - 300 ) K 105 K From part (a), H = n= PA (slope ) R 1 ¥ 105 Pa 0.027 m 2 ( )( ) ( 1 point 1 point ) 0.36 m 105 K 8.31 J (moliK ) For a numerical answer that follows from substitutions into the correct expression above n = 1.11 moles n= 1 point 1 point Copyright © 2005 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). 15 AP® PHYSICS B 2005 SCORING GUIDELINES Question 7 10 points total (a) Distribution of points 4 points For a correct calculation of the photon frequency c f= l ( f = 3.00 ¥ 108 m s 1 point ) (1.219 ¥ 10-7 m) = 2.46 ¥ 1015 Hz For correct calculation of the photon energy in electron-volts or joules ( Eph = hf = 4.14 ¥ 10 -15 )( eV is 2.46 ¥ 10 15 ) Hz = 10.2 eV OR 1 point 1.63 ¥ 10 -18 J The two points above were also awarded for correctly using E = hc l or using E = pc and the answer from part (b). For indicating that the photon energy is the difference between the two energy levels E4 = E2 + Eph 1 point E4 = -13.6 eV + 10.2 eV For the correct numerical answer E4 = -3.4 eV OR -5.44 ¥ 10 -19 J 1 point Alternate solution For use of energy levels and the Bohr model* En = E1 n2 For identifying the ground state energy E1 = -54.4 eV For using the correct quantum number n=4 For the correct answer E4 = -3.4 eV Alternate points 1 point 1 point 1 point 1 point *Note: This equation is not on the equation sheet, nor is the Bohr model part of the Physics B curriculum. However, students were given credit for this correct solution. (b) 2 points p=hl OR p=Ec For substitution of appropriate values into either of the above equations ( p = 6.63 ¥ 10 -34 J is ) (121.9 ¥ 10 -9 m ) OR ( p = 1.63 ¥ 10 For the correct answer with correct units p = 5.44 ¥ 10 -27 kgim s (or 3.40 ¥ 10 -18 J ) (3.00 ¥ 10 8 ms ) 1 point 1 point -8 eVis m ) Copyright © 2005 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). 16 AP® PHYSICS B 2005 SCORING GUIDELINES Question 7 (continued) Distribution of points (c) 2 points K max = Eph - f For correct substitution of photon energy from part (a), or a calculation of it K max = 10.2 eV - 4.7 eV For the correct answer in eV K max = 5.5 eV (d) 1 point 1 point 2 points K max = W = qV For using the definition of an eV as the work required to move a charge e through a 1-volt potential difference For the correct answer with units of volts V = 5.5 V Alternate solution For understanding the relationship between electrical potential and energy V = K max q ( V = (5.5 eV ) 1.6 ¥ 10 -19 J eV 1 point 1 point Alternate points 1 point ) (1.6 ¥ 10-19 C) 1 point For the correct answer with units of volts V = 5.5 V Copyright © 2005 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). 17 ...
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