ap04_sg_b_physb_37099

ap04_sg_b_physb_37099 - AP® Physics B 2004 Scoring...

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Unformatted text preview: AP® Physics B 2004 Scoring Guidelines Form B The materials included in these files are intended for noncommercial use by AP teachers for course and exam preparation; 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. This permission does not apply to any third-party copyrights contained herein. These materials and any copies made of them may not be resold, and the copyright notices must be retained as they appear here. 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 4,500 schools, colleges, universities, and other educational organizations. Each year, the College Board serves over three 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. For further information, visit www.collegeboard.com Copyright © 2004 College Entrance Examination Board. All rights reserved. College Board, Advanced Placement Program, AP, AP Central, AP Vertical Teams, APCD, Pacesetter, Pre-AP, SAT, Student Search Service, and the acorn logo are registered trademarks of the College Entrance Examination Board. PSAT/NMSQT is a registered trademark of the College Entrance Examination Board and National Merit Scholarship Corporation. Educational Testing Service and ETS are registered trademarks of Educational Testing Service. Other products and services may be trademarks of their respective owners. For the College Board’s online home for AP professionals, visit AP Central at apcentral.collegeboard.com. AP PHYSICS B 2004 SCORING GUIDELINES (Form B) General Notes about 2004 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 © 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). 2 AP PHYSICS B 2004 SCORING GUIDELINES (Form B) Question 1 15 points total (a) Distribution of points 4 points For any indication of conservation of energy For a correct conservation equation for this situation 12 1 mu + mgh0 = mu 2 + mghA A 20 2 2 u 2 = u0 + 2 g ( h0 - hA ) A For the correct substitutions u2 A ( 1 point 1 point 1 point ) = (1.5 m s ) + 2 9.8 m s (2.0 m - 1.9 m ) 2 2 2 u A = 4.2 ( m s ) (or 4.3 ( m s )2 using g = 10 m s 2 ) For the correct answer u A = 2.0 m s (or 2.1 m s if u 2 was not rounded or if g = 10 m s 2 was used) A 2 (b) 2 points For each correctly drawn and labeled force One point earned for correct forces was deducted for having any extraneous forces. (c) 1 point 1 pt each 3 points For indicating that the sum of the forces equals the centripetal force mu 2 A F= Â r For having the correct relative signs in the application of the above equation mu 2 A mg - N = r For solving for the normal force, substituting, and solving correctly mu 2 A N = mg r ( N = (0.50 kg ) 9.8 m s N = 2.7 N 2 )- 1 point 1 point 1 point (0.50 kg ) (4.21(m s )2 ) 0.95 m 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). 3 AP PHYSICS B 2004 SCORING GUIDELINES (Form B) Question 1 (continued) Distribution of points (d) 3 points For any indication that the work done must equal the kinetic energy at point A in the absence of friction 1 Wfriction = - mu 2 2A For correct substitution 1 Wfriction = - (0.50 kg ) 4.2 ( m s )2 2 For the correct answer, including the negative sign Wfriction = -1.1 J ( (e) ) 1 point 1 point 1 point 3 points Method 1: For indicating that one should decrease the radius of the curve of the second hill mu 2 A £ 0 . Decreasing the radius of the curve The cart will lose contact when mg r will cause the second term to increase and thus meet the condition. mu 2 A For referring to the equation N = mg r For indicating that the cart will loose contact when N £ 0 Method 2: For indicating that one should make the initial hill higher or the second hill lower mu 2 A £ 0 . Increasing the difference in The cart will loose contact when mg r heights will cause the speed at A to increase, and thus the second term will increase and the condition will be met. mu 2 A For referring to the equation N = mg and indicating that the cart will r loose contact when N £ 0 For indicating that the speed at A will increase 1 point 1 point 1 point (1 point) (1 point) (1 point) 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). 4 AP PHYSICS B 2004 SCORING GUIDELINES (Form B) Question 2 15 points total (a) Distribution of points 4 points For calculating the length of time t1 that the diving bell is accelerating (i.e. the time it takes to reach the constant speed uc ) uc = at1 t1 = uc a ( 1 point ) t1 = (2.0 m s) 0.10 m s2 = 20 s For calculating the distance the bell descends while accelerating 12 d1 = at1 2 1 2 d1 = 0.10 m s2 (20 s) = 20 m 2 The bell therefore descends a distance d 2 = 80 m - 20 m = 60 m at the constant speed. For calculating the time to descend this 60 m d2 = uc t2 ( 1 point ) 1 point t2 = d 2 uc t2 = (60 m ) (2.0 m s) = 30 s For calculating the total time ttot = t1 + t2 = 20 s + 30 s ttot = 50 s (b) 1 point 3 points For a correct expression for the weight of the water above the cross-sectional area A w = rVg = r Ahg For correct substitution w = 1025 kg m3 9.0 m 2 (80 m ) 9.8 m s 2 1 point For the correct answer, including units w = 7.2 ¥ 106 N (or 7.4 ¥ 106 N using g = 10 m s 2 ) 1 point ( )( ) ( ) 1 point Full credit could also be earned for determining the pressure due to the water alone, and using F = PA to determine the weight A maximum of 2 points could be earned for only determining the mass of the water, or for calculating the absolute pressure and using F = PA . 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). 5 AP PHYSICS B 2004 SCORING GUIDELINES (Form B) Question 2 (continued) Distribution of points (c) 3 points For indicating that the pressure at a depth h has a term r gh , or using P = w A and the value of the weight from part (b) For indicating that the atmospheric pressure must be added (in correct SI units – otherwise the r gh term must be converted to atmospheres for full credit) P = ( w A) + Patm ( 1 point 1 point ) P = 7.2 ¥ 106 N 9.0 m 2 + 1.0 ¥ 105 N m 2 For the correct answer, including units P = 9.0 ¥ 105 N m 2 (or 9.2 ¥ 105 N m 2 using g = 10 m s 2 ) (d) 1 point 3 points For a correct expression for the force on an area Ahatch F = PAhatch For a correct expression for the area of the hatch Ahatch = p r 2 Since there is one atmosphere pressure inside the diving bell, the net pressure corresponding to the minimum applied force is that from the water only. Fmin = r ghAhatch Substituting: Fmin = 1025 kg m3 9.8 m s 2 (80 m ) p (0.25 m )2 1 point For the correct answer Fmin = 1.6 ¥ 105 N 1 point ( )( ) ( 1 point ) Since the question could have been interpreted as asking for the minimum total force required, full credit was awarded for including atmospheric pressure. (e) 2 points For a correct modification that would reduce the force necessary to open the hatch For a correct justification Examples: Increase the pressure inside the diving bell. The internal pressure would then compensate for atmospheric pressure plus some of the pressure of the water, reducing the force needed. Reduce the size of the hatch. Pressure times a smaller area yields a smaller force. Use a tool that gives a mechanical advantage, such as a lever. Such a tool is designed so that one exerts a smaller force over a larger distance than one would without it. 1 point 1 point 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). 6 AP PHYSICS B 2004 SCORING GUIDELINES (Form B) Question 3 15 points total (a) Distribution of points 4 points There must be a node at the liquid surface and an antinode near the top of the tube, so the length of consecutive resonances differ by a half wavelength. For equating the difference in air column lengths to the difference in the number of wavelengths l L2 - L1 = 2 l = 2 ( L2 - L1 ) For correct substitution and answer l = 2 (0.80 m - 0.25 m ) l = 1.1 m A maximum of 3 points was awarded for using only one of the air column lengths to calculate a wavelength A maximum of 2 points was awarded for equating the difference in air column lengths to one or one-quarter wavelength (b) 1 point 2 points For using the relationship between wavelength, speed, and frequency f = uair l For correct substitutions (using l from part (a)) and a corresponding correct answer f = (343 m s) (1.1 m ) f = 312 Hz (c) 3 points 1 point 1 point 3 points For indicating the need to use the values of the wave properties appropriate for water lwater = uwater f water For indicating that the frequency in water is the same as in air For correct substitution and answer (1490 m s ) lwater = 312 Hz lwater = 4.8 m 1 point 1 point 1 point 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). 7 AP PHYSICS B 2004 SCORING GUIDELINES (Form B) Question 3 (continued) Distribution of points (d) 3 points 1 L3 is approximately 1 wavelengths, which is one-half wavelength longer than L2 4 For any indication that L3 equals L2 + l 2 or L1 + l 1.1 m L3 = 0.80 m + 2 For the correct answer (using whatever wavelength was determined previously) L3 = 1.35 m 2 points 1 point A maximum of 2 points were awarded for using L3 = 5l 2 or L3 = L2 + l One point was awarded for a good drawing of the standing wave in the air column with no calculation. (e) 3 points For indicating that the calculation of frequency was too low For a correct justification For example: As temperature increases, the speed of sound in air increases, so the speed used in part (b) was too low. Since f = uair l , that lower speed of sound yielded a frequency that was too low. 2 points 1 point 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). 8 AP PHYSICS B 2004 SCORING GUIDELINES (Form B) Question 4 15 points total (a) Distribution of points 4 points For a correct expression for the magnitude of the emf per turn in the coil e = D f OR e = B u Dt D e = ADtB = w ( B t- 0) OR e = BDtw D For correct substitutions in either equation (both yield the same value) e = (0.25 m) (0.15 m) (0.20 T ) 0.50 s For correct calculation e = 0.015 V per turn For recognizing that with 20 turns the total emf in the coil is 20 times the emf per turn etot = 20 (0.015 V per turn ) = 0.30 V (b) 1 point 1 point 1 point 2 points For correct expression for Ohm’s law, substitution from part (a), and magnitude V = IR 0.30 V V = = 0.06 A I= 5.0 W R For correct direction, i.e., counterclockwise (c) 1 point 1 point 1 point 3 points For a correct expression for the power dissipated in the coil P = IV OR P = I 2 R OR P = V 2 R For correct substitution of answers from (a) and/or (b) into one of these expressions (Must recognize that V = etot ) For example, P = (0.06 A ) (0.30 V ) For correct calculation including correct units P = 0.018 W 1 point 1 point 1 point 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). 9 AP PHYSICS B 2004 SCORING GUIDELINES (Form B) Question 4 (continued) Distribution of points (d) 3 points The force on the right side is zero, and forces on the top and bottom sides cancel, so the net force is that on the left side. For the correct expression for the force on a straight wire (force per turn in this situation) in a magnetic field F = BI sin q OR F = BI (recognizing that the wire is perpendicular to the field) For correct substitutions F = (0.20 T ) (0.60 A ) ( 0.15 m ) F = 0.0018 N For recognizing that with 20 turns the total force on the left side of the coil is 20 times the force per turn Ftot = 0.036 N Alternate Solution For using one of the equations P = F u sin q W Fd OR P = = t t P Pt OR F = d u sin q For correct substitutions (both approaches yield same value) (0.018 W ) (0.50 s) Ftot = 0.25 m For correct answer Ftot = 0.036 N 1 point 1 point 1 point Alternate points 1 point F= (e) 1 point 1 point 3 points For recognition that doubling the number of turns doubles the total emf, which would tend to increase the current For recognition that doubling the number of turns doubles the total resistance, which would tend to decrease the current For putting these together to show that the current is unchanged e f 2ei ei If = = = = Ii 2 Ri Ri Rf 1 point 1 point 1 point Note: The third point was awarded for an indication that the current is unchanged, even if the justification was wrong. 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). 10 AP PHYSICS B 2004 SCORING GUIDELINES (Form B) Question 5 10 points total (a) Distribution of points 2 points For recognizing that PA = PB At point A: PV1 = nRT1 1 V At point B: P 1 = nRT2 1 2 Dividing these equations and solving for T2 : PV1 T 1 =1 V1 T2 P 1 2 1 point T1 T2 For the correct answer T2 = T1 2 2= (b) 1 point 2 points Answer can be obtained by either comparing points B & C or points A & C using the ideal gas law at each point For recognizing that TC = 2TB OR TC = TA 1point Comparing points B & C V T At point B: P 1 = nR 1 1 2 2 V1 At point C: P2 = nRT1 2 Dividing the equations and solving for P2 : V T P1 nR 1 1 2= 2 V1 nRT1 P2 2 Comparing points C & A P 1 1 = 2 P2 For the correct answer P2 = 2 P 1 2P 1 =1 P2 For the correct answer P2 = 2 P 1 At point A: PV1 = nRT1 1 V1 = nRT1 2 Dividing the equations and solving for P2 : At point C: P2 PV1 1 =1 V P2 1 2 1 point 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). 11 AP PHYSICS B 2004 SCORING GUIDELINES (Form B) Question 5 (continued) Distribution of points (c) 2 points For correct equation for work done on the gas (regardless of sign) OR for recognition that work is the area under the line AB on the graph. (No work is done from B to C because the change in volume is zero.) W = - P DV ÊV ˆ W = - P Á 1 - V1 ˜ 1 Ë2 ¯ For the correct answer including correct sign PV W= 11 2 (d) 1 point 1 point 4 points Heat was added to the gas in processes BC and CA, but not in AB. For two or three correct indications of whether or not heat was added to the gas in each process (The absence of a check mark was taken as in indication that heat was not added.) 1 point For a reasonable justification for process AB. This point was awarded only if this process was indicated correctly (i.e., not checked) Example: The volume decreases so the work done on the gas is positive. The temperature decreases so the change in internal energy is negative. Therefore Q = DU - W is negative. Heat is expelled from the gas. (Note: Answer must mention work for credit.) 1 point For a reasonable justification for process BC. This point was awarded only if this process was indicated correctly (i.e., checked) Example: There is no change in volume so no work is done. The temperature increases so the internal energy increases. Therefore Q = DU - W is positive. (This point also awarded for only referring to increasing temperature or for referring to increasing speed of the molecules.) 1 point For a reasonable justification for process CA. This point was awarded only if this process was indicated correctly (i.e., checked). Example: There is no change in temperature or internal energy. The volume increases so work is done by the gas. Heat needs to be added to the gas to do this work. 1 point 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). 12 AP PHYSICS B 2004 SCORING GUIDELINES (Form B) Question 6 10 points total (a) Distribution of points 3 points For a smooth curve passing through or very close to all plotted points Partial credit points could be awarded for curves of lesser quality. For example: Showing all the data points connected by straight-line segments earned 2 points. Curves that generally fit the data points at small angles, but are concave upward for the whole range earned 1 or 2 points depending on how badly the curve misses the points at higher angles. A single straight “best fit” line or really bad curve earned 1 point. A curve that was monotonically decreasing earned no points. 3 points 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). 13 AP PHYSICS B 2004 SCORING GUIDELINES (Form B) Question 6 (continued) Distribution of points (b) 3 points For reading the wavelength shift from the graph From the graph shown, the wavelength shift at 120∞ is 8.000 ¥ 10 -17 m . The photon loses energy, which means the wavelength increases. For adding (not subtracting) the wavelength shift to the original wavelength ls = 1.400 ¥ 10 -14 m + 8.000 ¥ 10 -17 m For correct answer ls = 140.8 ¥ 10 (c) -16 m = 1.41 ¥ 10 -14 1 point 1 point m 2 points For using the de Broglie equation to calculate momentum (even if a value from (b) that was actually Dl was substituted) ls = h p s OR p = h l ps = h ls ( ps = 6.63 ¥ 10-34 J is 1 point ) (1.408 ¥ 10-14 m) For consistent answer including correct units ps = 4.71 ¥ 10-20 kg i m s Note: The answer point could also be awarded if the value of ls = li - Dl was used instead of the correct relationship. (d) 1 point 1 point 2 points For use of conservation of energy DEnuc = - DE photon DE photon = D ( hf ) = D ( hc ) OR DE l 1 point photon = D ( pc ) = D ( hc ) l 1ˆ Ê hc hc ˆ Ê1 DEnuc = - Á - ˜ = hc Á - ˜ Ë ls Ë li li ¯ ls ¯ ( ) 1 1 ˆ DEnuc = 1.99 ¥ 10 -25 J ◊ m Ê Á ˜ -14 Ë 1.400 ¥ 10-14 m 1.408 ¥ 10 m¯ For the correct answer DEnuc = 8.08 ¥ 10 -14 J (or 510 keV) 1 point Note: The answer point was awarded for correct use of whatever ls was obtained from part (b), but not for using the value of Dl . 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). 14 ...
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This note was uploaded on 02/25/2010 for the course PHY 15166 taught by Professor Mr.donald during the Spring '10 term at 4.1.

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