ap07_physics_b_form_b_sgs_complete

Ap07_physics_b_form_ - AP® Physics B 2007 Scoring Guidelines Form B The College Board Connecting Students to College Success The College Board is

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Unformatted text preview: AP® Physics B 2007 Scoring Guidelines Form B 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 5,000 schools, colleges, universities, and other educational organizations. Each year, the College Board serves seven million students and their parents, 23,000 high schools, and 3,500 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. © 2007 The College Board. All rights reserved. College Board, Advanced Placement Program, AP, AP Central, SAT, and the acorn logo are registered trademarks of the College Board. PSAT/NMSQT is a registered trademark of the College Board and National Merit Scholarship Corporation. 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. AP® PHYSICS B (Form B) 2007 SCORING GUIDELINES General Notes About 2007 AP Physics Scoring Guidelines 1. The solutions contain the most common method of solving the free-response questions and the allocation of points for this solution. Some also contain a common alternate solution. 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. However, when students are asked to derive and expression it is normally expected that they will begin by writing one or more fundamental equations, such as those given on the AP Physics exam equation sheet. For a description of the use of such terms as “derive” and “calculate” on the exams, and what is expected for each, see “The Free-Response Sections⎯Student Presentation” in the AP Physics Course Description . 4. The scoring guidelines typically show numerical results using the value g = 9.8 m s2 , but use of 10 m s 2 is of course also acceptable. Solutions usually show numerical answers using both values when they are significantly different. 5. Strict rules regarding significant digits are usually not applied to numerical answers. However, in some cases answers containing too many digits may be penalized. In general, two to four significant digits are acceptable. Numerical answers that differ from the published answer due to differences in rounding throughout the question typically receive full credit. Exceptions to these guidelines usually occur 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. © 2007 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for AP students and parents). AP® PHYSICS B 2007 SCORING GUIDELINES (Form B) Question 1 15 points total (a) Distribution of points 4 points For each of the forces above with arrow correctly drawn and labeled, 1 point was awarded Notes: The force vector T could be shown in component form or as one force, but not both. For extraneous forces, 1 point was deducted. (b) 4 points 4 points  Fy = 0 N + T sin q - mg = 0 For a correct force equation N = mg - T sin q For calculating the mg term correctly For calculating the T sin q term correctly ( 1 point 1 point 1 point ) N = (15 kg + 5 kg) 9.8 m s2 - ( 55 N ) sin 20∞ For the correct numerical answer with units 1 point N = 177 N (181 N if g = 10 m s is used) 2 (c) 3 points  Fx = ma For a correct Newton’s second law equation involving horizontal forces T cos q - f = ma T cos q - f m For the correct relationship between the frictional and normal forces f = mN For correct calculation of the frictional force using the value of N from part (b) 1 point a= 1 point 1 point f = ( 0.22) (177 N) = 38.9 N (39.8 N if g = 10 m s is used) (55 N) cos 20∞ - 38.9 N a= 20 kg 2 a = 0.64 m s2 ( 0.59 m s2 if g = 10 m s2 is used) © 2007 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents). AP® PHYSICS B 2007 SCORING GUIDELINES (Form B) Question 1 (continued) Distribution of points (d) 2 points For the correct work equation W = (T cos q ) d For substituting the correct displacement W = ( 55 N ) cos 20∞ ( 7.0 m ) W = 360 J (e) 1 point 1 point 2 points For each section of the graph correctly drawn as above, 1 point was awarded. Note: The second point was awarded only if the change at tr was abrupt. 2 points © 2007 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents). AP® PHYSICS B 2007 SCORING GUIDELINES (Form B) Question 2 10 points total Distribution of points (a) (i) 2 points For at least two correct electric field lines in the right directions For the lines going through the entire Region I from top to bottom Note: A single line going from top to bottom could earn a maximum of 1 point. (ii) 2 points For either of the first two equations below qu B = qE u=EB u = ( 4800 N C) ( 0.12 T ) u = 4.0 ¥ 10 4 m s For the correct answer with units (b) 1 point 1 point 1 point 1 point 2 points mu 2 r For the correct equation for the radius mu r= qB For correct substitutions consistent with the answer to (a)(ii) 6.68 ¥ 10 -26 kg 4.0 ¥ 10 4 m s r= 3.2 ¥ 10 -19 C ( 0.12 T ) qu B = ( ( r = 0.070 m )( ) ) 1 point 1 point © 2007 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents). AP® PHYSICS B 2007 SCORING GUIDELINES (Form B) Question 2 (continued) Distribution of points (c) 2 points For indicating that the initial force is “Toward the bottom of the page” For a correct justification indicating that the magnetic force ( FB = qu B ) decreases as 1 point 1 point velocity decreases, while the electric force ( FE = qE ) remains the same, so FE > FB . (d) 2 points For the path in Region I being straight and horizontal For the path in Region II being a circular arc, curving downward 1 point 1 point © 2007 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents). AP® PHYSICS B 2007 SCORING GUIDELINES (Form B) Question 3 15 points total (a) Distribution of points 3 points For a statement of Ohm’s law, recognizing that IC = 0 V = IR For the calculation of the total resistance Rtotal = 1000 W + 500 W = 1500 W For the correct answer, including units 12 V I= = 8.0 ¥ 10 -3 A 1500 W 1 point 1 point 1 point (b) (i) 2 points For the ammeter in series anywhere in the circuit except the capacitor branch (ii) 2 points For the voltmeter in parallel across the 1000 W resistor (c) 2 points 2 points 3 points For a correct equation relating the charge, voltage, and capacitance Q Q = CVC or C = VC For recognizing that the voltage drop across the capacitor is the same as the voltage drop across the 500 W resistor ( 1 point 1 point ) VC = IR500 = 8.0 ¥ 10 -3 A ( 500 W) = 4.0 V For the correct answer with the correct units ( Q = 30 ¥ 10 -6 ) 1 point F ( 4.0 V ) Q = 1.2 ¥ 10 -4 C © 2007 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents). AP® PHYSICS B 2007 SCORING GUIDELINES (Form B) Question 3 (continued) Distribution of points (d) 2 points For a correct equation for the power dissipated V2 P = I 2 R1000 or V1000 I or 1000 R1000 Calculation for the second two relationships ( 1 point ) V1000 = IR1000 = 8.0 ¥ 10 -3 A (1000 W) = 8.0 V For the correct substitutions ( P = 8.0 ¥ 10 -3 A P = 6.4 ¥ 10 (e) -2 ) 2 (1000 W) or (8.0 V) (8.0 ¥ 10 -3 A) or 1 point (8.0 V ) 2 1000 W W 3 points For choosing “Larger” For correct justification in words or with numerical example. For example: 1 point 2 points “Replacing the 500 W resistor with a larger resistor lowers the steady state current, causing the voltage across the 1000 W resistor to decrease and the voltage across the replacement resistor to increase.” (1 point) “The capacitor is in parallel with the replacement resistor, and so its voltage increases and therefore its charge increases since Q = CV .” (1 point) © 2007 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents). AP® PHYSICS B 2007 SCORING GUIDELINES (Form B) Question 4 10 points total (a) Distribution of points 3 points Applying Bernoulli’s equation For example, taking point 1 to be at the top of the liquid and point 2 at the hole 12 12 P + rgy1 + ru1 = P2 + rgy2 + ru2 1 2 2 P = P2 = Patm 1 u1 = 0 12 ru 22 For a correct expression for the speed u2 = 2 g ( y1 - y2 ) For correct substitutions rg ( y1 - y2 ) = ( u2 = 2 9.8 m s 2 ) (0.70 m) For the correct answer, including units u2 = 3.7 m s (b) 1 point 1 point 1 point 2 points For any indication that the volume rate of flow is the area multiplied by the speed Define the symbol V for the volume flow rate. V = uA For correct substitutions V = (3.7 m ) p ( 0.0010 m ) 1 point 1 point 2 V = 1.2 ¥ 10 -5 m3 s (c) 2 points For any indication that the volume is the volume rate multiplied by the time V = Vt For correct substitutions ( V = 1.2 ¥ 10 -5 ) 1 point 1 point m s ( 2 min ) (60 s min ) 3 V = 1.4 ¥ 10 -3 m 3 © 2007 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents). AP® PHYSICS B 2007 SCORING GUIDELINES (Form B) Question 4 (continued) Distribution of points (d) 3 points For using the kinematic equation for distance as a function of time 1 y = y0 + u0t + at 2 2 Taking down as the positive direction, and using a = g and y = h 12 gt + u0t - h = 0 2 For solving the equation for t using the quadratic formula -u0 ± u0 + 2 gh g For correct substitutions Using the + sign to avoid negative time 1 point 2 t= t= 1 point -3.7 m s + 1 point (3.7 m s)2 + 2 (9.8 m s2 ) (0.25 m ) 9.8 m s2 t = 0.062 s Alternate solution For using the kinematic equation relating speed, acceleration, and distance 2 u 2 = u0 + 2 a ( x - x 0 ) For using the kinematic equation for speed as a function of time u = u0 + at Alternate points 1 point 1 point u - u0 a Substituting for u from the initial equation into the above equation for t t= 2 u 0 + 2 a ( x - x 0 ) - u0 t= a For correct substitutions (3.7 m s) + 2 (9.8 m s ) (0.25 m ) - 3.7 m s 2 t= 1 point 2 9.8 m s2 t = 0.062 s © 2007 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents). AP® PHYSICS B 2007 SCORING GUIDELINES (Form B) Question 5 10 points total Distribution of points (a) (i) 3 points For recognition that one component of the force is Patm A For recognition that another component of the force is Mg F = Patm A + Mg For A = p F= (ii) 2 = p D2 4 1 point 1 point Patm p D 2 + Mg 4 1 point For P = Pabs Pabs (b) () D 2 1 point F , with answer to (a) substituted for F A 1 point Patm p D 2 + Mg 4 = p D2 4 4 Mg = Patm + p D2 3 points For checking the “Pressure goes up” answer space For a correct and complete justification, 2 points were awarded, with partial credit given where appropriate Example: For indicating that if heat is added, then the temperature must increase, recognizing that the volume is constant For then using the ideal gas law to show that with the volume constant, an increase in temperature implies an increase in pressure 1 point 1 point 1 point Alternate example Alternate points For indicating that if heat is added, then the internal energy and thus the kinetic energy 1 point of the gas molecules must increase, recognizing that the volume is constant For then indicating that as the kinetic energy of the gas molecules increase, they exert 1 point more force on the walls of the cylinder, thus increasing the pressure © 2007 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents). AP® PHYSICS B 2007 SCORING GUIDELINES (Form B) Question 5 (continued) Distribution of points (c) 3 points For correct equation for work in terms of force and distance W = Fx For correct substitution of x0 for x W = Fx0 For substitution of force from part (a)(i) Ê P p D2 ˆ W = Á atm + Mg ˜ x 0 4 Ë ¯ Alternate solution For correct equation for work in terms of pressure and volume change W = Pabs DV For correct expression for DV 1 point 1 point Alternate points 1 point 1 point 2 pD 4 2ˆ Ê pD W = Pabs x0 Á Ë4˜ ¯ For substitution of absolute pressure from part (a)(ii) 4 Mg ˆ Ê p D 2 ˆ W = Ê Patm + Á ˜ x0 Á ˜ Ë p D2 ¯ Ë 4 ¯ DV = x 0 A = x 0 1 point 1 point Ê P p D2 ˆ W = Á atm + Mg ˜ x 0 4 Ë ¯ © 2007 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents). AP® PHYSICS B 2007 SCORING GUIDELINES (Form B) Question 6 10 points total (a) Distribution of points 3 points For at least three data points plotted correctly For a straight line drawn For the line being a “best fit” to the data points (with equal number of points above and below the line) 1 point 1 point 1 point © 2007 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents). AP® PHYSICS B 2007 SCORING GUIDELINES (Form B) Question 6 (continued) Distribution of points (b) 3 points na sin qa = ng sin qg na = 1 For recognizing that ng is the slope of the graph of sin qa versus sin qg . 1 point sin qa = ng sin qg For using at least two widely separated points on the best-fit line (not two data points) For example, selecting two points on the line in the graph above, such as (0.08,0.10) and (0.60,0.88) Dy 0.88 - 0.10 = = 1.5 Slope = Dx 0.60 - 0.08 For the correct slope value, hence the value for ng 1 point 1 point ng = 1.5 (c) 2 points The critical angle qc is equal to qg when sin qa = 1 For extending the best-fit line to the point at the top of the graph where sin qa = 1 1 point For indicating that qc = sin -1 sin qg at this point. (Note: To earn this point it was not 1 point ( ) required to calculate the actual value for qc .) © 2007 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents). AP® PHYSICS B 2007 SCORING GUIDELINES (Form B) Question 6 (continued) Distribution of points (d) 2 points For a line with a slope greater than the best-fit line of part (a) For the line intercepting the origin (0,0) 1 point 1 point © 2007 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents). AP® PHYSICS B 2007 SCORING GUIDELINES (Form B) Question 7 10 points total (a) Distribution of points 3 points For using the correct equation for energy Ee = me c 2 For a correct calculation of the energy in joules ( )( ) = 8.20 ¥ 10-14 J Ee = (8.20 ¥ 10 -14 J ) (1.60 ¥ 10-19 J eV ) Ee = 9.11 ¥ 10 -31 kg 3.00 ¥ 108 m s 1 point 2 For the correct answer in eV as instructed in the question Ee = 5.12 ¥ 10 5 eV (answers in keV and MeV also accepted) (b) 1 point 1 point 2 points For recognizing that the photon energy must be twice that of one of the particles Eg = 2 Ee 1 point For substituting the value of energy from part (a) 1 point ( Eg = 2 5.12 ¥ 10 eV 5 ) Eg = 1.02 ¥ 106 eV (c) 2 points For a correct relationship between photon energy and wavelength hc Eg = hf = l For substituting the value of energy from part (b) 1.24 ¥ 103 eV i nm hc l= = Eg 1.02 ¥ 106 eV 1 point 1 point l = 1.22 ¥ 10 -3 nm = 1.22 ¥ 10 -12 m © 2007 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents). AP® PHYSICS B 2007 SCORING GUIDELINES (Form B) Question 7 (continued) Distribution of points (d) 3 points For a correct relationship between photon wavelength and momentum h l= p For substituting the value of wavelength from part (c) 6.63 ¥ 10 -34 J i s h p= = l 1.22 ¥ 10 -12 m For the correct answer with units consistent with the values substituted p = 5.43 ¥ 10 -22 kg i m s or equivalent (such as 3.39 ¥ 10 -3 1 point 1 point 1 point eVis m ) Alternate solution For a correct relationship between photon energy and momentum Eg = pc Alternate points 1 point Ê 2 Ee ˆ 2 me c 2 = = = 2 me c ˜ Á c c Ë ¯ For substituting the value of energy from part (b) 1.02 ¥ 106 eV 1.6 ¥ 10 -19 J eV p= or 2 9.11 ¥ 10 -31 kg 3 ¥ 108 m s 8 3.00 ¥ 10 m s For units on the final answer consistent with the values substituted p = 5.44 ¥ 10 -22 kg i m s or 5.46 ¥ 10 -22 kg i m s or equivalent p= Eg c ( )( ) ( ( ( )( ) 1 point )) 1 point © 2007 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents). ...
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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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