AP Physics B 007 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, 3,000 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. 007 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.
(Form B) 007 SCORING GUIDELINES General Notes About 007 AP Physics Scoring Guidelines 1. The solutions contain the most common method of solving the free-response questions and the allocation for this solution. Some also contain a common alternate solution. 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. 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 s, but use of 10 m s 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., 0.95 and 0.78). Rounding to three digits will lose the accuracy required to determine the difference in the numbers, and some credit may be lost. 007 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for AP students and parents).
007 SCORING GUIDELINES (Form B) Question 1 15 points total Distribution (a) 4 points For each of the forces above with arrow correctly drawn and labeled, was awarded Notes: The force vector T could be shown in component form or as one force, but not both. For extraneous forces, was deducted. 4 points (b) 4 points  F y = 0 N + Tsinq - mg = 0 For a correct force equation N = mg - Tsinq For calculating the mg term correctly For calculating the T sinq term correctly ( )( ) ( ) N = 15 kg + 5 kg 9.8 m s - 55 N sin 0 For the correct numerical answer with units N = 177 N (181 N if g = 10 m s is used) (c) 3 points  Fx = ma For a correct Newton s second law equation involving horizontal forces Tcosq - f = ma Tcosq - f a = 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) g = 10 m s is used) f = ( 0.)( 177 N) = 38.9 N (39.8 N if ( 55 N) cos0-38.9 N a = 0 kg a = 0.64 m s ( 0.59 m s if g = 10 m s is used) 007 The College Board. All rights reserved.
007 SCORING GUIDELINES (Form B) (d) points Question 1 (continued) Distribution For the correct work equation W = ( Tcosq) d For substituting the correct displacement W = ( 55 N) cos0 ( 7.0 m) W = 360 J (e) points For each section of the graph correctly drawn as above, was awarded. Note: The second point was awarded only if the change at t was abrupt. r points 007 The College Board. All rights reserved.
007 SCORING GUIDELINES (Form B) Question 10 points total Distribution (a) (i) 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. (ii) points For either of the first two equations below qu B = qe u = u = E B ( 4800 N C) ( 0.1 T) 4 u = 4.0 10 m s For the correct answer with units (b) points mu qu B = r For the correct equation for the radius mu r = qb For correct substitutions consistent with the answer to (a)(ii) -6 4 ( 6.68 10 kg)( 4.0 10 m s) r = -19 3. 10 C 0.1 T r = 0.070 m ( )( ) 007 The College Board. All rights reserved.
007 SCORING GUIDELINES (Form B) (c) points Question (continued) Distribution For indicating that the initial force is Toward the bottom of the page For a correct justification indicating that the magnetic force ( F = qub) decreases as velocity decreases, while the electric force ( F E B = qe) remains the same, so FE FB >. (d) points For the path in Region I being straight and horizontal For the path in Region II being a circular arc, curving downward 007 The College Board. All rights reserved.
007 SCORING GUIDELINES (Form B) Question 3 15 points total Distribution (a) 3 points For a statement of Ohm s law, recognizing that I C = 0 V = IR For the calculation of the total resistance Rtotal = 1000 W + 500 W = 1500 W For the correct answer, including units 1 V -3 I = = 8.0 10 A 1500 W (b) (i) points For the ammeter in series anywhere in the circuit except the capacitor branch points (ii) points For the voltmeter in parallel across the 1000 W resistor points (c) 3 points For a correct equation relating the charge, voltage, and capacitance Q Q = CV C or C = V C For recognizing that the voltage drop across the capacitor is the same as the voltage drop across the 500 W resistor -3 ( )( ) VC = IR500 = 8.0 10 A 500 W = 4.0 V For the correct answer with the correct units ( 30 10-6 F )( 4.0 V ) Q = -4 Q = 1. 10 C 007 The College Board. All rights reserved.
007 SCORING GUIDELINES (Form B) Question 3 (continued) Distribution (d) points For a correct equation for the power dissipated 1000 1000 or 1000 or V R1000 P = I R V I Calculation for the second two relationships -3 ( )( ) V1000 = IR1000 = 8.0 10 A 1000 W = 8.0 V For the correct substitutions - - ( ) ( W) ( )( ) ( ) 3 3 8.0 V P = 8.0 10 A 1000 or 8.0 V 8.0 10 A or 1000 W - P = 6.4 10 W (e) 3 points For choosing Larger For correct justification in words or with numerical example. For example: 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. () The capacitor is in parallel with the replacement resistor, and so its voltage increases and therefore its charge increases since Q = CV. () 007 The College Board. All rights reserved.
007 SCORING GUIDELINES (Form B) Question 4 10 points total Distribution (a) 3 points Applying Bernoulli s equation For example, taking point 1 to be at the top of the liquid and point at the hole 1 1 P1 + rgy1 + ru1 = P + rgy + ru P = P = P 1 atm 1 0 u = 1 rg( y1 - y) = ru For a correct expression for the speed u = g( y1 - y ) For correct substitutions u = ( 9.8 m s )( 0.70 m) For the correct answer, including units u = 3.7 m s (b) 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) -5 3 V = 1. 10 m s (c) points For any indication that the volume is the volume rate multiplied by the time V = Vt For correct substitutions ( 1. 10-5 m 3 s )( min )( 60 s min ) V = - V = 1.4 10 m 3 3 007 The College Board. All rights reserved.
007 SCORING GUIDELINES (Form B) (d) 3 points Question 4 (continued) Distribution For using the kinematic equation for distance as a function of time 1 y = y0 + u0t + at Taking down as the positive direction, and using a = g and y = h 1 0 gt u t h + - = 0 For solving the equation for t using the quadratic formula - u0 ± u0 + gh t = g For correct substitutions Using the + sign to avoid negative time ( ) ( )( ) - 3.7 m s + 3.7 m s + 9.8 m s 0.5 m t = 9.8 m s t = 0.06 s Alternate solution For using the kinematic equation relating speed, acceleration, and distance u ( x ) = u + a x - 0 0 For using the kinematic equation for speed as a function of time u = u 0 + at u - u0 t = a Substituting for u from the initial equation into the above equation for t ( x ) u0 + a x - 0 - u0 = t a For correct substitutions ( ) ( )( ) 3.7 m s + 9.8 m s 0.5 m - 3.7 m s t = 9.8 m s t = 0.06 s Alternate points 007 The College Board. All rights reserved.
007 SCORING GUIDELINES (Form B) Question 5 10 points total Distribution (a) (i) 3 points For recognition that one component of the force is PatmA For recognition that another component of the force is Mg F = P A + Mg atm D For ( ) pd A = p = 4 PatmpD F = + Mg 4 (ii) F For P =, with answer to (a) substituted for F A P P abs abs PatmpD + Mg = 4 pd 4 4Mg = Patm + pd (b) 3 points For checking the Pressure goes up answer space For a correct and complete justification, 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 Alternate example Alternate points For indicating that if heat is added, then the internal energy and thus the kinetic energy 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 more force on the walls of the cylinder, thus increasing the pressure 007 The College Board. All rights reserved.
007 SCORING GUIDELINES (Form B) (c) 3 points Question 5 (continued) Distribution For correct equation for work in terms of force and distance W = Fx For correct substitution of for x x0 W = Fx 0 For substitution of force from part (a)(i) Ê PatmpD ˆ W = Á + M 4 0 Ë g x Alternate solution For correct equation for work in terms of pressure and volume change W = P DV abs For correct expression for DV D V = x A = x pd 0 0 4 Ê pd ˆ = abs 0 Á 4 W P x Ë For substitution of absolute pressure from part (a)(ii) 4Mg ÊpD ˆ W = Ê P ˆ Á atm + x Ë 0 Á pd Ë 4 ÊPatmpD ˆ W = Á + M 4 Ë g x 0 Alternate points 007 The College Board. All rights reserved.
007 SCORING GUIDELINES (Form B) Question 6 10 points total Distribution (a) 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 above and below the line) 007 The College Board. All rights reserved.
007 SCORING GUIDELINES (Form B) (b) 3 points Question 6 (continued) Distribution n sinq a a g = n sinq g g n a = 1 For recognizing that ng is the slope of the graph of sinq a versus sinq g. sinq a = ng sinq 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 Slope = = = 1.5 Dx 0.60-0.08 For the correct slope value, hence the value for ng n g = 1.5 (c) points The critical angle q is equal to q when sinq = 1 c g a For extending the best-fit line to the point at the top of the graph where sinq a = 1-1 sin sinq at this point. (Note: To earn this point it was not For indicating that q c = ( g) required to calculate the actual value for q c.) 007 The College Board. All rights reserved.
007 SCORING GUIDELINES (Form B) (d) points Question 6 (continued) Distribution For a line with a slope greater than the best-fit line of part (a) For the line intercepting the origin (0,0) 007 The College Board. All rights reserved.
007 SCORING GUIDELINES (Form B) Question 7 10 points total Distribution (a) 3 points For using the correct equation for energy E e = mc e For a correct calculation of the energy in joules E e E e ( )( ) ( 10-14 J ) ( 10-19 ) -31 8-14 = 9.11 10 kg 3.00 10 m s = 8.0 10 J = For the correct answer in ev as instructed in the question 5 E = 5.1 10 ev (answers in kev and MeV also accepted) e (b) points For recognizing that the photon energy must be twice that of one of the particles E E g = e For substituting the value of energy from part (a) 5 ( ) E g = 5.1 10 ev 6 E g = 1.0 10 ev (c) points For a correct relationship between photon energy and wavelength hc Eg = hf = l For substituting the value of energy from part (b) hc 1.4 10 evi nm l = = E 6 g 1.0 10 ev 3-3 -1 l = 1. 10 nm = 1. 10 m 007 The College Board. All rights reserved.
007 SCORING GUIDELINES (Form B) (d) 3 points Question 7 (continued) Distribution For a correct relationship between photon wavelength and momentum h l = p For substituting the value of wavelength from part (c) -34 h 6.63 10 Ji s p = = l -1 1. 10 m For the correct answer with units consistent with the values substituted - p = 5.43 10 kgi ms or equivalent (such as 3.39 10 evi s m ) Alternate solution For a correct relationship between photon energy and momentum E pc g = Eg Ê Ee mec ˆ p = mc e c Á= = = c c Ë For substituting the value of energy from part (b) ( 6-1.0 10 ev)( 1.6 10 19 J ev) 31 8 p = 8 3.00 10 m s or 9.11 10 - kg 3 10 m s For units on the final answer consistent with the values substituted p ( ( )( )) - - = 5.44 10 kgi ms ( or 5.46 10 kg ms) -3 i or equivalent Alternate points 007 The College Board. All rights reserved.