AP Physics C: Mechanics 007 Scoring Guidelines The College Board: Connecting Students to College Success The College Board is a not-for-profit ebership association whose ission is to connect students to college success and opportunity. Founded in 1900, the association is coposed of ore than 5,000 schools, colleges, universities, and other educational organizations. Each year, the College Board serves seven illion students and their parents, 3,000 high schools, and 3,500 colleges through ajor progras and services in college adissions, guidance, assessent, financial aid, enrollent, and teaching and learning. Aong its best-known progras are the SAT, the PSAT/NMSQT, and the Advanced Placeent Progra (AP ). The College Board is coitted to the principles of excellence and equity, and that coitent is ebodied in all of its progras, services, activities, and concerns. 007 The College Board. All rights reserved. College Board, Advanced Placeent Progra, AP, AP Central, SAT, and the acorn logo are registered tradearks of the College Board. PSAT/NMSQT is a registered tradeark of the College Board and National Merit Scholarship Corporation. Perission to use copyrighted College Board aterials ay be requested online at: www.collegeboard.co/inquiry/cbperit.htl. Visit the College Board on the Web: www.collegeboard.co. AP Central is the official online hoe for the AP Progra: apcentral.collegeboard.co.
007 SCORING GUIDELINES General Notes About 007 AP Physics Scoring Guidelines 1. The solutions contain the ost coon ethod of solving the free-response questions and the allocation for this solution. Soe also contain a coon alternate solution. Other ethods of solution also receive appropriate credit for correct work.. Generally, double penalty for errors is avoided. For exaple, 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 ay be cases when the nuerical answer to a later part should be easily recognized as wrong, e.g., a speed faster than the speed of light in vacuu. 3. Iplicit stateents of concepts norally receive credit. For exaple, if use of the equation expressing a particular concept is worth, and a student s solution contains the application of that equation to the proble but the student does not write the basic equation, the point is still awarded. However, when students are asked to derive an expression, it is norally expected that they will begin by writing one or ore fundaental equations, such as those given on the AP Physics exa equation sheet. See pages 1 of the AP Physics Course Description for a description of the use of such ters as derive and calculate on the exas, and what is expected for each. 4. The scoring guidelines typically show nuerical results using the value g 9.8 s, but use of 10 s is of course also acceptable. Solutions usually show nuerical answers using both values when they are significantly different. 5. Strict rules regarding significant digits are usually not applied to nuerical answers. However, in soe cases answers containing too any digits ay be penalized. In general, two to four significant digits are acceptable. Nuerical answers that differ fro the published answer due to differences in rounding throughout the question typically receive full credit. Exceptions to these guidelines usually occur when rounding akes a difference in obtaining a reasonable answer. For exaple, suppose a solution requires subtracting two nubers 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 deterine the difference in the nubers, and soe credit ay be lost. 007 The College Board. All rights reserved. Visit apcentral.collegeboard.co (for AP professionals) and www.collegeboard.co/apstudents (for AP students and parents).
007 SCORING GUIDELINES Question 1 15 points total Distribution (a) 4 points For each of the forces shown above with arrow correctly drawn and labeled, was awarded For each incorrect or extraneous vector, such as acceleration or velocity, a point was deducted, with the iniu possible score being 0. 4 points (b) points  F y 0 For the correct y coponent of F1 N + F 1 sinq - g 0 For the correct answer N g - F 1 sinq (c)  F x a For showing correct expressions for the horizontal forces and setting the equal to a F cosq - N a 1 1 For substituting the expression for N fro part (b) F1cosq - ( g - F1sin q) a 1 For the correct answer F1cosq - a 1 g - F sinq 1 1 007 The College Board. All rights reserved. 3
007 SCORING GUIDELINES (d) Question 1 (continued) Distribution For a linear relationship on the u versus t graph with positive slope and with u 0 at t 0 For a parabolic relationship on the x versus t graph that is concave upward, with x 0 at t 0 For the two graphs being consistent with each other (e) For indicating that N 0 is the condition for the axiu acceleration of the block before it loses contact For indicating that the friction force is zero f N 0 ÂFx Fax cosq a ax Fax cosq aax  Fy Fax sin q - g 0 g Fax sinq Substituting F into the expression for a above ax g cosq aax sinq For the correct answer a gcotq ax Note: Since is a variable quantity in this proble and since the initial directions included F 1 F 1 expression a ax as a quantity that could be used in expressions for the answers, the ax F1 cosq was also acceptable for the answer point. 007 The College Board. All rights reserved. 4
007 SCORING GUIDELINES Question 15 points total Distribution (a) points For a correct expression of the relationship aong T, R, and u pr T u ut R p ( 3.40 10 3 s )( 7.08 10 3 s ) R p For the correct nuerical answer 6 R 3.83 10 (b) points For correctly equating centripetal force and gravitational force su GsM M R R u R MM G For substituting the value of R fro (a) into either the original equation or the siplified expression for M above M M M ( 3.40 10 3 s) ( 3.83 10 6 ) -11 3 i 6.67 10 kg s 3 M 6.64 10 kg M 007 The College Board. All rights reserved. 5
007 SCORING GUIDELINES (c) 4 points Question (continued) Distribution For a correct expression that equates Etot energies K + U Etot For a negative sign on a correct expression for to the su of kinetic and gravitational potential UG 1 GsMM Etot su - R For explicit substitution of the value of R fro (a) and the value of equation above or for correct nuerical answer if worked as follows: u R Fro (b), MM G 1 Gs u R 1 1 Etot su - su - su - su R G 1 3 E ( 930 kg )( 3.40 10 s ) tot - For a negative sign on the final answer E - 5.38 10 J tot 9 M M fro (b) in the (d) For correct selection of Less than check space For a correct justification Exaple 1: Fro Kepler s third law ( r 3 T constant ), if r decreases, then T ust also decrease Exaple : Use relationships aong R, u, and T with no incorrect physics such as the u R following: Fro (b), MM, so as R decreases, u ust increase. Fro (a), G pr T, so both a decrease in R and an increase in u contribute to a decrease in T. u pr Note: partial credit was awarded for using only T, unless it was stated u that u was constant, in which case no credit was awarded. points 007 The College Board. All rights reserved. 6
007 SCORING GUIDELINES (e) points Question (continued) Distribution For a correct expression of conservation of angular oentu su11 r sur or equivalent such as I1w1 Iw or u11 r ur r1 RC + RM u u1 u r 1, where R C and R F are the distances of closest and farthest R + R F M approaches, respectively, and R M is the radius of Mars For explicit substitution of radii (not altitudes) into the equation or for the correct nuerical answer u 3 ( ) 5 5 3.71 10 + 34.3 10 3.40 10 s 4.36 10 + 34.3 10 5 5 3 u 3.34 10 s Alternatively, if the longer approach using conservation of energy was taken, was awarded for a correct stateent of conservation of energy if explicitly written as 1 GsMM 1 GsMM su1 - r 1 su -, and was awarded for the explicit r substitution of radii (not altitudes) or for a correct nuerical answer. Units point For including correct units on at least three nuerical answers Significant figures point For including less than five significant digits on at least three nuerical answers for which a calculation was shown 007 The College Board. All rights reserved. 7
007 SCORING GUIDELINES Question 3 15 points total Distribution (a) points For a correct equation using conservation of energy 1 1 u kx For a correct substitution of the nuerical value of k in part (a) or in a subsequent part of the proble 1 u 1 ( 40 ) x (b) and (c) (b) For correct axis labels and units on both axes For correct linear scales on both axes For plotting at least 4 of 5 points in the correct location Note: Full credit was awarded if both axes were reversed fro the graph shown above and everything else was correct. 007 The College Board. All rights reserved. 8
007 SCORING GUIDELINES (c) (i) Question 3 (continued) Distribution For a reasonable best-fit straight line Note: This point was awarded only if the axes had linear scales. (ii) 1 1 u kx k x u, so kis the slope of the graph of u versus x For use of a slope derived fro the data For using two points in the calculation of the slope that are clearly on the best-fit line (Students using data points not on the line could not receive this second point.) - Exaple: Selecting the points (.4 10, 4.8) and ( 0.5 10 -, 1.0), which are on the line shown in the graph ) Slope ( 4.8-1.0 s - k.0 10 s -.4-0.5 10 ( ) k 40 N slope -.0 10 s For a nuerical answer in the range 0.18 kg to 0. kg 0.0 kg (d) (i) 4 points For use of the correct energy types (K, U, and U ) in a single equation For recognition that the difference in height is greater than h in the figure For a correct expression for U For substitution of Ug g into a correct equation g 1 1 u kx + g( h + xsinq) Note: Third and fourth points were awarded only if the first two points were awarded. s (ii) points For checking No For a clear justification explaining that u varies with both x and x. 007 The College Board. All rights reserved. 9