AP Physics C: Mechanics 2003 Scoring Guidelines

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AP Physics C: Mechanics 003 Scoring Guidelines The materials included in these files are intended for use by AP teachers for course and eam preparation; permission for any other use must be sought

1 AP Physics C: Mechanics 003 Scoring Guidelines The materials included in these files are intended for use by AP teachers for course and eam 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 noncommercial, face-to-face teaching purposes. This permission does not apply to any third-party copyrights contained herein. This material may not be mass distributed, electronically or otherwise. These materials and any copies made of them may not be resold, and the copyright notices must be retained as they appear here. These materials were produced by Educational Testing Service (ETS ), which develops and administers the eaminations of the Advanced Placement Program for the College Board. The College Board and Educational Testing Service (ETS) are dedicated to the principle of equal opportunity, and their programs, services, and employment policies are guided by that principle. The College Board is a national nonprofit membership association whose mission is to prepare, inspire, and connect students to college and opportunity. Founded in 1900, the association is composed of more than 4,300 schools, colleges, universities, and other educational organizations. Each year, the College Board serves over three million students and their parents,,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 equity and ecellence, and that commitment is embodied in all of its programs, services, activities, and concerns. For further information, visit Copyright 003 College Entrance Eamination Board. All rights reserved. College Board, Advanced Placement Program, AP, AP Vertical Teams, APCD, Pacesetter, Pre-AP, SAT, Student Search Service, and the acorn logo are registered trademarks of the College Entrance Eamination Board. AP Central is a trademark owned by the College Entrance Eamination Board. PSAT/NMSQT is a registered trademark jointly owned by the College Entrance Eamination Board and the 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.

2 AP PHYSICS C: MECHANICS 003 SCORING GUIDELINES Question 1 15 points total (a) 3 points For indicating speed as the time derivative of position d = dt For taking the correct derivative = 1.5t + For finding the correct initial speed at t = 0 = m/s 0 (b) 6 points i. () 1 = m For correctly substituting for the mass and the epression for found in (a) 1 (100)(1.5 ) 50(1.5 ) = t + = t + ii. (3 points) Fnet = ma For indicating acceleration as the time derivative of the velocity d a = dt For taking the correct derivative a= 3t For the correct epression F = (100)(3 t) = 300t net Copyright 003 by College Entrance Eamination Board. All rights reserved.

3 003 SCORING GUIDELINES Question 1 (cont d.) iii. ( points) For the correct equation relating power to force and velocity P= F For substituting epressions for F and found in previous parts 3 P= (300 t)(1.5t + ) = 450t + 600t Alternate method points For indicating power as the time derivative of kinetic energy d P = dt For substituting the epression for kinetic energy from (b)i. d 4 3 P= ( 11.5t + 300t + 00) = 450t + 600t dt Alternate (c) 4 points For a statement that the work done on the bo is equal to the change in its kinetic energy W = For finding at seconds = (1.5)() + = 8 m/s Substituting, using the value ofυ 0 from part (a): (( ) ( ) ) 1 W = (100 kg) 8 m/s m/s with correct unit W = 3000 J Alternate method points For a statement that the work done by the bo is equal to the integral of power over time W = Pdt For substituting the epression for power found in (b)iii 3 ( ) 0 W = t + t dt W = ( t ) + ( t ) W = 1800 J J with unit W = 3000 J point Alternate points Copyright 003 by College Entrance Eamination Board. All rights reserved. 3

4 003 SCORING GUIDELINES (d) points Question 1 (cont d.) For checking the bo that the work done by the student is greater than in part (c) For a reasonable justification recognizing that the student had to perform work against friction, such as Wstudent = E+ Wfriction Copyright 003 by College Entrance Eamination Board. All rights reserved. 4

5 AP PHYSICS C: MECHANICS 003 SCORING GUIDELINES Question 15 points total (a) points For a statement of conservation of energy 1 MgH = M c = gh c Alternate solution points For use of correct kinematics equation c 0 = + gh, OR the combination of a= g; c = gt ; and H = gh c 1 = gt, Alternate (b) 3 points For recognition that momentum is conserved in the inelastic collision For use of the correct equation epressing conservation of momentum Mc = Mp 1 p = gh (c) 4 points For use of the correct equation for the period of a mass on a spring T = π m k For recognition that m= M For correct calculation of k using the force equation for the initial stretching of the spring Mg Mg = kd, giving k = D after substituting for m and k T = π D g Copyright 003 by College Entrance Eamination Board. All rights reserved. 5

6 003 SCORING GUIDELINES Question (cont d.) (d) 3 points For recognition that the speed is a maimum at the equilibrium point, which can be correctly described by one or more of the following statements: equilibrium point, F = 0, a = 0, kinetic energy is a maimum, midpoint of the oscillation, etc. For recognition that there is a new equilibrium point given by the following equation k = Mg, where is the distance the spring is stretched from its initial unstretched length Substituting the value of k found in part (c) Mg = Mg D = D For a correct answer, = D, but with no justification, only was awarded (e) 3 points For a check in the Less than space in part (c) For a correct justification that states that in the second case there is less mass oscillating than m in part (c) and that the period decreases with decreasing mass, T = π. k (The formula is not necessary for full credit.) points Copyright 003 by College Entrance Eamination Board. All rights reserved. 6

7 AP PHYSICS C: MECHANICS 003 SCORING GUIDELINES Question 3 15 points total (a) points i. () For a smooth concave downward curve in the region between the points, that passes near all the points. ii. () For a reasonable interpolation of the value of when M = 50 kg, based on the graph that was drawn For eample, using the above graph 33 m (b) 10 points i. ( points) For using correct kinematic equation(s) y = 1/ gt can be used to directly solve for the time For eample, the equation ( ) ( ) t = y g = 15m 9.8m s t = 1.75 s (or 1.73 s using g = 10 m s ) ii. (3 points) For determining the potential energy of both the load in the counterweight bucket and the projectile For the correct value of the potential energy of the bucket load Ub = mgh= M( 9.8) 3 = 9.4M For the correct value of the potential energy of the projectile U = mgh= = 94 p ( )( ) U = U + U = 9.4M + 94 (or 30M using init b p g = 10 m s ) Copyright 003 by College Entrance Eamination Board. All rights reserved. 7

8 003 SCORING GUIDELINES (b) (continued) Question 3 (cont d.) iii. (5 points) For a valid statement or equation indicating conservation of energy Uinit = U final + For the correct final potential energy of the bucket load For the correct final potential energy of the projectile U final = M( 9.8)( 1) + ( 10)( 9.8)( 15) = 9.8M For having terms for the final kinetic energy of both the bucket load and the projectile p = ( 1/) 10 and b = ( 1/ ) M b OR p = ( 1/ )( 1440) M and b = ( 1/)( 4M) M For using one of the following relationships to write all epressions in terms of b = ( 1/6) OR M= /1 Substituting into the conservation of energy equation above and solving for : ( ) ( ) ( 5 ( 7) ) (or ( 0M 100) 5 ( M 7) 9.4M + 94 = 9.8M M 7 = M + M ( ) + using Alternate solution For an application of the equation for torque J = I= = I( dm dt) For determining the torque applied by the bucket load g = 10 m s ) Jb = Fr = Mgr sin G = 19.6M sing For determining the torque applied by the projectile J = 10( 9.8) sin G p ( 1) = 940sin G For determining the total rotational inertia I = 10(1) + M() = M For using the proper relationship to change from a rotational to a linear solution M= ( 1/1) Substituting: 19.6M sin G 940sin G = ( 1 1)( M) ( d dt) This equation can then be solved to obtain the epression for Alternate points Copyright 003 by College Entrance Eamination Board. All rights reserved. 8

9 003 SCORING GUIDELINES Question 3 (cont d.) (c) 3 points i. () Using the given relationship for = t For substituting the answers answer from parts (b) iii. and (b) i. = M M 7 ( ) ( ( )) (or 1.73 ( 0M 100) ( 5 ( M 7) ) + using g = 10 m s ) ii. ( points) For using the equation from part (c) i. to predict theor ( ( ) ) ( ( )) theo = = 39.7 m (or 40.0 m using g = 10 m s ) For a reasonable eplanation for the fact that ep < theor Eamples: friction at the pivot, air resistance, neglected masses are not really negligible One point was awarded if no equation is available from (c) i. to make a theoretical prediction but the student developed the reasonable eplanation for ep < theor One point was awarded for a reasonable eplanation if evaluation of equation in part (c) resulted in ep > theor. Copyright 003 by College Entrance Eamination Board. All rights reserved. 9

AP Calculus AB 1999 Free-Response Questions

AP Calculus AB 1999 Free-Response Questions The materials included in these files are intended for non-commercial use by AP teachers for course and eam preparation; permission for any other use must be