AP Physics C: Mechanics 2011 Scoring Guidelines

1 AP Physics C: Mechanics 2011 Scoring Guidelines The College Board 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 College Board is composed of more than 5,700 schools, colleges, universities and other educational organizations. Each year, the College Board serves seven million students and their parents, 23,000 high schools, and 3,800 colleges through major programs and services in college readiness, college admission, guidance, assessment, financial aid and enrollment.

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3 PSAT/NMSQT is a registered trademark of the College Board and National Merit Scholarship Corporation. All other products and services may be trademarks of their respective owners. Permission to use copyrighted College Board materials may be requested online at: Visit the College Board on the Web: AP Central is the official online home for the AP Program: AP Physics C: Mechanics 2011 Scoring Guidelines Question 1 15 points total Distribution of points (a) 2 points dt= JF For a correct equation relating the given force, time and impulse 1 point pavgJFtD= For the correct answer 1 point pavgtJFD= Alternate solution Alternate points For using both kinematics and Newton s second law 1 point 0xavatuD=+g avgavgm=Fa Combining the above equations xavgFmtuD = avgxpFtm JuD== For the correct answer 1 point pavgtJFD= (b)

4 2 points For the correct relationship between impulse and the change in momentum 1 point mDD==Jpv ()0pxxJmmuu=-= For the correct answer 1 point pxmJu= Note: A correct kinematics and Newton s laws approach is also acceptable. 2011 The College Board. Visit the College Board on the Web: AP Physics C: Mechanics 2011 Scoring Guidelines Question 1 (continued) Distribution of points (c) 3 points For using the work-energy theorem 1 point WKD= 2102xWmu=- For substituting the expression for m from part (b)

5 1 point 212pxxJWuu=- 12pxWJu=- For an indication that the work done is negative 1 point Alternate Solution Alternate points Using kinematics and Newton s second law to determine the average net force 222fi avgaduu-= 22xavgadu-= 22xavgadu=- avgavgm=Fa 22xnetFmdu =- For substituting this expression for the force into the equation for work 1 point 22xavgWdFdmdu ===- Frid 22xWmu=- For substituting the expression for m from part (b) 1 point 22pxxJWuu=- 12pxWJu=- For an indication that the work done is negative 1 point 2011 The College Board.

6 Visit the College Board on the Web: AP Physics C: Mechanics 2011 Scoring Guidelines Question 1 (continued) Distribution of points (d) 2 points avgWd== FrFrii For using as the average force in the equation for work bF 1 point bWFd= bWFd= For substituting the expression for W from part (c), with or without a negative sign 1 point 2pxbJFdu= (e) 4 points Applying the work-energy relationship ifKWK+= For correctly relating the initial kinetic energy of the projectile with the work done by the block on the projectile and the work done on the block by friction with the table 1 point 0iblockfrictionKWW++ = For substituting for the work done by the block on the projectile ( , the energy lost to heat in the block-projectile collision)

7 1 point 0ibn frictionKFd W-+ = For substituting the work done on the block by friction with the table ( , the energy lost to heat as the block slides to rest on the table) 1 point 0ibnTKFd fD--= The initial kinetic energy of the projectile is the same as in the first case when the block was clamped. Therefore, it can be equated to the work done in stopping the projectile from part (d). For substituting for the initial kinetic energy of the block bFd 1 point 0bbnTFd Fdf D--= bnbTFdFd f D=- Full credit could not be earned for just writing this equation.

8 The student needed to have some indication that the work-energy relationship was being applied, and that was associated with the initial kinetic energy. dF bTnbFd f DdF-= D TnbfddF=- 2011 The College Board. Visit the College Board on the Web: AP Physics C: Mechanics 2011 Scoring Guidelines Question 1 (continued) Distribution of points (f) 2 points For a correct application of conservation of momentum to the block-projectile collision 1 point ()xmMmu=+V ()xmVMmu=+ The kinetic energy of the block/projectile system immediately after the collision is equal to the work done by friction in stopping it.

9 ()212 TMmV fD+= For substituting for V 1 point ()()212xTmMmfMmu += +D ()2212xTmfDMmu=+ ()212xTmmfMmu=+D From part (c) the kinetic energy factor in the equation above is equal to the total work done.

10 From part (d) that work is equal to . bFd bTmFdf DMm=+ Using the expression from part (e) to substitute for bnbTFdFd f D=-TfD bbbmFd Fd FdMm=-+n nmdddMm=-+ ()1nmddMm=-+ Note: Because the work for parts (e) and (f) is interrelated, the two parts are scored as a whole. Credit is earned for work related to part (f) even when it is shown in part (e) and vice versa. 2011 The College Board. Visit the College Board on the Web: AP Physics C: Mechanics 2011 Scoring Guidelines Question 2 15 points total Distribution of points 2011 The College Board.