2022 AP exam administration scoring guidelines AP physics c: mechanics (set 1)

2022 AP Exam Administration Scoring Guidelines AP Physics C Mechanics (Set 1) 2022 AP ® Physics C Mechanics Scoring Guidelines Set 1 © 2022 College Board College Board, Advanced Placement, AP, AP Cent[.]

2022 AP Physics C: Mechanics ® Scoring Guidelines Set © 2022 College Board College Board, Advanced Placement, AP, AP Central, and the acorn logo are registered trademarks of College Board Visit College Board on the web: collegeboard.org AP Central is the official online home for the AP Program: apcentral.collegeboard.org AP® Physics C: Mechanics 2022 Scoring Guidelines Question 1: Free-Response Question (a) 15 points For correctly drawing and labeling the force of gravity and the normal force on the block of mass m point For correctly drawing and labeling the force of friction on the block of mass m point For correctly drawing and labeling the force of tension on the block of mass m point Example Response Scoring Notes:  Examples of appropriate labels for the force due to gravity include: FG , Fg , Fgrav , W , mg , Mg , “grav force,” “F Earth on block,” “F on block by Earth” FEarth on block , FE,Block The labels G and g are not appropriate labels for the force due to gravity Fn , FN , N , “normal force,” “ground force,” or similar labels may be used for the normal force Fstring , Fs , FT , FTension , T , “string force,” “tension force,” or similar  labels may be used for the tension force exerted by the string A response with extraneous forces or vectors can earn a maximum of two points Total for part (a) (b) points For a trigonometric expression relating the angle to the horizontal distance of the block from the left corner of the table, x point For any correct trigonometric expression for  in terms of the given quantities point Example Responses First Point H sin   H  x2 x cos  H  x2 H tan   x Second Point  H  H  x2  x   cos 1   H  x2 H   tan 1 x   sin 1          Total for part (b) points © 2022 College Board AP® Physics C: Mechanics 2022 Scoring Guidelines (c)(i) For using Newton’s second law to sum the forces in the vertical direction and write an equation that is consistent with part (a) point Fy  ma Fnet, y  FN  FT , y  Fg  FN  Fg  FT , y For correctly substituting the vertical component of the tension in terms of the given variables consistent with part (b) point FN  mg  FT sin    H FN  mg  FT  2   H x  (c)(ii) For using Newton’s second law to sum the forces in the horizontal direction and write an equation that is consistent with part (a) point Fnet , x  FT , x  F f For correctly substituting the horizontal component of the force of tension in terms of the given variables consistent with part (b) point Fnet,x  FT cos  F f  x   Fnet , x  FT    Ff  H  x2  For correctly substituting the expression for the normal force from part (c)(i) into the expression for the force of friction point  x   Fnet,x  FT     k FN  H  x2   x      H Fnet,x  FT    k  mg  FT  2  2   H x    H  x  Total for part (c) (d) For any indication that the work done on the block by the string is due only to the horizontal component of the tension in the string points point W   FT ,x dx For using the horizontal component of the force of tension consistent with part (c) point For indicating that work is the integral of the force with respect to x, including limits or a constant of integration point W  x 0  x  L  FT   dx H x  x 2 Total for part (d) points © 2022 College Board AP® Physics C: Mechanics 2022 Scoring Guidelines (e) For selecting “More work …” with an attempt at a relevant justification point For a correct justification relating the smaller angle to a larger component of the force of tension, thus resulting in greater work point Example Response FT stays the same for both halves, the displacement is the same in both halves, but from x  L to x  L the angle is smaller, resulting in a larger component of the tension force that aligns with the displacement Total for part (e) points Total for question 15 points â 2022 College Board APđ Physics C: Mechanics 2022 Scoring Guidelines Question 2: Free-Response Question (a) 15 points For selecting “Equal to” with an attempt at a relevant justification point For a correct justification point Example Response Newton’s third law says equal/opposite forces, time intervals are same during same collision, so magnitudes of impulse must be equal (b) Total for part (a) points point For correctly drawing the momentum for carts and for the time interval  t  tC : Linear increasing momentum for Cart and zero for Cart For drawing a horizontal line for Cart when t  tC that is smaller in magnitude than the point momentum of Cart at time t  tC For drawing a horizontal line for Cart when t  tC that is greater in magnitude than the point momentum of Cart after time t  tC For carts and having a change in momentum that is equal in magnitude, such that Cart loses momentum and Cart gains momentum or a response with changes in momentum consistent with the response in part (a) point Example Response Total for part (b) points (c) For using conservation of energy to find the speed of Cart at the bottom of the incline point OR For a correct substitution of acceleration and displacement in a kinematics equation to find the speed of Cart at the bottom of the incline For using conservation of momentum to find the speed of the two-cart system after the collision point For combining correct equations from above point © 2022 College Board AP® Physics C: Mechanics 2022 Scoring Guidelines Example Response Conservation of energy: m1 gH  m1v12 v1  gH OR v 2f  vi2  2g sin( )L H  Lsin( ) v 2f  vi2  2g sin( )  sinH  v 2f  2gH Conservation of momentum: m1v1   m1  m2  v f vf  m1 v m1  m2 Combining: m1 gH vf  m1  m2 m1  v f  g   H  m1  m2  Total for part (c) points â 2022 College Board APđ Physics C: Mechanics 2022 Scoring Guidelines (d)(i) For drawing an appropriate best-fit line including approximately the same number of points above and below the line point Example Response (d)(ii) For calculating the slope using two points on the best-fit line point For correctly relating the slope of the best-fit line to the mass of Cart point For a correct mass of Cart point Example Response slope  1.20  0.60  m/s m  1.72 s  0.70  0.35  m slope  m1 2g m1  m2 m2  m1 2g  m1 slope m  0.25 kg   9.8   m 1.72 s  m2  0.39 kg m2  s    0.25 kg  Scoring Note: Acceptable responses for mass are 0.30 to 0.60 kg Total for part (d) points â 2022 College Board APđ Physics C: Mechanics 2022 Scoring Guidelines (e) For selecting “ m1 '  0.250 kg ” with an attempt at a relevant justification point For a correct justification point Example Response A smaller m2 indicates that the initial energy and momentum was smaller With identical slope and height H this means that the mass m1 ' must be smaller Total for part (e) points Total for question 15 points â 2022 College Board APđ Physics C: Mechanics 2022 Scoring Guidelines Question 3: Free-Response Question (a) 15 points For indicating that the sum of the torques on the disk equals zero Σ on disk  point g  s OR For indicating that the sum of the forces equals zero F  Fg  Fs For correctly substituting the expressions for the forces Fg R  Fs R point mB gR  k xR mB g  k x OR Fg  Fs m B g  kΔx For correctly substituting for x mB g  kR kR mB  g (b) point Total for part (a) For drawing and labeling the force of the tension exerted on the disk anywhere between point P and the left edge of the disk, including point P and the left edge of the disk, tangent to the disk points point For correct location and label of the force due to gravity exerted on the disk, directed straight down point For correct location and label of the force exerted on the disk by the axle, directed such that the disk remains in translational equilibrium (i.e., F  ) point © 2022 College Board AP® Physics C: Mechanics 2022 Scoring Guidelines Example Response Scoring Notes:  Examples of appropriate labels for the force due to gravity include: FG , Fg , Fgrav , W , mg , Mg , “grav force,” “F Earth on block,” “F on block by Earth,” FEarth on block , FE,Block The labels G and g are not appropriate labels for the force due to gravity Fn , FN , N , “normal force,” “ground force,” or similar labels may be used for the normal force, which can be used instead of Faxle Fspring , Fs , Tspring , T , “spring  (c) force,” or similar labels may be used for the tension force exerted by the spring A response with extraneous forces or vectors can earn a maximum of two points Total for part (b) For indicating that the net torque is due only to the force exerted on the disk by the tension in the rotational form of Newton’s second law  s  I d points point For correctly expressing the torque on the disk by the tension in terms of the spring force, which is equal to the tension, and the lever (moment) arm Fs R  I d point For correctly substituting for Fs point  k xR  I d For correctly substituting I d and x , or an expression for x consistent with part (a)  k ( R )R    2k Md point M R 2 d Scoring Note: The negative sign is not necessary to earn this point Total for part (c) points © 2022 College Board AP® Physics C: Mechanics 2022 Scoring Guidelines (d) For a sketch that starts at zero and monotonically increases until time t  t1 point For a sketch that is concave down between time t  and t  t1 point Example Response Scoring Note: Any part of the graph beyond t1 is not considered in scoring (e) Total for part (d) For indicating that the torque exerted by the force due to gravity on the disk increased points point Example Response The force due to gravity on the disk now has a non-zero lever arm and hence it exerts a larger torque on the disk For indicating that the torque exerted by the tension caused by the force due to gravity on the block increased point Example Response The force exerted by the right side of the string (from the block) on the disk has a longer lever arm, hence the torque it exerts is larger For indicating that the torque exerted by the tension increased point Example Response The counterclockwise torque due to the tension caused by the spring must increase to counteract the increase in clockwise torques due to the force due to gravity of the disk and tension caused by the force of gravity due to block to keep the disk in equilibrium Scoring Notes:  A response that references the torque due to the force at the axle staying the same can earn all points  A response that references the torque due to the force on the axle changing, or any additional torques can earn a maximum of points Total for part (e) points Total for question 15 points © 2022 College Board ... translational equilibrium (i.e., F  ) point © 2022 College Board AP? ? Physics C: Mechanics 2022 Scoring Guidelines Example Response Scoring Notes:  Examples of appropriate labels for the force due to... m2  Total for part (c) points â 2022 College Board AP? ? Physics C: Mechanics 2022 Scoring Guidelines (d)(i) For drawing an appropriate best-fit line including approximately the same number of... 2022 College Board AP? ? Physics C: Mechanics 2022 Scoring Guidelines (e) For selecting “ m1 ''  0.250 kg ” with an attempt at a relevant justification point For a correct justification point Example