【AP物理C】【真题】2003年力学解答题答案

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Copyright 2003 by College Entrance Examination Board. All rights reserved. Available at .
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AP PHYSICS C: MECHANICS 2003 SCORING GUIDELINES
Question 1 (cont’d.) Distribution of points
iii. (2 points) For the correct equation relating power to force and velocity P = FK For substituting expressions for F and K found in previous parts P = (300t )(1.5t 2 + 2) = 450t 3 + 600t Alternate method points For indicating power as the time derivative of kinetic energy dK P= dt For substituting the expression for kinetic energy from (b)i. d P= 112.5t 4 + 300t 2 + 200 = 450t 3 + 600t dt
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(b)
6 points i. (1 point) 1 K = mK 2 2 For correctly substituting for the mass and the expression for K found in (a) 1 K = (100)(1.5t 2 + 2)2 = 50(1.5t 2 + 2) 2 2 ii. (3 points) Fnet = ma For indicating acceleration as the time derivative of the velocity dK a= dt For taking the correct derivative a = 3t For the correct expression Fnet = (100)(3t ) = 300t
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1 point Alternate 1 point
For substituting the expression for power found in (b)iii
W = ò (450t 3 + 600t ) dt
0 2
Alternate method points For a statement that the work done by the box is equal to the integral of power over time W = ò Pdt
2 points
450 4 2 600 2 2 ( t ) 0 + 2 (t ) 0 4 W = 1800 J + 1200 J For the correct answer with unit W = 3000 J W=
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Copyright 2003 by College Entrance Examination Board. All rights reserved. Available at .
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AP PHYSICS C: MECHANICS 2003 SCORING GUIDELINES
Question 1 (cont’d.) Distribution of points
(d)
2 points For checking the box 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 = ∆KE + W friction 1 point 1 point
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AP® Physics C: Mechanics 2003 Scoring Guidelines
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(c)
4 points For a statement that the work done on the box is equal to the change in its kinetic energy W = ∆K For finding K at 2 seconds K = (1.5)(2)2 + 2 = 8 m/s Substituting, using the value of υ0 from part (a): 1 2 2 W = (100 kg) ( 8 m/s ) − ( 2 m/s ) 2 For the correct answer with correct unit W = 3000 J 2 point 1 point
AP PHYSICS C: MECHANICS 2003 SCORING GUIDELINES
Question 1 15 points total (a) 3 points For indicating speed as the time derivative of position dx K= dt For taking the correct derivative K = 1.5t 2 + 2 For finding the correct initial speed at t = 0 K0 = 2 m/s 1 point Distribution of points