circular & gravitation ap questions worksheet key(missing 2009 sg)

AP* Circular & Gravitation Free Response Questions KEY

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1992 Q1

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AP* Circular & Gravitation Free Response Questions

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1978 Q1

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1984 Q1

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1977 Q2

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AP® PHYSICS B 2002 FORM B SCORING GUIDELINES

Copyright © 2002 by College Entrance Examination Board. All rights reserved. Advanced Placement Program and AP are registered trademarks of the College Entrance Examination Board.

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Question 2 15 points total Distribution of points (a) 3 points

1 point for each correctly drawn and appropriately labeled force 2 points For no incorrect forces 1 point The horizontal and vertical components of the tension were acceptable if properly labeled

(b) 3 points

For indicating that the sum of the vertical forces is zero 1 point 0yF ��

For correctly substituting the applicable forces 1 point cos 0T θ mg� �

For the correct answer 1 point cosT θm g�

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AP® PHYSICS B 2002 FORM B SCORING GUIDELINES

Copyright © 2002 by College Entrance Examination Board. All rights reserved. Advanced Placement Program and AP are registered trademarks of the College Entrance Examination Board.

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Question 2 (cont’d.) Distribution of points (c) 4 points

The centripetal force is supplied by the horizontal component of the tension sincF T θ�

For using a correct expression for the centripetal force cF 1 point 2

sinmυ T θr �

For eliminating the tension or the mass using the answer to part (b) 1 point 2 sin tancos

mυ θmg mg θr θ� � OR 2cos sinT θ υ T θgr �

For using the substitution sinr θ� � 1 point 2

tansinmυ mg θθ �

� OR

2cos sinsinT θ υ T θg θ �

�

For the correct answer 1 point

sin tanυ g θ θ� � or 2sin

cosg θ

θ�

(d) 3 points

For using a correct expression for period or frequency 1 point 2π rT υ� or 2

υf π r�

For substituting the velocity from part (c) 1 point For the correct answer (unsimplified acceptable) 1 point

sin tan2 sing θ θ

f π θ�

�

� or tan1

2 sing θ

π θ� or 1

2 cosg

π θ�

(e) 2 points

For any indication that the initial velocity of the ball is horizontal 1 point For any indication that the subsequent trajectory is parabolic 1 point

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1994 Q2

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*missing 2009B scoring guide


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1995 Q3

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AP PHYSICS B 2004 SCORING GUIDELINES (Form B)

Question 1

15 points total Distribution of points (a) 4 points

For any indication of conservation of energy 1 point For a correct conservation equation for this situation 1 point

2 20 0

1 12 2 A Am mgh m mghu u+ = +

( )2 20 02A Ag h hu u= + -

For the correct substitutions 1 point ( ) ( )( )22 21.5 m s 2 9.8 m s 2.0 m 1.9 mAu = + -

( )22 4.2 m sAu = (or ( )24.3 m s using 210 m sg = )

For the correct answer 1 point 2.0 m sAu = (or 2.1 m s if 2

Au was not rounded or if 210 m sg = was used)

(b) 2 points

For each correctly drawn and labeled force 1 pt each One point earned for correct forces was deducted for having any extraneous forces.

(c) 3 points

For indicating that the sum of the forces equals the centripetal force 1 point 2AmF r

u=Â

For having the correct relative signs in the application of the above equation 1 point 2Am

mg N ru

- =

For solving for the normal force, substituting, and solving correctly 1 point 2Am

N mg ru

= -

( )( ) ( ) ( )( )22 0.50 kg 4.21 m s

0.50 kg 9.8 m s 0.95 mN = -

2.7 NN =

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AP PHYSICS B 2004 SCORING GUIDELINES (Form B)

Question 1 (continued)

Distribution of points (d) 3 points

For any indication that the work done must equal the kinetic energy at point A in the absence of friction

1 point

2friction

12 AW mu= -

For correct substitution 1 point

( ) ( )( )2friction

1 0.50 kg 4.2 m s2W = -

For the correct answer, including the negative sign 1 point friction 1.1 JW = -

(e) 3 points

Method 1: For indicating that one should decrease the radius of the curve of the second hill 1 point

The cart will lose contact when 2

0Ammg ru

- £ . Decreasing the radius of the curve

will cause the second term to increase and thus meet the condition.

For referring to the equation 2Am

N mg ru

= - 1 point

For indicating that the cart will loose contact when 0N £ 1 point Method 2: For indicating that one should make the initial hill higher or the second hill lower (1 point)

The cart will loose contact when 2

0Ammg ru

- £ . Increasing the difference in

heights will cause the speed at A to increase, and thus the second term will increase and the condition will be met.

For referring to the equation 2Am

N mg ru

= -

0

and indicating that the cart will

loose contact when N £

(1 point)

For indicating that the speed at A will increase (1 point)

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circular & gravitation ap questions worksheet key(missing 2009 sg)

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