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Unformatted text preview: AP® Physics B
2006 Scoring Guidelines
Form B The College Board: Connecting Students to College Success
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Visit the College Board on the Web: www.collegeboard.com. AP Central is the official online home for the AP Program: apcentral.collegeboard.com. AP® PHYSICS B 2006 SCORING GUIDELINES (Form B)
General Notes About 2006 AP Physics Scoring Guidelines
1. The solutions contain the most common method of solving the freeresponse questions and the
allocation of points for this solution. Some also contain a common alternate solution. Other methods of
solution also receive appropriate credit for correct work. 2. Generally, double penalty for errors is avoided. For example, if an incorrect answer to part (a) is
correctly substituted into an otherwise correct solution to part (b), full credit will usually be awarded.
One exception to this may be cases when the numerical answer to a later part should be easily
recognized as wrong, e.g., a speed faster than the speed of light in vacuum.
3. Implicit statements of concepts normally receive credit. For example, if use of the equation expressing a
particular concept is worth 1 point, and a student’s solution contains the application of that equation to
the problem but the student does not write the basic equation, the point is still awarded. However, when
students are asked to derive an expression, it is normally expected that they will begin by writing one or
more fundamental equations, such as those given on the AP Physics exam equation sheet. See pages
21–22 of the AP Physics Course Description for a description of the use of such terms as “derive” and
“calculate” on the exams, and what is expected for each.
4. The scoring guidelines typically show numerical results using the value g = 9.8 m s 2 , but use of
10 m s 2 is of course also acceptable. Solutions usually show numerical answers using both values
when they are significantly different.
5. Strict rules regarding significant digits are usually not applied to numerical answers. However, in some
cases answers containing too many digits may be penalized. In general, two to four significant digits are
acceptable. Numerical answers that differ from the published answer due to differences in rounding
throughout the question typically receive full credit. Exceptions to these guidelines usually occur when
rounding makes a difference in obtaining a reasonable answer. For example, suppose a solution requires
subtracting two numbers that should have five significant figures and that differ starting with the fourth
digit (e.g., 20.295 and 20.278). Rounding to three digits will lose the accuracy required to determine the
difference in the numbers, and some credit may be lost. © 2006 The College Board. All rights reserved.
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2006 SCORING GUIDELINES (Form B)
Question 1
15 points total
(a) Distribution
of points 3 points For a line that is close to all of the data points
For a smooth curve
For a nonlinear curve that is concave up (b) 1 point
1 point
1 point 2 points 12
gt
2
For a correct pair of quantities, expressed in terms of D and t, that will yield a straight line Distance and time are related by the equation D = Examples: D and t 2 OR 2 points D and t © 2006 The College Board. All rights reserved.
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2006 SCORING GUIDELINES (Form B)
Question 1 (continued)
Distribution
of points (c) 4 points
For correctly scaling and labeling the horizontal axis for a quantity cited in part (b)
For correctly scaling and labeling the vertical axis for a quantity cited in part (b)
For a reasonably correct plotting of the data
For a reasonably straight line through the data points 1 point
1 point
1 point
1 point Example graphing D versus t 2 : Note: If part (b) contains incorrect variables and they are correctly graphed in part (c),
a maximum of 2 points could be earned. (d) 3 points
For determining the slope of the line drawn on the graph
(2.0  0.1) m
1.9 m
Using the example graph above, slope =
=
= 4.9 m s2
2
2
0.39 s
(0.41  0.02 ) s
For an expression relating g to the slope
1
1
In the example given, D = gt 2 , so g = slope
2
2 1 point For a value of g in the range 911 m s2 1 point ( 1 point ) In the example given, g = 2 4.9 m s2 = 9.8 m s2
(e) 3 points
For a good, specific improvement
For an explanation of how this would improve accuracy
Example: Do several trials for each value of D and take averages. This reduces personal
and random error.
One point could be earned for less appropriate or less specific answers, for example “do
trials in a vacuum” or “cut down on air resistance.” 2 points
1 point © 2006 The College Board. All rights reserved.
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2006 SCORING GUIDELINES (Form B)
Question 2
15 points total
(a) Distribution
of points 4 points
For any use of conservation of energy
For example, initially the small block has only potential energy, and it is all converted
to kinetic energy when it reaches the bottom of the ramp.
For a correct expression for the initial potential energy
For a correct expression for the kinetic energy at the bottom of the ramp
1
2
Mgh = M (3.5u0 )
2
For the correct answer
2
3.52 u0
or equivalent
h=
2g (b) 1 point
1 point 1 point 4 points
For any use of conservation of momentum
For a correct expression for the initial momentum of the blocks
For a correct expression for the final momentum of the blocks
M (3.5u0 ) = M u + (1.5M ) (2u0 ) u = 3.5u0  3u0
For the correct answer
u = 0.5u0 (c) 1 point 1 point
1 point
1 point 1 point 4 points
For a correct relationship between friction and the acceleration of the block
Â F = ma = f fric 1 point For a correct kinematic equation relating acceleration and distance that does not
contain time
2
u f = ui2  2 aD 1 point For using the correct initial speed of the block 1 point 0= 2
4u0  2aD a=
D
Substituting expressions for a and f into the first equation above
2
(1.5M ) 2 u0 D = m (1.5M ) g
For the correct answer
2
m = 2u0 Dg
2
2u0 1 point © 2006 The College Board. All rights reserved.
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2006 SCORING GUIDELINES (Form B)
Question 2 (continued)
Distribution
of points (c) (continued)
Alternate solution
For any indication that the work done on the block as it slides is equal to its initial
kinetic energy
1
f fric d = mui2
2
For a correct expression for the work done on the block
For a correct expression for the initial kinetic energy of the block
1
2
m (1.5M ) gD = (1.5M ) (2u0 )
2
For the correct answer
2u 2
m= 0
Dg (d) Alternate points
1 point 1 point
1 point 1 point 3 points
For indicating that the collision is inelastic
For indicating that the reason it is inelastic is because the change in kinetic energy
is not zero, or because kinetic energy is lost in the collision
For showing that the change in kinetic energy is not zero
1
1
1
2
2
2
DK = K f  K i = È M (0.5u0 ) + (1.5 M ) (2u0 ) ˘  M (3.5u0 )
Í2
˙2
2
Î
˚ 1 point
1 point
1 point 2
DK = 3M u0 © 2006 The College Board. All rights reserved.
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2006 SCORING GUIDELINES (Form B)
Question 3
15 points total
(a) Distribution
of points 2 points For indicating the correct direction for the force due to the +Q charge ( F1 as drawn above)
For indicating the correct direction for the force due to the Q charge ( F2 as drawn above) (b) 1 point
1 point 6 points
For any indication that the magnitudes of F1 and F2 are the same
The xcomponents of F1 and F2 cancel.
For any indication that the magnitude of the net force is the sum of the ycomponents
of F1 and F2 , which are equal
Example: Ftotal = F1 cos q + F2 cos q = 2 F cos q , where q is the angle between the
yaxis and the dashed lines in the figure
For a correct expression for cos q
d
cos q =
2
x + d2
For a correct substitution for F into the above expression for Ftotal F= kqQ = ( 1 point 1 point 1 point kqQ x + d2
kqQ
d
Ftotal = 2 2
2
2
x + d x + d2
For the correct magnitude of the total force
2 kqQd
Ftotal =
or equivalent
32
x2 + d 2
r 2 1 point 2 1 point ) For indicating the correct direction for the total force, e.g., negative ydirection,
toward the bottom of the page, etc. 1 point © 2006 The College Board. All rights reserved.
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2006 SCORING GUIDELINES (Form B)
Question 3 (continued)
Distribution
of points (c) 2 points
The field can be found from the force.
E = Ftotal q
For the correct magnitude of the electric field
2 kQd
E=
32
2
x + d2 1 point For indicating the correct direction for the electric field, e.g., negative ydirection,
toward the bottom of the page, etc. 1 point ( (d) ) 2 points
The total potential is the sum of the individual point charge potentials.
kQ
 kQ
V = V1 + V2 =
+
2
2
x +d
x2 + d 2
For indicating that the electric potential is zero
Note: One point partial credit could be earned for only recognizing that the potentials
from the two charges must be added. (e) 2 points 3 points
For any indication that as x gets large, the hypotenuse and x are approximately equal or
d is negligible compared to x 1 point For indicating that the above implies that x 2 + d 2 ª x
For indicating that substituting the approximate equality into the answer from part (b)
2 kqQd
yields Ftotal =
x3 1 point
1 point © 2006 The College Board. All rights reserved.
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2006 SCORING GUIDELINES (Form B)
Question 4
15 points total Distribution
of points (a) (i) 2 points
For drawing a reflected ray at approximately the same angle to the normal as
the incident ray
For clearly indicating that this is the reflected ray 1 point
1 point (ii) 4 points
Snell’s law is used to find the angle of refraction
n1 sin q1 = n2 sin q2
For correctly substituting values into Snell’s law
1.0 sin 27∞ = 1.51sin q2
sin q2 = sin 27∞ 1.51 = 0.30
For the correct value of the angle
q2 = 17.5∞
For drawing a ray at approximately the correct angle
For clearly indicating that this is the refracted ray 1 point 1 point
1 point
1 point (iii) 1 point
The speed in the block can be determined using the definition of index of refraction.
u = c n = 3.00 ¥ 108 m s 1.51 ( ) For the correct answer
u = 1.99 ¥ 108 m s 1 point © 2006 The College Board. All rights reserved.
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2006 SCORING GUIDELINES (Form B)
Question 4 (continued)
Distribution
of points
(a) (continued)
(iv) 2 points
For a statement that the frequency is the same in the two materials, or an equation
that is an application of that fact
uplastic
u
f = air =
lair
lplastic
l
OR l plastic = air
n
uplastic lair
lplastic =
uair 1 point } lplastic = 1.99 ¥ 108 m s (650 nm ) 3 ¥ 10 m s
For the correct answer with units
lplastic = 431 nm OR 430 nm
(b) 8 OR l plastic = 650 nm
1.51
1 point 2 points
The following points were only awarded if rays were shown or described in part (a)
For indicating that the angle of reflection does not change
For indicating that the angle of refraction becomes smaller 1 point
1 point (c)
(i) 2 points
Example in which the dark lines in the drawn pattern represent the bright bands of blue light For indicating a central peak in the pattern
For having approximately even spacing between maxima
A sketch of the intensity graph was also acceptable 1 point
1 point © 2006 The College Board. All rights reserved.
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2006 SCORING GUIDELINES (Form B)
Question 4 (continued)
Distribution
of points (c) (continued)
(ii) 2 points
For using an appropriate formula (or combination of formulas) and correctly substituting
For example
ml L
xm ª
d
(1) 450 ¥ 10 9 m (1.4 m )
xm ª
0.15 ¥ 10 3 m
For the correct answer
x = 4.2 mm ( 1 point ) 1 point © 2006 The College Board. All rights reserved.
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2006 SCORING GUIDELINES (Form B)
Question 5
10 points total Distribution
of points (a)
(i) 2 points
From the ideal gas law, PV T = a constant
Points A and B are on the isothermal, so they are at the same temperature.
Therefore, PBVB = PAVA
PB 2V0 = PAV0
For the correct answer
PB
1
=
2
PA
For a correct justification (such as the reasoning shown above) 1 point 1 point (ii) 2 points
Points C and B are at the same pressure.
P
P
Therefore, C = B
PA
PA
For the correct answer
PC
1
=
2
PA
For a correct justification (such as the reasoning shown above) 1 point 1 point (iii) 2 points
Points A and B are on the isothermal, so they are at the same temperature.
For the correct answer
TB
=1
TA
For a correct justification (such as the reasoning shown above) 1 point 1 point © 2006 The College Board. All rights reserved.
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2006 SCORING GUIDELINES (Form B)
Question 5 (continued)
Distribution
of points
(a) (continued)
(iv) 2 points
Points C and A are at the same volume.
P
T
Therefore, from the ideal gas law C = C .
PA
TA PC
1
= , which was determined in part (ii) above
2
PA
For the correct answer
TC
1
=
2
TA
For a correct justification (such as the reasoning shown above) (b) 1 point 1 point
For a correct explanation
Internal energy depends only on the temperature. Since step I is isothermal there is no
change in temperature and thus no change in internal energy (c) 1 point 1 point 1 point
For a correct explanation
W =  P DV . In step III there is no change in volume, and thus no work done. 1 point © 2006 The College Board. All rights reserved.
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2006 SCORING GUIDELINES (Form B)
Question 6
10 points total
(a) Distribution
of points 1 point
For a correct expression for kinetic energy
K = mu 2 2
Note: This point was only awarded if no extraneous energy formulas were used. (b) 2 points
For using the correct expression for de Broglie wavelength
l=h p
For the correct answer in terms of the given quantities
l = h mu (c) 1 point 1 point
1 point 2 points
For a correct expression for the total energy of the electron and positron
Etotal = 2 mu 2 2 + mc 2 ( ) 1 point Can also add that since u << c , Etotal ª 2mc2
The two photons share this energy equally.
For the correct answer
E photon = mu 2 2 + mc 2 OR E photon ª mc 2 (d) 1 point 3 points
For using the given expression for the photon energy
E photon = hf 1 point For expressing the energy in terms of the wavelength
f = c l so E photon = hc l 1 point Substituting the energy obtained in part (c)
OR
mu 2 2 + mc 2 = hc l
mc 2 = hc l
For the correct answer
OR l = h m c
l = 2 hc mu 2 + 2 mc 2 ( (e) 1 point ) 2 points
For any indication that conservation of momentum applies
For a correct explanation of why conservation of momentum requires two photons
Example: since the total momentum of the electron and positron was zero, the total
momentum of the products must be zero. Since a photon cannot have zero
momentum, two photons traveling in opposite directions are required.
Note: Only 1 point total was awarded for attempts to explain using Newton’s third law. 1 point
1 point © 2006 The College Board. All rights reserved.
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This note was uploaded on 02/25/2010 for the course PHY 15166 taught by Professor Mr.donald during the Spring '10 term at 4.1.
 Spring '10
 mr.donald
 Physics

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