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AP Physics 1: Algebra-Based Exam
SECTION II: Free Response
DO NOT OPEN THIS BOOKLET UNTIL YOU ARE TOLD TO DO SO.
At a Glance
Total Time
1 hour and 40 minutes
Number of Questions
4
Percent of Total Score
50%
Writing Instrument
Either pencil or pen with
black or dark blue ink
Month
Day
Electronic Device
Calculator allowed
Suggested Time
Approximately 25 minutes
each for questions 1 and
3, 30 minutes for
question 2, and 20
minutes for question 4
Percent of Section II
Score
Questions 1 and 3: 12.5%
Question 2: 15%
Question 4: 10%
Instructions
The questions for Section II are printed in this booklet. A table of information and lists of
equations that may be helpful are printed in the Reference booklet. You may use any
blank space in the Reference booklet for scratch work, but you must write your answers
in the spaces provided for each answer in this Free Response booklet. No credit will be
given for any work written in the Reference booklet. Calculators, rulers, and
straightedges may be used in this section.
All final numerical answers should include appropriate units. Credit for your work
depends on demonstrating that you know which physical principles would be appropriate
to apply in a particular situation. Therefore, you should show your work for each part in
the space provided after that part. If you need more space, be sure to clearly indicate
where you continue your work. Credit will be awarded only for work that is clearly
designated as the solution to a specific part of a question. Credit also depends on the
quality of your solutions and explanations, so you should show your work.
Write clearly and legibly. Do not write outside the box. Cross out any errors you make;
erased or crossed-out work will not be scored. You may lose credit for incorrect work that
is not crossed out. When constructing a graph or diagram, use only one color of ink or
pencil.
Manage your time carefully. You may proceed freely from one question to the next. You
may review your responses if you finish before the end of the exam is announced.
38 AP Physics 1: Algebra-Based Practice Exam
ADVANCED PLACEMENT PHYSICS 1 TABLE OF INFORMATION
CONSTANTS AND CONVERSION FACTORS
Acceleration due to gravity at Earth’s surface,
Universal gravitational constant,
g = 9.8 m s 2
G = 6.67 × 10−11 m 3 (kg s 2 ) 6.67 10−11 N m 2 kg 2
Magnitude of the gravitational field strength at the
Earth’s surface, g = 9.8 N kg
1 atmosphere of pressure,
5
2
5
1 atm = 1.0 × 10 N m = 1.0 × 10 Pa
10−2
PREFIXES
Prefix
tera
giga
mega
kilo
centi
Symbol
T
G
M
k
c
10−3
milli
m
10−6
micro
10−9
nano
µ
n
−12
pico
p
Factor
1012
109
106
103
10
hertz,
joule,
kilogram,
meter,
UNIT
SYMBOLS
Hz
J
kg
m
newton,
pascal,
second,
watt,
N
Pa
s
W
VALUES OF TRIGONOMETRIC FUNCTIONS FOR
COMMON ANGLES
0°
30°
37°
45°
53°
60°
90°
sin
0
12
35
2 2
45
3 2
1
cos
1
3 2
45
2 2
35
12
0
tan
0
3 3
34
1
4 3
3
The following conventions are used in this exam:
• The frame of reference of any problem is assumed to be inertial unless otherwise stated.
• Air resistance is assumed to be negligible unless otherwise stated.
• Springs and strings are assumed to be ideal unless otherwise stated.
• Fluids are assumed to be ideal, and pipes are assumed to be completely filled by fluid, unless otherwise
stated.
GEOMETRY AND TRIGONOMETRY
Rectangle
A = bh
Rectangular Solid
V = wh
Triangle
1
A = bh
2
Cylinder
V = r 2
Circle
A = r2
Sphere
4 3
V=
r
3
S = 4 r2
C=2 r
s=r
A = area
b = base
C = circumference
h = height
 = length
r = radius
s = arc length
S = surface area
V = volume
w = width
q = angle
S = 2 r + 2
s
r
2
Right Triangle
a 2 + b2 = c 2
a
sin =
c
b
cos =
c
a
tan =
b
c
a
90°
b
1
AP Physics 1: Algebra-Based Practice Exam
39
MECHANICS AND FLUIDS
v x = v x 0 + ax t
1
x = x0 + vx 0t + ax t 2
2
2
2
vx = v x 0 + 2 ax x − x0

mi xi

xcm =
mi


F Fnet

=
asys =
msys msys
(
)

mm
Fg = G 1 2 2
r


F f µ Fn


Fs = − k x
2
v
r
1
K = mv 2
2
W = F d = Fd cos
ac =
K
Wi =
a = acceleration
d = distance
E = energy
F = force
J = impulse
k = spring constant
K = kinetic energy
m = mass
p = momentum
P = power
r = radius, distance, or
position
t = time
U = potential energy
v = velocity or speed
W = work
x = position
y = height
q = angle
m = coefficient of friction
F ,i d i
1
k ( x )2
2
Gm1m2
UG = −
r
U g mg y
=
W
E
=
t
t
= F v = Fv cos
p = mv
v
p
= ma
=m
t
t
Favg t
p
Fnet =
J
vcm =
pi
=
mi
mi vi
mi
a = acceleration
A = amplitude or area
d = distance
f = frequency
F = force
h = height
I = rotational inertia
k = spring constant
K = kinetic energy
 = length
L = angular momentum
m = mass
M = mass
P = pressure
r = radius, distance, or
position
t = time
T = period
v = velocity or speed
V = volume
W = work
x = position
y = vertical position
a = angular acceleration
q = angle
r = density
t = torque
w = angular speed
1 2
t
2
2
= 02 + 2 ( − 0 )
0
t+
v=r
aT = r
= r F = rF sin
mi ri2
I=
I = I cm + Md 2
sys
K=
=
=
I sys
1
I
2
net
I sys
2
W
L= I
L = rmv sin
L
t
xcm r
1
f
Ts = 2
m
k
Tp = 2

g
Pavg =
P
+ t
= 0+
T=
Us
0
x = A cos(2 ft )
x = A sin(2 ft )
m
=
V
F
P=
A
P = P0 + gh
Pgauge = gh
Fb = Vg
A1v1 = A2 v2
P1 + gy1 +
40 AP Physics 1: Algebra-Based Practice Exam
2
1 2
v =
2 1
2
+
y2 +
1 2
v
2 2
Begin your response to QUESTION 1 on this page.
PHYSICS 1
SECTION II
Time—1 hour and 40 minutes
4 Questions
Directions: Question 1 and 3 require approximately 25 minutes each to answer and are worth 10 points each.
Question 2 requires approximately 30 minutes to answer and is worth 12 points. Question 4 requires approximately
20 minutes to answer and is worth 8 points. Show your work for each question part in the space provided after each
part.
1. A large container is filled with water. The container is filled to a height D , as shown in Figure 1. A release valve is
opened at a height d above the floor, and water exits horizontally from the valve, and initially hits the floor a
distance x from the side of the container. Assume the water in the container is still. The effects of friction,
turbulence, and viscosity are negligible.
GO ON TO THE NEXT PAGE.
AP Physics 1: Algebra-Based Practice Exam
41
Continue your response to QUESTION 1 on this page.
(a)
i. Derive an expression for the speed of the water v leaving the valve in terms of D , d , and physical
constants as appropriate. Begin your derivation by writing a fundamental physics principle or an equation
from the reference book.
ii. Derive an expression for the horizontal distance x traveled by the water before hitting the floor in
terms of D , d , and physical constants as appropriate. Begin your derivation by writing a fundamental
physics principle or an equation from the reference book.
GO ON TO THE NEXT PAGE.
42 AP Physics 1: Algebra-Based Practice Exam
Continue your response to QUESTION 1 on this page.
iii. When the container is filled to a height D , the speed of the water exiting the valve is v0. On the axis
provided, sketch a graph of the speed of the water leaving the valve as a function of the height of the
water in the container.
(b) Suppose that the container is filled with salt water which has a greater density than fresh water. How will this
change affect the horizontal distance x traveled by the water before it reaches the floor? Justify your response
beyond derivations or referencing equations.
GO ON TO THE NEXT PAGE.
AP Physics 1: Algebra-Based Practice Exam
43
Begin your response to QUESTION 2 on this page.
2. Two identical rolls of paper have mass M and radius R. Roll 1 is held at a height h1 above the ground and
dropped from rest. Roll 1 falls to the ground without unrolling. Roll 2 is held a height h2 above the ground,
where h2 < h1. When Roll 2 is released from rest, the end of Roll 2 is held in place. Roll 2 unrolls and rotates
while it falls, as shown in Figure 1. Both rolls are released from rest at time t = 0 and reach the ground at the
same time t = t1. The rotational inertia of both rolls of paper can be modeled as I =
1
MR 2 .
2
GO ON TO THE NEXT PAGE.
44 AP Physics 1: Algebra-Based Practice Exam
Continue your response to QUESTION 2 on this page.
(a) Draw and label a force diagram of the forces (not components) exerted on each roll as they fall between t = 0
and t = t1. Each force in your force diagram must be represented by a distinct arrow starting on, and pointing
away from, the point at which the force is exerted on the roll.
(b)
i. Determine an expression for the linear acceleration a1 of Roll 1 as it falls in terms of h1, h2, M , R, and
physical constants, as appropriate.
ii. Starting with Newton’s second law in rotational or translational form, derive an expression for the
linear acceleration a 2 of Roll 2 as it unrolls in terms of h1, h2, M , R, and physical constants, as
appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the
reference book.
GO ON TO THE NEXT PAGE.
AP Physics 1: Algebra-Based Practice Exam
45
Continue your response to QUESTION 2 on this page.
(c) Figure 2 shows a graph of the linear speed of Roll 1 as a function of time between t = 0 and t = t1. The linear
speed of Roll 1 just before it hits the ground is v1. On the same grid, sketch the linear speed of Roll 2 as a
function of time between t = 0 and t = t1. Clearly label the final speed of Roll 2 as v2.
(d) Justify how the force diagram created in part (a) is or is not consistent with the graph drawn in part (c).
GO ON TO THE NEXT PAGE.
46 AP Physics 1: Algebra-Based Practice Exam
Begin your response to QUESTION 3 on this page.
3. A group of students are given a glider and track. The track is leveled and turned on, so that the glider floats gently
on a cushion of air as shown in Figure 1. The manufacturer of the glider/track claims that when the track is turned
on, friction between the glider and track is negligible. The students want to determine whether the manufacturer’s
claim is correct.
(a) Describe an experimental procedure for collecting data that can be graphed to determine if the manufacturer’s
claim is correct. Include any steps necessary to reduce experimental uncertainty. If needed, you may include a
simple diagram of the setup with your procedure.
(b) Describe how the data collected in part (a) could be graphed and how that graph would be analyzed to
determine whether friction between the track and glider is negligible.
GO ON TO THE NEXT PAGE.
AP Physics 1: Algebra-Based Practice Exam
47
Continue your response to QUESTION 3 on this page.
After performing their procedure, the students conclude that the force of friction between the track and the glider
is negligible. In a second experiment, the students are tasked with calculating the mass of a hanger using the glider
and track. The students tie the hanger to the glider with a string and place the string over a pulley. The students
add six 300 g washers to their hanger. The masses of the string and the pulley are negligible compared to the total
mass of the washers, hanger, and glider.
The students release the glider – hanger – washer system and measure the acceleration of the glider with a motion
sensor. In each of the following trials, the students move one washer from the hanger to the glider and repeat the
experiment.
The students correctly derive the following relationship between the mass M of the glider with washers, the
acceleration a of the system, and the total mass C of the glider – hanger – washer system: M = C −
Ca
g
The data collected by the students is shown in the table.
• Mass of glider: 0.500 kg
• Mass of each washer: 300 g
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48 AP Physics 1: Algebra-Based Practice Exam
Continue your response to QUESTION 3 on this page.
Total Mass of glider
with Washers,
Acceleration of
glider (m / s2)
0.8
6.8
1.1
5.8
1.4
4.7
1.7
3.6
2
2.7
(c) The students create a graph with M plotted on the vertical axis.
i. Indicate which measured or calculated quantity could be plotted on the horizontal axis to yield a linear
graph that could be used to determine the mass of the hanger. Use the blank columns to list any quantities
you will graph other than the data provided. The students create a graph with M plotted on the vertical
axis.
Vertical axis:
M (kg)
Horizontal axis: __________
ii. On the grid shown in Figure 3, plot the quantities identified in part (c)(i) that can be used to determine
the mass of the hanger. Scale the graph, as appropriate. Clearly label the horizontal axis, including units.
GO ON TO THE NEXT PAGE.
AP Physics 1: Algebra-Based Practice Exam
49
Continue your response to QUESTION 3 on this page.
ii. On the grid shown in Figure 3, plot the quantities identified in part (c)(i) that can be used to determine
the mass of the hanger. Scale the graph, as appropriate. Clearly label the horizontal axis, including units.
iii. Draw the best-fit-straight line for the data graphed in part (c) (ii).
(d) Calculate an experimental value for the mass of the hanger using the best - fit line that you drew in Figure 3 in
part (c)(iii.).
GO ON TO THE NEXT PAGE.
50 AP Physics 1: Algebra-Based Practice Exam
Begin your response to QUESTION 4 on this page.
4. Spheres 1 and 2 have masses m1 and m 2, respectively. Both spheres are suspended from the ceiling by strings of
identical lengths. Sphere 2 is pulled back so that there is tension in the string and the center of Sphere 2 is a
vertical distance H above the center of Sphere 1, as shown in Figure 1. Sphere 2 is released and then collides
with and sticks to Sphere 1. The two spheres continue to swing forward, as shown in Figure 2 , and momentarily
come to rest when the center of mass of the two-sphere system is a height hCM above the original height of the
center of Sphere 1 as shown in Figure 3.
(a) If the mass of Sphere 2 is increased, does hCM increase, decrease, or remain the same? Justify your answer
using appropriate physics principles and qualitative reasoning beyond referencing equations.
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AP Physics 1: Algebra-Based Practice Exam
51
Continue your response to QUESTION 4 on this page.
(b) Using conservation of energy and conservation of momentum derive an expression for hCM in terms of m1,
m 2, H , and physical constants, as appropriate. Begin your derivation by writing a fundamental physics
principle or an equation from the reference book.
(c) A group of students want to create a collision where hCM is as small as possible. Describe the relative masses
of spheres 1 and 2 that will result in the smallest hCM . Justify your answer using your derivation from part
(b).
GO ON TO THE NEXT PAGE.
52 AP Physics 1: Algebra-Based Practice Exam
DO NOT WRITE ON THIS PAGE.
STOP
END OF EXAM
IF YOU FINISH BEFORE TIME IS CALLED,
YOU MAY CHECK YOUR WORK ON THIS SECTION.
___________________________________________
THE FOLLOWING INSTRUCTIONS APPLY TO THE COVERS OF THIS SECTION II: FREE
RESPONSE BOOKLET. MAKE SURE YOU HAVE DONE THE FOLLOWING:
• COMPLETED THE IDENTIFICATION INFORMATION AS REQUESTED ON THE
FRONT AND BACK COVERS OF THIS FREE RESPONSE BOOKLET
• CHECKED THAT YOUR AP ID LABEL IS IN THE BOX ON THE FRONT COVER
AP Physics 1: Algebra-Based Practice Exam
53