2021
AP Physics 1:
Algebra­Based
®
Free­Response Questions
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trademarks of College Board. Visit College Board on the web: collegeboard.org.
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AP® PHYSICS 1 TABLE OF INFORMATION
CONSTANTS AND CONVERSION FACTORS
Proton mass, mp
1.67 – 1027 kg
Electron charge magnitude,
e
1.60 – 10 19 C
Neutron mass, mn
1.67 – 10 27 kg
Coulomb’s law constant,
k
1 4 pe0
Electron mass, me
9.11 – 10 31 kg
Speed of light,
3.00 – 108 m s
Universal gravitational
constant, G
Acceleration due to gravity
at Earth’s surface, g
UNIT
SYMBOLS
Factor
12
10
c
meter,
kilogram,
second,
ampere,
PREFIXES
Prefix
Symbol
tera
T
m
kg
s
A
kelvin,
hertz,
newton,
joule,
K
Hz
N
J
watt,
coulomb,
volt,
ohm,
9.0 – 10 9 N  m 2 C2
6.67 – 10 11 m 3 kgs2
9.8 m s2
W
C
V
W
’C
degree Celsius,
VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES

q
0
30

37

45

53

60

90

10 9
giga
G
sinq
0
12
35
2 2
45
3 2
1
10 6
mega
M
cosq
1
3 2
45
2 2
35
12
0
10 3
kilo
k
tanq
0
3 3
34
1
43
2
3
‡
centi
c
3
milli
m
6
micro
m
9
nano
n
10 12
pico
p
10
10
10
10
The following conventions are used in this exam.
I. The frame of reference of any problem is assumed to be inertial unless
otherwise stated.
II. Assume air resistance is negligible unless otherwise stated.
III. In all situations, positive work is defined as work done on a system.
IV. The direction of current is conventional current: the direction in which
positive charge would drift.
V. Assume all batteries and meters are ideal unless otherwise stated.
AP® PHYSICS 1 EQUATIONS
MECHANICS
Ãx
Ãx 0 a x t
x
1
x0 Ãx 0 t ax t 2
2
Ãx2

a

Ff
ac
Ãx20 2 a x x x0


Ç F Fnet
m
m

m Fn
2
Ã
r

p

mv

Dp

F Dt
K
1 2
mv
2
DE
W
P
DE
Dt
q
q0 w0t w
w0 at
x
A cos 2 p ft


Ç t t net
I
I

a
t
rA F
L
Iw
DL
t Dt
K
1 2
Iw
2

Fs

kx
Fd cos q
Fd
1 2
at
2
rF sin q
ELECTRICITY
a = acceleration
A = amplitude
d = distance
E = energy
f = frequency
F = force
I = rotational inertia
K = kinetic energy
k = spring constant
L = angular momentum
 = length
m = mass
P = power
p = momentum
r = radius or separation
T = period
t = time
U = potential energy
V = volume
v = speed
W = work done on a system
x = position
y = height
a = angular acceleration
m = coefficient of friction
q = angle
r = density
t = torque
w = angular speed
DUg
mg Dy

FE
k
A = area
F = force
I = current
 = length
P = power
q = charge
R = resistance
r = separation
t = time
V = electric potential
r = resistivity
q1q2
r
2
Dq
Dt
r
A
DV
R
I
R
I
P
I DV
Rs
Ç Ri
1
Rp
Ç Ri
i
1
i
WAVES
v
f
l
f = frequency
v = speed
l = wavelength
GEOMETRY AND TRIGONOMETRY
Rectangle
A bh
Triangle
A
1
bh
2
Circle
A
C
pr 2
2 pr
T
2p
w
1
f
Rectangular solid
V wh
Ts
2p
m
k
Cylinder
V
pr 2
Tp
2p

g
S
2 pr  2 pr 2

Fg
G
Us
1 2
kx
2

g

Fg
m
r
m
V
UG
m1m2
r2
Sphere
V
S
Gm1m2
r
4 3
pr
3
4pr 2
A = area
C = circumference
V = volume
S = surface area
b = base
h = height
 = length
w = width
r = radius
Right triangle
c2
a 2 b2
a
sin q
c
b
cos q
c
a
tan q
b
c
q
a
90°
b
AP® Physics 1 2021 Free­Response Questions
Begin your response to QUESTION 1 on this page.
PHYSICS 1
SECTION II
Time—1 hour and 30 minutes
5 Questions
Directions: Questions 1, 4, and 5 are short free-response questions that require about 13 minutes each to answer and
are worth 7 points each. Questions 2 and 3 are long free-response questions that require about 25 minutes each to
answer and are worth 12 points each. Show your work for each part in the space provided after that part.
1. (7 points, suggested time 13 minutes)
A stunt cyclist builds a ramp that will allow the cyclist to coast down the ramp and jump over several parked
cars, as shown above. To test the ramp, the cyclist starts from rest at the top of the ramp, then leaves the ramp,
jumps over six cars, and lands on a second ramp.
H0 is the vertical distance between the top of the first ramp and the launch point.
q 0 is the angle of the ramp at the launch point from the horizontal.
X 0 is the horizontal distance traveled while the cyclist and bicycle are in the air.
m 0 is the combined mass of the stunt cyclist and bicycle.
(a) Derive an expression for the distance X 0 in terms of H0 , q 0, m 0, and physical constants, as appropriate.
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AP® Physics 1 2021 Free­Response Questions
Continue your response to QUESTION 1 on this page.
(b) If the vertical distance between the top of the first ramp and the launch point were 2H0 instead of H0 , with
no other changes to the first ramp, what is the maximum number of cars that the stunt cyclist could jump over?
Justify your answer, using the expression you derived in part (a).
(c) On the axes below, sketch a graph of the vertical component of the stunt cyclist’s velocity as a function of
time from immediately after the cyclist leaves the ramp to immediately before the cyclist lands on the second
ramp. On the vertical axis, clearly indicate the initial and final vertical velocity components in terms of H0 , q 0,
m 0, and physical constants, as appropriate. Take the positive direction to be upward.
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3
AP® Physics 1 2021 Free­Response Questions
Begin your response to QUESTION 2 on this page.
2. (12 points, suggested time 25 minutes)
A group of students is investigating how the thickness of a plastic rod affects the maximum force Fmax with which
the rod can be pulled without breaking. Two students are discussing models to represent how Fmax depends on rod
thickness.
Student A claims that Fmax is directly proportional to the radius of the rod.
Student B claims that Fmax is directly proportional to the cross-sectional area of the rod—the area of the base of the
cylinder, shaded gray in the figure above.
(a) The students have a collection of many rods of the same material. The rods are all the same length but come
in a range of six different thicknesses. Design an experimental procedure to determine which student’s model,
if either, correctly represents how Fmax depends on rod thickness.
In the table below, list the quantities that would be measured in your experiment. Define a symbol to represent
each quantity, and also list the equipment that would be used to measure each quantity. You do not need to fill
in every row. If you need additional rows, you may add them to the space just below the table.
Quantity to be Measured
Symbol for Quantity
Equipment for Measurement
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AP® Physics 1 2021 Free­Response Questions
Continue your response to QUESTION 2 on this page.
Describe the overall procedure to be used, referring to the table. Provide enough detail so that another student
could replicate the experiment, including any steps necessary to reduce experimental uncertainty. As needed,
use the symbols defined in the table and/or include a simple diagram of the setup.
(b) For a rod of radius r0 , it is determined that Fmax is F0, as indicated by the dot on the grid below. On the
grid, draw and label graphs corresponding to the two students’ models of the dependence of Fmax on rod
radius. Clearly label each graph “A” or “B,” corresponding to the appropriate model.
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AP® Physics 1 2021 Free­Response Questions
Continue your response to QUESTION 2 on this page.
The table below shows results of measurements taken by another group of students for rods of different
thicknesses.
Rod radius (mm )
0.5
1.0
1.5
2.0
2.5
Fmax (N)
40
120
320
520
900
(c) On the grid below, plot the data points from the table. Clearly scale and label all axes, including units.
Draw either a straight line or a curve that best represents the data.
(d) Which student’s model is more closely represented by the evidence shown in the graph you drew in
part (c) ?
____ Student A’s model: Fmax is directly proportional to the radius of the rod.
____ Student B’s model: Fmax is directly proportional to the cross-sectional area of the rod.
Explain your reasoning.
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AP® Physics 1 2021 Free-Response Questions
Begin your response to QUESTION 3 on this page.
3. (12 points, suggested time 25 minutes)
(a) A student of mass MS, standing on a smooth surface, uses a stick to push a disk of mass MD . The student
exerts a constant horizontal force of magnitude FH over the time interval from time t  0 to t  t f while
pushing the disk. Assume there is negligible friction between the disk and the surface.
i. Assuming the disk begins at rest, determine an expression for the final speed vD of the disk relative
to the surface. Express your answer in terms of FH , t f , MS, MD , and physical constants, as
appropriate.
ii. Assume there is negligible friction between the student’s shoes and the surface. After time t f , the
student slides with speed vS . Derive an equation for the ratio vD / vS . Express your answer in terms
of MS, MD , and physical constants, as appropriate.
(b) Assume that the student’s mass is greater than that of the disk (MS  MD). On the grid below, sketch graphs
of the speeds of both the student and the disk as functions of time t between t  0 and t  2tf . Assume that
neither the disk nor the student collides with anything after t  t f . On the vertical axis, label vD and vS. Label
the graphs “S” and “D” for the student and the disk, respectively.
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AP® Physics 1 2021 Free­Response Questions
Continue your response to QUESTION 3 on this page.
(c) The disk is now moving at a constant speed v1 on the surface toward a block of mass MB , which is at rest on
the surface, as shown above. The disk and block collide head-on and stick together, and the center of mass of
the disk-block system moves with speed vcm .
i. Suppose the mass of the disk is much greater than the mass of the block. Estimate the velocity of
the center of mass of the disk-block system. Explain how you arrived at your prediction without
deriving it mathematically.
ii. Suppose the mass of the disk is much less than the mass of the block. Estimate the velocity of the
center of mass of the disk-block system. Explain how you arrived at your prediction without
deriving it mathematically.
iii. Now suppose that neither object’s mass is much greater than the other but that they are not
necessarily equal. Derive an equation for vcm . Express your answer in terms of v1, MD , MB , and
physical constants, as appropriate.
iv. Consider the scenario from part (c)(i), where the mass of the disk was much greater than the mass
of the block. Does your equation for vcm from part (c)(iii) agree with your reasoning from part
(c)(i) ?
____ Yes
____ No
Explain your reasoning by addressing why, according to your equation, vcm becomes (or
approaches) a certain value when MD is much greater than MB .
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AP® Physics 1 2021 Free­Response Questions
Begin your response to QUESTION 4 on this page.
4. (7 points, suggested time 13 minutes)
A cylinder of mass m 0 is placed at the top of an incline of length L 0 and height H0 , as shown above, and released
from rest. The cylinder rolls without slipping down the incline and then continues rolling along a horizontal surface.
(a) On the grid below, sketch a graph that represents the total kinetic energy of the cylinder as a function of the
distance traveled by the cylinder as it rolls down the incline and continues to roll across the horizontal surface.
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AP® Physics 1 2021 Free­Response Questions
Continue your response to QUESTION 4 on this page.
The cylinder is again placed at the top of the incline. A block, also of mass m 0, is placed at the top of a
separate rough incline of length L 0 and height H0 , as shown above. When the cylinder and block are released
at the same instant, the cylinder begins to roll without slipping while the block begins to accelerate uniformly.
The cylinder and the block reach the bottoms of their respective inclines with the same translational speed.
(b) In terms of energy, explain why the two objects reach the bottom of their respective inclines with the same
translational speed. Provide your answer in a clear, coherent paragraph-length response that may also contain
figures and/or equations.
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10
AP® Physics 1 2021 Free­Response Questions
Begin your response to QUESTION 5 on this page.
5. (7 points, suggested time 13 minutes)
Two pulleys with different radii are attached to each other so that they rotate together about a horizontal axle
through their common center. There is negligible friction in the axle. Object 1 hangs from a light string
wrapped around the larger pulley, while object 2 hangs from another light string wrapped around the smaller
pulley, as shown in the figure above.
m 0 is the mass of object 1.
1.5m 0 is the mass of object 2.
r0 is the radius of the smaller pulley.
2r0 is the radius of the larger pulley.
(a) At time t = 0, the pulleys are released from rest and the objects begin to accelerate.
i. Derive an expression for the magnitude of the net torque exerted on the objects-pulleys system about the axle
after the pulleys are released. Express your answer in terms of m 0, r0 , and physical constants, as appropriate.
ii. Object 1 accelerates downward after the pulleys are released. Briefly explain why.
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AP® Physics 1 2021 Free­Response Questions
Continue your response to QUESTION 5 on this page.
(b) At a later time t = tC , the string of object 1 is cut while the objects are still moving and the pulley is still
rotating. Immediately after the string is cut, how do the directions of the angular velocity and angular
acceleration of the pulley compare to each other?
___ Same direction
___ Opposite directions
Briefly explain your reasoning.
(c) On the axes below, sketch a graph of the angular velocity w of the system consisting of the two pulleys as a
function of time t . Include the entire time interval shown. The pulleys are released at t = 0, and the string is cut
at t = tC .
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AP® Physics 1 2021 Free­Response Questions
STOP
END OF EXAM
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13
2021
AP Physics 1:
Algebra-Based
®
Scoring Guidelines
© 2021 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 1 2021 Scoring Guidelines
Question 1: Short Answer
(a)
7 points
For using conservation of energy to find the speed v of the bicycle as it leaves the ramp
1 point
For using kinematics, vertical components, attempting to find the time the bicycle is in the air
1 point
For a correct expression for X 0 in terms of given quantities
1 point
Example response for part (a)
Etop = Ebottom
2sin θ 0 2gH 0 = gt
m0 gH 0 = 12 m0 v 2
t =
v = 2 gH 0
v f y = vi y + at
−v sin θ = v sin θ − gt
−2v sin θ = − gt
2sin θ 0 2gH 0
g
X 0 = vx t
X 0 = cos θ 0 2 gH 0
2sin θ 0 2 gH 0
g
X 0 = 4 H 0 cos θ 0 sin θ 0
Scoring Note:
Using the range equation to get X 0 = 2 H 0 sin 2θ 0 is sufficient to earn the second and third
points.
(b)
Total for part (a)
3 points
For an answer and justification that attempts to use the functional dependence of the horizontal
distance on the initial height
For an answer consistent with the expression derived in part (a)
1 point
Total for part (b)
2 points
Correct answer: 12 cars
1 point
© 2021 College Board
AP® Physics 1 2021 Scoring Guidelines
(c)
For a linear graph with a constant negative slope
1 point
For a graph that starts at v y and ends at −v y , using only allowed variables
1 point
Example response for part (c)
Total for part (c)
2 points
Total for Question 1
7 points
© 2021 College Board
AP® Physics 1 2021 Scoring Guidelines
Question 2: Experimental Design
(a)
12 points
For measuring the radius or diameter of rods with different radii using an appropriate tool
For measuring force using an appropriate tool
For a plausible/practical way to directly or indirectly determine Fmax for a given rod
For attempting to reduce experimental uncertainty in an experiment that involves breaking
the rods
Example response for part (a)
Measure the diameter D of each rod with a ruler.
Students should pull on the rod with the force probe until the rod breaks.
Record the force Fmax just before breaking.
1 point
1 point
1 point
1 point
Repeat each trial several times to reduce error.
Then trade for a new set of rods with different radii.
Repeat this experiment for several different radii rods.
Total for part (a)
(b)
For a straight-line graph marked “A” with a slope of
F0
r0
For a graph marked “B” that is concave up
For a graph marked “B” that shows a quadratic relationship at the correct points
4 points
1 point
1 point
1 point
1 point
For two graphs that both contain the point r0 , F0
Example response for part (b)
Total for part (b)
4 points
© 2021 College Board
AP® Physics 1 2021 Scoring Guidelines
(c)
For linear scales with appropriate labels and units
AND
for a graph where the plotted points cover at least half of the grid’s width and height
For plotting the points correctly
For drawing a reasonable best-fit curve
Example response for part (c)
Total for part (c)
(d)
For identifying Model B and for indicating that Fmax increases as the square of the radius
1 point
1 point
1 point
3 points
1 point
increases
Example response for part (d)
In this graph, Fmax seems to be proportional to R 2 , so that if we graph Fmax on the
vertical axis and R 2 on the horizontal axis, it should show a linear graph.
Total for question 2 12 points
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AP® Physics 1 2021 Scoring Guidelines
Question 3: Qualitative/Quantitative Translation
(a)
i.
For a correct answer vD =
12 points
1 point
FH t f
MD
ii. For indicating the total momentum of the system is the same before and after the collision
Scoring Note: If the response only includes a correct final answer of
1 point
MS
, the response
MD
earns this point but not the next point.
For correctly substituting the appropriate variables into a conservation of momentum
equation
AND
v
an answer in the form D = ...
vS
1 point
Scoring Notes:
This point can be earned only if the first point is earned.
The answer need not be correct to earn this point.
Example response for part (a)(ii)
pi = p f
0 = M S vS − M D vD
vD M S
=
vS M D
Total for part (a)
(b)
For two functions that
are straight segments for t
3 points
1 point
tf ,
AND
begin at the origin,
AND
have two different positive slopes
For two functions that are
horizontal functions for t t f
AND
are continuous over the entire time range 0
1 point
t
2t f
For labeling values on the vertical axis with vD
vS
1 point
OR
The curve labeled D is greater than the curve labeled S for all t > 0
Scoring note: This point can still be earned if the labels are not on the vertical axis but
clearly indicate that vD vS .
© 2021 College Board
AP® Physics 1 2021 Scoring Guidelines
Example response for part (b)
(c)
Total for part (b)
i. For stating or mathematically representing that if the disk is much more massive, then the
block will have little effect on the motion of disk 1
OR
M B , vcm = v1
For stating or mathematically representing that when M D
3 points
1 point
ii. For correct reasoning.
Correct answer: When M D
1 point
M B , vcm = 0
Example response for part (c) (ii)
If the block is much more massive, then it will barely move when the disk collides and
sticks to it.
iii. For using conservation of momentum
For a correct answer
vcm =
1 point
1 point
mD v1
mD + mB
iv. For an attempt to use limiting-case reasoning or functional dependence with the equation
in part (c)(iii)
For recognizing the equation from (c)(iii) reduces to a simpler form and the simplified
form is correctly compared to their answer in (c)(i)
Example 1 response for part (c) (iv)
Yes. If M B is very small, then the denominator of the equation simplifies to M D , which
1 point
1 point
then can cancel out of the equation leaving vcm = v1 .
Total for part (c) 6 points
Total for question 3 12 points
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AP® Physics 1 2021 Scoring Guidelines
Question 4: Paragraph-Length Response
(a)
7 points
For a straight line with a positive slope beginning at the origin and reaching a maximum
value when the distance traveled is L0
1 point
For a nonzero horizontal line between L0 and 2L0
1 point
Example response for part (a)
(b)
Total for part (a)
2 points
For indicating that both objects start with the same gravitational potential energy in the
object-Earth system
For a correct statement about the energy transformations that occur to the cylinder as it
travels down the ramp
For a correct statement about the energy transformations that occur to the block as it travels
down the ramp
For indicating that the cylinder’s final rotational kinetic energy is equal to the amount of the
block-Earth system’s initial mechanical energy that is dissipated by friction
For a logical, relevant, and internally consistent argument that addresses the required
argument or question asked, and follows the guidelines described in the published
requirements for the paragraph-length response
Example response for part (b)
Both objects start with the same gravitational potential energy in the object-Earth system.
The block-Earth system’s mechanical energy is converted into kinetic energy, and some of
it is dissipated by friction as the block slides down the ramp. The cylinder-Earth system’s
mechanical energy is transformed into translational kinetic energy and some is transformed
into rotational kinetic energy. The cylinder’s final rotational kinetic energy is equal to the
amount of the block-Earth system’s initial mechanical energy that is dissipated by friction.
1 point
1 point
1 point
1 point
1 point
Total for part (b)
5 points
Total for question 4
7 points
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AP® Physics 1 2021 Scoring Guidelines
Question 5: Short Answer
(a)
7 points
1 point
i. For correct expressions for the torques from the weight of each object
The torques are m0 g 2r0 for object 1 and 1.5m0 g r0 for object 2
For indicating that the two torques are exerted in opposite directions
net = m0 g
1 point
2r0 − 1.5m0 g r0
1 point
For the derivation of a correct answer of 0.5m0 gr0
Example response for part (a)(i)
net = 1 − 2
net = m0 g (2r0 ) − (1.5m0 g ) r0
net = 0.5m0 gr0
ii. For an explanation that object 1 exerts a larger torque than object 2
1 point
Example response for part (a)(ii)
Object 1 is twice as far from the axle as object 2, while object 2 has only 1.5 times the weight
of object 1. So, object 1 exerts a larger torque.
Total for part (a)
(b)
4 points
Correct answer: “Opposite directions”
Scoring note: If the wrong answer is selected, the response is not graded.
For a correct answer and a correct explanation
1 point
Example response for part (b)
The objects exerted torques in opposite directions, with object 1 exerting a larger torque, so
object 1 determines the net torque direction. With the torque from object 1 removed, the net
torque and angular acceleration switch direction (becoming clockwise) to the torque from
object 2. The angular velocity does not change direction immediately and is still
counterclockwise.
© 2021 College Board
AP® Physics 1 2021 Scoring Guidelines
(c)
For a linear graph between 0 and tC , with an initial angular velocity of zero and nonzero slope
1 point
Scoring note: The slope can be positive or negative.
For a change in the sign of the slope at t = tC
1 point
AND
no discontinuity.
Example response for part (c)
Total for part (c)
2 points
Total for question 5
7 points
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