AP® Physics 1: Algebra-Based Free-Response Questions 2021 r F ORNTUL AG & N R = U"Sin20 One-2<SRtSS@fORSE ARG A Que-3 <0cm=M10,+H282 my + Mz one-4 <mgh=tmo surse-Ex twin vs A
CONSTANTS AND CONVERSION FACTORS
Proton mass, 271.6710 kgmp
Neutron mass, 271.6710 kgmn
Electron mass, 319.1110 kgme
Speed of light, 3.00108 msc
UNIT SYMBOLS
PREFIXES
meter, m kilogram, kg second, s ampere, A
Factor Prefix Symbol
1012 tera T
910 giga G 610 mega M 310 kilo k 210 centi c
310 milli m 610 micro m 910 nano n
1210 pico p
Electron charge magnitude, 191.6010 Ce Coulomb’s law constant, 92149.010 NmCk pe0
2 Universal gravitational constant, 11326.6710 mkgsG
Acceleration due to gravity at Earth’s surface, 29.8 msg
kelvin, K hertz, Hz newton, N joule, J
watt, W coulomb, C volt, V ohm, W
degree Celsius, C
VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES
q 0
sin q 0 12 35 22 45 32 1 cos q 1 32 45 22 35 12 0 tan q 0 33 34 1 43 3
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.
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AP® PHYSICS 1 TABLE OF INFORMATION
30 37 45 53 60 90
MECHANICS
a = acceleration
amplitude
distance
energy
frequency
force
I
rotational
= kinetic energy
= spring constant
= angular momentum
length
m
mass
= power p
momentum
radius
= period
= time
separation
= potential energy
volume
speed
position
height
AND TRIGONOMETRY
torque
AP® PHYSICS 1 EQUATIONS
A =
d =
E =
f =
F =
=
inertia K
k
L
=
=
P
=
r =
or
T
t
U
V =
v =
W = work done on a system x =
y =
a = angular acceleration m = coefficient of friction q = angle r = density t =
w = angular speed 0 xxxatÃà 2 00 1 2x xxtat à x 22 0 2 xxxaxxÃà 0 aFFnet mm fn FF m 2 ac r à p mv p FtDD 21 2 Kmv cosEWFdFd qD PE t D D 2 00 1 2 tt qqwa 0 twwa cos2x Aft p net II tt a sinrFrF tq LI w Lt t DD 21 2 KI w s Fkx 21 2s Ukx m Vr g UmgyD D 21T f p w 2s Tm k p 2Tp g p 12 2g mm FG r g F g m 12 G Gmm U r ELECTRICITY A = area F = force I = current = length P = power q = charge R = resistance r = separation t = time V = electric potential r = resistivity 12 2E Fkqq r Iq t D D R A r IV R D PIV D si i RR 11 pi i RR WAVES f = frequency v = speed l = wavelength v f l GEOMETRY
A = area C = circumference V = volume S = surface area b = base h = height = length w = width r = radius Rectangle A bh Triangle 1 2 Abh Circle 2Ar p 2 Cr p Rectangular solid Vwh Cylinder 2Vr p 222Srpp r Sphere 34 3 Vr p 24 Sr p Right triangle 222 cab sin a c q cos b c q tan a b q c a b 90°q
Begin
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.
,
AP® Physics 1 2021 FreeResponse Questions
your response to QUESTION 1 on this page. GO ON TO THE NEXT PAGE. Use a pencil or pen with black or dark blue ink only. Do NOT write your name. Do NOT write outside the box. © 2021 College Board. Visit College Board on the web: collegeboard.org. 2 A Using v Billreso -x o ↳ sh 6-CARS WIDTH of CAR-R do= 4HoCs00 Goo consider conservation of energy between a oPoint 1B-Mogho: I more ⑧ = /2gho 20 = NCOSE) (t) , t= CIRMO I 8. Ro=VCo (GO)-2OCoD24Gox
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 2 H0 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.
AP® Physics 1 2021 FreeResponse Questions
GO ON TO THE NEXT PAGE. Use a pencil or pen with black or dark blue ink only. Do NOT write your name. Do NOT write outside the box. © 2021 College Board. Visit College Board on the web: collegeboard.org. 3 F or 2H0,20 =4(2Ho) C08 3M @ -> OHO COSO SOo then Range becomes twice, hence He will Cross-12-caUS + EFHo lEHo Best phys isfutaes
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
SE
THe
of mm Rulev
vod
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GO ON TO THE NEXT PAGE.
Use a pencil or pen with black or dark blue ink only. Do NOT write your name. Do NOT write outside the box. © 2021 College Board. Visit College Board on the web: collegeboard.org.
AP® Physics 1 2021 FreeResponse Questions
4
FORC-TO E f OR
& ReAK
SENSOR. ROD Radius
the
of the setup.
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
① calculate A, for which I should be calculated. * =DUS ② Record H. see by applying force and measure force by using face sensor, and Repeat buth rod of same thickness ③ Repeat step 4 & step 8 rods of different material ④ student will then make a graph between F sU to find the best fit and analyse Best physics tutor for a physics fORC-↓ Rob g SON SO R
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(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.
⑭ * No Be ↑ "B A
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.
B’s model: Fmax is directly proportional to the cross-sectional area of the rod.
AP® Physics 1 2021 FreeResponse Questions
? ____
Student
Explain your reasoning. GO ON TO THE NEXT PAGE. Use a pencil or pen with black or dark blue ink only. Do NOT write your name. Do NOT write outside the box. © 2021 College Board. Visit College Board on the web: collegeboard.org. 6 1000A fmax- X 8 00N GCN x 4 OON 200 F * X 5 i is 28 Uchim) W Fan CU? 2 A A: DUL
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 tf 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, tf , MS, MD, and physical constants, as appropriate.
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ii. Assume there is negligible friction between the student’s shoes and the surface. After time tf , 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.
# *D H o RATR # ,Ms, Ne #H = MD a voo te- f vo = (#) + Ans *s # S * No frictional force it means conservation of linear momentum. is all d MpVD=4s vs = = fs
(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 tf . 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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# Md & A My Mos For student as = fis for DIsC VD ap = fd Vs D ↑is > TID S as Lap No = o f aptf vs = 0 + as +8. Up > Vs
(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.
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⑭ D B m O= O Apply conservation of linear Dn momentum ↑x Un+ +3 (0) (t1p ++13) Vcm Vcm = 40n+ M310) = MDO1 ↑p > T4 B (Mx + 19B) (Mx+M B) Hence Vam <01 slightly less than Un
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.
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Velocity of (ask-block
system is much less than
Un, Due to conservation
of linear momentum
larger mass collision
decreases the
velocity · m = "B As per the conservation of linear momentum. of Vid = (M3 +Mb) Vcm Vam Un Tn StB ++1p).
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) ?
room
____ 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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W **D *
B.
Vam=
Un Ho CTB++1p).
↑D 2 d +B +
Mp
Un <
Vamo
4. (7 points, suggested time 13 minutes)
⑭ Es MADo
A cylinder of mass m0 is placed at the top of an incline of length L0 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.
Begin your response to QUESTION 4 on this page.
Ihv"=mgle
(e. Varies
from zero KE = mgre to HO). KE acc Hillc = Ho Atc= Ho KE: sonsvart
Mo
Ar * Ad
The cylinder is again placed at the top of the incline. A block, also of mass m0, is placed at the top of a separate rough incline of length L0 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.
↳Blinder block↳ total PE < a b TRANSLAT) TRANSLATIONAL &of ATIONAL KE HfAT DUE TO fRICTION KE IC E ↳GVAL Hence Reach at ground at same translational speed.
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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.
m0 is the mass of object 1.
1.5m0 is the mass of object 2.
o
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 m0, r0, and physical constants, as appropriate.
Begin your response to QUESTION 5 on this page.
# I AM
Ad ↳Do *No Torque about centre ofthe bulley =)C200) = to (80) = 2 Mog (200) 1.5 Mog (U) = 2 a T2 a To 0.5 Mog0o = 2 Mog 1.5mog
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ii. Object 1
accelerates downward after the pulleys are released. Briefly explain why.
Torque at the sentre ofthe pulley due to object Mo en = mog <200). Torque due to object 1.5 mo 2 = 15 Mog (r) 2) 22.-stence accelerated downward.
Ado
(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.
v
After out of string P
Due
to mass 15mo acceleration atf=+o
<ut<-X
and angular velocity would go in the same direction
↳
a cut same direction
&
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(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.
released at t = 0
cut at = t = fo
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