2021 AP® Physics C: Mechanics Free-Response Questions Set 1 One-1
F
Que-2
m
=
-=
-
(a)
mp3 y
aNc>=
astae
mgh=↓Kz?
KE+ PF
3
-
=
I
faucet
=
S
consvast
seem
sedm
am S
ADVANCED PLACEMENT PHYSICS C TABLE OF INFORMATION CONSTANTS AND CONVERSION FACTORS
Neutron mass, mn
27
kg
10
27
kg
9.11 10
31
1.67
Electron mass, me Avogadro’s number, N 0
1
8.31 J (mol K)
Boltzmann’s constant, k B
1.38
10
23
e
1.60
10
19
C
1 electron volt, 1 eV
1.60
10
19
J
Electron charge magnitude,
kg
10 23 mol
6.02
R
Universal gas constant,
10
1.67
Proton mass, m p
Speed of light, Universal gravitational constant, Acceleration due to gravity at Earth’s surface,
c
3.00
10 m s
G
6.67
10
11
1u
1.66
10
27
kg
931 MeV c 2
Planck’s constant,
h
6.63
10
34
Js
4.14
10
25
8.85 10
12
e0
Vacuum permittivity, Coulomb’s law constant, k Vacuum permeability, 1 atmosphere pressure,
PREFIXES Factor Prefix Symbol
mole, hertz, newton, pascal, joule,
1 4 pe0 m0
Magnetic constant, k
m kg s A K
kg 2
9.8 m s2
g
1 unified atomic mass unit,
meter, kilogram, second, ampere, kelvin,
N m2
J K
hc
UNIT SYMBOLS
8
m0 4 p
1 atm mol Hz N Pa J
1.99
Jm C
2
1.24 Nm
109 N m 2
9.0
7
(T m) A
1 10
7
(T m) A
1.0
105 N m 2
watt, coulomb, volt, ohm, henry,
W C V W H
15
eV s
3
10 eV nm
2
C2
10
4p
10
1.0
105 Pa
farad, tesla, degree Celsius, electron volt,
F T C eV
VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES q 0 30 37 45 53 60 90
109
giga
G
sin q
0
12
35
2 2
45
3 2
1
106
mega
M
cos q
1
3 2
45
2 2
35
12
0
103
kilo
k
tan q
0
3 3
34
1
43
3
10 2
centi
c
10 3
milli
m
6
micro
m
10 9
nano
n
12
pico
p
10
10
The following assumptions are used in this exam. I. The frame of reference of any problem is inertial unless otherwise stated. II. The direction of current is the direction in which positive charges would drift. III. The electric potential is zero at an infinite distance from an isolated point charge. IV. All batteries and meters are ideal unless otherwise stated. V. Edge effects for the electric field of a parallel plate capacitor are negligible unless otherwise stated.
ADVANCED PLACEMENT PHYSICS C EQUATIONS MECHANICS
Ãx
x
ax t
Ãx 0
x0
1 2 at 2 x
Ãx 0 t
Ãx2
Ãx 0 2
2ax x
a
F m
Fnet m
F
dp dt
J
p
F dt
m FN
DE
W
K
1 2 mà 2
P
dE dt
P
F v
DUg
Ã2 r
r
F t net I
I 2
I
r dm
mr
kDx
Us
1 k Dx 2
x
xmax cos( wt
T
2p w
p
Iw
2p
Tp
2p
1 2 Iw 2
w
w0
at
q
q0
w0 t
FG UG
1 2 at 2
2
1 f
Ts
rw r
acceleration energy force frequency height rotational inertia impulse kinetic energy spring constant length angular momentum mass power momentum radius or distance period time potential energy velocity or speed work done on a system position coefficient of friction angle torque angular speed angular acceleration phase angle
Fs
2
mi xi mi
x cm
K
w2r
t
a
L
F dr
mg Dh
ac
Ã
Dp
mv
Ff
t
x0
a = E= F = f = h = I = J = K = k = = L = m= P = p = r = T = t = U= v = W= x = m = q = t = w = a = f =
ELECTRICITY AND MAGNETISM
m k
FE q
E
DV
DV
Q C
UC
r2
Gm1m2 r
i
i
= = = = = = = = = = = =
N =
qi ri
= = = = = = = V= v = r = F = k = P Q q R r t U
1 q1q2 4pe0 r
k e0 A d
1 Cs
Ci
1 C i i
area magnetic field capacitance distance electric field emf force current current density inductance length number of loops of wire per unit length number of charge carriers per unit volume power charge point charge resistance radius or distance time potential or stored energy electric potential velocity or speed resistivity flux dielectric constant
FM
qv
B d
dQ dt
1 QDV 2
1 C DV 2
2
B m0 I
dB
m0 I d r 4p r 2
R
r A
F
I d
E
rJ
Bs
m0 nI
I
Nevd A
FB
I
DV R
e
E d
e
L
UL
1 2 LI 2
g
Gm1m2
1 4pe0
qV
Cp
n
E dr
UE
C
F I J L
dV dx
Ex
V
e
Q e0
E dA
I f
A B C d E
1 q1q2 4pe0 r 2
FE
Rs 1 Rp
P
Ri
i
i
I DV
1 Ri
B
B dA
dI dt
d FB dt
ADVANCED PLACEMENT PHYSICS C EQUATIONS GEOMETRY AND TRIGONOMETRY Rectangle A bh Triangle
A
1 bh 2
Circle
A
pr2
C
2p r
s rq Rectangular Solid V wh Cylinder 2
V
pr
S
2p r
CALCULUS
A = area C = circumference V = volume S = surface area b = base h = height = length w = width r = radius s = arc length q = angle
df dx
d f du du dx
d n x dx
nx n
d ax e dx
aeax 1 x
d ln ax dx d sin ax dx
a cos ax
d cos ax dx
s
x n dx
r
q 2p r 2
eax dx
Sphere
dx
a sin ax 1
n
ln x
V
x
S
4p r 2
cos ax dx sin ax dx
Right Triangle
b2
c2
sin q
a c
cos q
b c
tan q
a b
a
c q
a 90°
b
xn 1, n
1
1 ax e a
4 3 pr 3
a2
1
a 1 sin ax a 1 cos ax a
VECTOR PRODUCTS A B AB cos q A B AB sin q
1
Begin your response to QUESTION 1 on this page. PHYSICS C: MECHANICS SECTION II Time—45 minutes 3 Questions Directions: Answer all three questions. The suggested time is about 15 minutes for answering each of the questions, which are worth 15 points each. The parts within a question may not have equal weight. Show all your work in this booklet in the spaces provided after each part.
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1. A 0.50 kg fan cart is placed on a level, horizontal track of negligible friction, as shown. The fan is turned on, and the fan cart is released from rest and moves to the right. The cart travels along the horizontal track and then down an incline. Motion detector 1 measures the acceleration a of the cart from time t *A 0 to t h 3 s. Att A 3 s, the cart makes a smooth transition to the incline, and motion detector 2 measures the acceleration of the cart after t B 3 s. The fan exerts the same magnitude of force on the cart during the entire motion. The graphs below show a as functions of t. For each motion detector, the positive direction is away from the detector. If you are looking for a physics tutor in Virginia who can teach you AP and IB Physics, then you land on the right website because now India's famous Physics tutor Kumar sir has started online physics classes in Virginia, then you can take advantage of it. You can directly contact Mr Kumar and clear all your concepts of physics. If you live in any city in Viginia and your child is facing a problem in physics, your child is not able to solve physics numericals, then you can directly contact an online physics tutor in Virginia Kumar sir today
Continue your response to QUESTION 1 on this page. (a) On the dots below that represent the cart at t wo different locations, draw and label the forces (not components) that act on the cart at each location. Each force must be represented by a distinct arrow starting on, and pointing away from, the dot. FH
Fx
Fan
Fam
mg
mg
(b) Calculate the magnitude of the net force exerted on the fan cart when it is on the horizontal track.
Aten
(Meart)
=
(a)
(0.50) (08)
-
=
0.20N
(c) Calculate the angle ⑤q of the incline.
fantmg
sino-man
mgsinO= Man-fan 30= M92-ffan
mg 38
=
(0.50) (2.4)
-
=
9.40
Yngsio
(050) (0.0)
(0.50) (9.0) O
mycosef
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(d) Suppose careful measurement determines the angle of the incline to be 3° larger than that calculated in part (c). Consider the following explanation. “The scale used to measure the mass of the fan cart was not calibrated properly before the measurement, and this could account for the obser ved difference in the angle.”
Does the explanation sufficiently account for the observed discrepancy? _____ Yes _____ No Justify your answer. From the answer (c)
sino-man-ftan_Ma--M9,
mg IB Physics Tutor In Accomack Virginia, IB Physics Tutor In Albemarle Virginia, IB Physics Tutor In Alexandria Virginia, IB Physics Tutor In Alleghany Virginia, IB Physics Tutor In Amelia Virginia, IB Physics Tutor In Amherst Virginia, IB Physics Tutor In Appomattox Virginia, IB Physics Tutor In Arlington Virginia, IB Physics Tutor In Augusta Virginia, IB Physics Tutor In Bath Virginia, IB Physics Tutor In Bedford Virginia, IB Physics Tutor In Bland Virginia, IB Physics Tutor In Botetourt Virginia, IB Physics Tutor In Bristol Virginia, IB Physics Tutor In Brunswick Virginia, IB Physics Tutor In Buchanan Virginia, IB Physics Tutor In Buckingham Virginia, IB Physics Tutor In Buena Vista Virginia, IB Physics Tutor In Campbell Virginia, IB Physics Tutor In Caroline Virginia, IB Physics Tutor In Carroll Virginia, IB Physics Tutor In Charles City Virginia, IB Physics Tutor In Charlotte Virginia, IB Physics Tutor In Charlottesville Virginia, IB Physics Tutor In Chesapeake Virginia, IB 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mg
to
Hence
the cart cancels
equation used the ayle of the
of
mass
out
to
the
find
Incline
Continue your response to QUESTION 1 on this page. The experiment is repeated for several trials, each with a different angle for the incline. The acceleration of the cart down the incline is measured for each angle. The graph below shows the plot of the acceleration a of the cart as a function of the sine of the angle sin ⑧ q.
(e) i. Draw a best-fit line for the data. ii. Using the straight line, calculate an experimental value for the acceleration due to gravity g. (f) If the cart were replaced with a second cart of mass 1.0 kg that has a fan that exerts the same magnitude of force as the original fan, explain how the graph given in part (e) would change.
scope: ma: a
=
teflon= ffan
+mg
1052M52
5i8
gSio+an m
3
=
mx
(Slope (Sing + [Intercept =8=1052M52
+b=
Slope
Begin your response to QUESTION 2 on this page.
2. A block of mass m starts from rest at point A and travels with negligible friction through the loop onto a mg . All motion of ·m
horizontal surface, where the block makes contact with a spring of spring constant k
the spring is in the horizontal direction. Point C is the highest point on the loop, and point B is the rightmost point on the loop. Express all algebraic answers in terms of m, h, R, and physical constants, as appropriate. (a) On the dot below, which represents the block, draw an arrow that represents the direction of the acceleration of the block at point B in the figure above. The arrow must start on and point away from the dot. Justify your answer
Rosentripetal component owards
-
adownward
once
=
the
g
-
grtas"
centre
aa
↓. are-
B
.
.
.
g
(b) i. Derive an expression for the speed v of the block at point B. conservation
Adbly
Point A 2
ITE)
A
=
at
point B.
(TE) B
mgR+ mos MOB => UB 25Ch-R)
mg2+mc0 m5 (2-R)
of energy
=
=
=
FC
ii. Derive an expression for the magnitude of the net force F on the block at point B.
FNex
=
-
-
(mg)" + (FTTh might mag
=mightgFeT2
FNGTo <
W
B
mg
Continue your response to QUESTION 2 on this page. (c) In terms of R, derive an expression for the minimum height hmin Wh necessary for the block to maintain contact with the track through point C.
CTE)
A
=
CTE) c
m=mg (24)
mgeAt
+
the
Mg-= Mg(2K) Me, +
g2 UC
=
18R= R
=
=
+
och
28 (n-2R)
I
-
R
8(2R)
2
B(n-20)
2
Ch-2R)
2h-4Q
2h=5R =
=
50+2.5R
For
point o, minimum to complete the
velocity
circular motor,
N=O
mg + N-moc
for
which
put N=o
Wo =
9R
(d) It is determined that h ⑭ 0.30 m and R * 0.10 m . If the block is released from a height greater than that found in part (c), what would be the maximum compression Ar xMAX of the spring? ·
mg2=1K Ceme 2mg2
=
k
mac
rmae=
=>
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<mg2 K.
anger
-
a
-
(4)
=>
=
(0.30) 2010)
0.35 m
(e) A graph of the maximum compression of the spring as a function of height is shown below. The height hmin is the height calculated in part (c).
i. Explain why section I appears as a horizontal line segment on the horizontal axis. Block does not make it the
It
look can
at
this
height
not reach
through so
near to
spring ii. Explain the reason for the shape of section II on the graph.
high-ket a
ace
"
stence
barebollc
Begin your response to QUESTION 3 on this page.
↑
3. A triangular rod of length L and mass M has a nonuniform linear mass density given by the equation * l gx2, where g 3M and x is the distance from point P at the left end of the rod. L3 (a) Using integral calculus, show that the rotational inertia I of the rod about an axis perpendicular to the page and through point P is* 3 ML2. 5
AT
I
dF= =
S
dI
I
=
dice dice
*
So
L
Ucedix"=Ucax
05 of(15-05] P 325 --M =
=
=
-
-2 -
5
dee
am =X -
are
am X de =
(b) Determine the horizontal location of the center of mass of the rod relative to point P. Express your answer in terms of L.
rem=Sance I
am
am L
(xceace
=
->
I a ·
are
lny"
So
L
Usece.
dr
x
a m x de
=
=
Juson
usidm -
=
(_o7
Os? ↑E-0)
I -
L
vide
th(3)
3
(c) For an axis perpendicular to the page, is the value of the rotational inertia of the rod around point P greater than, less than, or equal to the value of the rotational inertia of the rod around the rod’s center of mass? _____ Greater than _____ Less than _____ Equal to Justify your answer. -
1p=Ic Ip] Ec
+11
(ecm)"
-
As per
New pendicular aris theorem
Continue your response to QUESTION 3 on this page. The rod is released from rest in the position shown, and the rod begins to rotate about a horizontal axis perpendicular to the page and through point P. (d) On the axes below, sketch graphs of the magnitude of the net torque t on the rod and the angular speed w of the rod as functions of time t from the time the rod is released until the time its center of mass reaches its lowest point.
↑
2=
-
ExT force
X
1 distance
W:
Not a t
(e) As the rod rotates from the horizontal position down through vertical, is the magnitude of the angular acceleration on the rod increasing, decreasing, or not changing? _____ Increasing _____ Decreasing _____ Not changing Justify your answer. 2
=Ex1 of
As
O
S10
=
1
F
(a)
(a)
approaches
epproaching tends
=
to
to
to IER0
ICRO,
zero.
hence
hence
towele is also
angular acceleration
(f) The mass of the rod is 3.0 kg, and the length of the rod is 1.0 m . Calculate the linear speed v of point S as the rod swings through the vertical position shown.
#gz
=
IW
(**(Y)() 18L f(x) f
#8 (52) v
=
=
=
18LOX1G9mi
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