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Unformatted text preview: AP® Physics C: Mechanics
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For the College Board’s online home for AP professionals, visit AP Central at apcentral.collegeboard.com. TABLE OF INFORMATION FOR 2004 and 2005
CONSTANTS AND CONVERSION FACTORS
27 = 1.66 = 931 MeV/c ¥ 1 unified atomic mass unit, 10  1u UNITS
Name Symbol 10 9 giga G kilogram kg 10 6 mega M 10 3 kilo k centi c milli m micro µ nano n pico p mn = 1.67 × 10 −27 kg second s Electron mass, me = 9.11 × 10 −31 kg ampere A e = 1.60 × 10 C kelvin N0 = 6.02 × 10 23 mol −1
R = Universal gas constant, K mole mol hertz 8.31 J / ( mol K )
◊ Avogadro’s number, Hz Boltzmann’s constant, k B = 1.38 × 10 −23 J / K Speed of light, c = 3.00 × 10 8 m / s newton N Planck’s constant, h = 6.63 × 10 −34 J ⋅ s pascal Pa = 4.14 × 10 −15 eV ⋅ s hc = 1.99 × 10 −25 k = 1 / 4π J
W θ sin θ cos θ tan θ C 0 0 1 0 V
Ω 30 1/2 3 /2 3 /3 henry H 37 3/5 4/5 3/4 farad F tesla T 45 2 /2 2 /2 1 degree
Celsius C 53 4/5 3/5 4/3 electronvolt eV 60 3 /2 1/2 3 90 k = µ 0 / 4π = 10 −7 (T ⋅ m) / A = G 6.67 ¥ 1 atmosphere pressure, VALUES OF TRIGONOMETRIC
FUNCTIONS FOR COMMON ANGLES volt 2 = 9.0 × 10 9 N ⋅ m 2 / C 2 g = 9.8 m / s 10 11  Acceleration due to gravity
at the Earth’s surface, 10 −12 1 0 ∞ ' Universal gravitational constant, 10 −9 ohm C / N⋅m
2 µ 0 = 4π × 10 −7 (T ⋅ m) / A Vacuum permeability,
Magnetic constant, 0 = 8.85 × 10 10 −6 coulomb 3 m / kg s
◊ Coulomb’s law constant, 0 10 −3 watt J⋅m −12 10 −2 joule = 1.24 × 10 3 eV ⋅ nm Vacuum permittivity, Symbol m Neutron mass, Magnitude of the electron charge, Prefix meter 2 −19 Factor kg m p = 1.67 × 10 −27 kg Proton mass, PREFIXES 2 1 atm = 1.0 × 10 5 N / m 2 2 = 1.0 × 10 5 Pa 1 electron volt, 1 eV = 1.60 × 10 −19 J The following conventions are used in this examination.
I. Unless otherwise stated, the frame of reference of any problem is assumed to be inertial.
II. The direction of any electric current is the direction of flow of positive charge (conventional current).
III. For any isolated electric charge, the electric potential is defined as zero at an infinite distance from the charge. 2 ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 2004 and 2005 = q
t a= = w = w q = q + = w + 0t 12
t
2 w 1
Ri FM = qv × B
B•d = 1
f m
k Bs = =
= = p m ˆ
r e r2
Gm1m2
r 0 nI = B • dA dm
dt
dI
= −L
dt
12
U L = LI
2 e p g
Gm1m2 0I F= Id ×B f = FG i 3 =− f w
p 2 = Tp 1
=
Rp Ri z =
2 i P = IV 12
kx
2 2 = UG Rs = t
a + 0 a Ts w= T A
V = IR z u Us R= I kx Fs 0 dQ
dt
1
1
Uc = QV = CV 2
2
2
I= m ¥=
w=
Â=
Ú= K rp
12
I
2 1
1
=
Cs
i Ci m t = tÂ
=t ¥ r m Ci i ∑ Â
Â= mr mr 2 Cp = d ∑ = r 2 dm a
w u = w I net rcm
L m D = F 0A r u I r Q
V ∑ = r 2 0 q1 q 2
r Q
q
R
r
t
U
V =
=
=
=
=
=
=
=
=
m=
= k = u r C= 4 1 f Ú= ∑ 2 C= ∑ £ m ac UE = qV = r
u =
Ú= F dr
12
K
m
2
dW
P
dt
P Fv
Ug
mgh k N p D= = W = F fric p acceleration
force
frequency
height
rotational inertia
impulse
kinetic energy
spring constant
length
angular momentum
mass
normal force
power
momentum
radius or distance
position vector
period
time
potential energy
velocity or speed
work done on a system
position
coefficient of friction
angle
torque
angular speed
angular acceleration p =Â
=u u dp
dt
F dt
mv ma =
=
=
=
=
=
=
=
=
L=
m=
N=
P=
p=
r=
r=
T=
t=
U=
=
W=
x=
=
=
=
=
= ∑ + J
p ( F Fnet  F ) = 2 0 a
F
f
h
I
J
K
k e + u u
2 12
at
2
2 a x x0 0t + = u x0 at + x 0 ELECTRICITY AND MAGNETISM
1 q1 q 2
A = area
F=
2
B = magnetic field
40r
C = capacitance
F
d = distance
E=
q
E = electric field
= emf
Q
E • dA =
F = force
0
I = current
dV
L = inductance
E=−
= length
dr
n = number of loops of wire
qi
1
V=
per unit length
4 0 i ri
P = power
p MECHANICS charge
point charge
resistance
distance
time
potential or stored energy
electric potential
velocity or speed
resistivity
magnetic flux
dielectric constant ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 2004 and 2005
GEOMETRY AND TRIGONOMETRY
area
circumference
volume
surface area
base
height
length
width
radius d f d f du
dx du dx
dn
x
nxn 1
dx
dx
e
ex
dx
1
d
1n x
dx
x
d
sin x cos x
dx
d
cos x
sin x
dx
1 n1
xn dx
x ,n
n1
ex dx ex
dx
ln x
x
cos xdx sin x
(
(
( =) ( =) = Ú = Ú Ú
Ú
4 sin xdx =
= p q a
b = p
p p Ú
b + p
p p 90° q + a cos x 1 π ( =) c b
c = =) q
q tan = =) cos  A=
C=
V=
S=
b=
h=
=
w=
r= = Rectangle
A = bh
Triangle
1
A = bh
2
Circle
A = r2
C=2r
Parallelepiped
V = wh
Cylinder
V = r2
S = 2 r + 2 r2
Sphere
43
V=
r
3
S = 4 r2
Right Triangle
a 2 + b2 = c2
a
sin =
c CALCULUS 2004 AP® PHYSICS C: MECHANICS FREERESPONSE QUESTIONS
PHYSICS C
Section II, MECHANICS
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 the
booklet in the spaces provided after each part, NOT in this green insert. Mech. 1.
A rope of length L is attached to a support at point C. A person of mass m1 sits on a ledge at position A holding
the other end of the rope so that it is horizontal and taut, as shown above. The person then drops off the ledge
and swings down on the rope toward position B on a lower ledge where an object of mass m2 is at rest. At
position B the person grabs hold of the object and simultaneously lets go of the rope. The person and object then
land together in the lake at point D, which is a vertical distance L below position B. Air resistance and the mass
of the rope are negligible. Derive expressions for each of the following in terms of m1, m2, L, and g.
(a) The speed of the person just before the collision with the object
(b) The tension in the rope just before the collision with the object
(c) The speed of the person and object just after the collision
(d) The ratio of the kinetic energy of the personobject system before the collision to the kinetic energy after the
collision
(e) The total horizontal displacement x of the person from position A until the person and object land in the
water at point D. Copyright © 2004 by College Entrance Examination Board. All rights reserved.
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5 2004 AP® PHYSICS C: MECHANICS FREERESPONSE QUESTIONS Mech. 2.
A solid disk of unknown mass and known radius R is used as a pulley in a lab experiment, as shown above.
A small block of mass m is attached to a string, the other end of which is attached to the pulley and wrapped
around it several times. The block of mass m is released from rest and takes a time t to fall the distance D to
the floor.
(a) Calculate the linear acceleration a of the falling block in terms of the given quantities.
(b) The time t is measured for various heights D and the data are recorded in the following table.
D (m) t (s) 0.5 0.68 1 1.02 1.5 1.19 2 1.38 i. What quantities should be graphed in order to best determine the acceleration of the block? Explain
your reasoning. Copyright © 2004 by College Entrance Examination Board. All rights reserved.
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6 2004 AP® PHYSICS C: MECHANICS FREERESPONSE QUESTIONS
ii. On the grid below, plot the quantities determined in (b)i., label the axes, and draw the bestfit line to
the data. iii. Use your graph to calculate the magnitude of the acceleration.
(c) Calculate the rotational inertia of the pulley in terms of m, R, a, and fundamental constants.
(d) The value of acceleration found in (b)iii, along with numerical values for the given quantities and your
answer to (c), can be used to determine the rotational inertia of the pulley. The pulley is removed from its
support and its rotational inertia is found to be greater than this value. Give one explanation for this
discrepancy. Copyright © 2004 by College Entrance Examination Board. All rights reserved.
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7 2004 AP® PHYSICS C: MECHANICS FREERESPONSE QUESTIONS Mech. 3.
A uniform rod of mass M and length L is attached to a pivot of negligible friction as shown above. The pivot is
L
located at a distance
from the left end of the rod. Express all answers in terms of the given quantities and
3
fundamental constants.
(a) Calculate the rotational inertia of the rod about the pivot.
(b) The rod is then released from rest from the horizontal position shown above. Calculate the linear speed of
the bottom end of the rod when the rod passes through the vertical. (c) The rod is brought to rest in the vertical position shown above and hangs freely. It is then displaced slightly
from this position. Calculate the period of oscillation as it swings. END OF SECTION II, MECHANICS Copyright © 2004 by College Entrance Examination Board. All rights reserved.
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