Unformatted text preview: AP® Physics C: Mechanics
2006 FreeResponse Questions The College Board: Connecting Students to College Success
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AP Central is the official online home for the AP Program: apcentral.collegeboard.com. TABLE OF INFORMATION FOR 2006 and 2007
CONSTANTS AND CONVERSION FACTORS
UNITS
1 unified atomic mass unit, 1 u = 1.66 × 10−27 kg
= 931 MeV c Proton mass, Name
meter
kilogram m p = 1.67 × 10−27 kg Electron mass, me = 9.11 × 10−31 kg
e = 1.60 × 10−19 C ampere Boltzmann’s constant,
Speed of light,
Planck’s constant, N 0 = 6.02 × 1023 mol−1 kelvin R = 8.31 J (moli K)
k B = 1.38 × 10 −23 c = 3.00 × 10 m/s = 4.14 × 10
eVis
−25 i
hc = 1.99 × 10
Jm Vacuum permittivity,
Vacuum permeability, 0 1 atmosphere pressure,
1 electron volt, G = 6.67 × 10 m nano n pico p VALUES OF
TRIGONOMETRIC
FUNCTIONS FOR COMMON
ANGLES 1 atm = 1.0 × 10 N m
5 = 1.0 × 105 Pa
1 eV = 1.60 × 10−19 J 2 W θ sin θ cos θ coulomb C 0 0 1 0 V 30 1/2 3 /2 3 /3 W henry H 37 3/5 4/5 3/4 F 45 2 /2 2 /2 1 tesla g = 9.8 m s 2 kg is 2 watt farad m 3 J ohm µ0 = 4π × 10−7 (T i m) A Magnetic constant, k ′ = µ0 / 4π = 10−7 (T ⋅ m) A
Universal gravitational constant,
Acceleration due to gravity
at Earth’s surface, Pa 10 m micro 1 2 c milli 6 k centi 3 10 9 Hz
N kilo 2 M volt = 9.0 × 109 Nim 2 C 2 −11 10 mega 3 joule = 1.24 × 103 eV i nm
−12 2
C Nim2
0 = 8.85 × 10 Coulomb’s law constant, k = 1 4π 10 mol pascal −15 10 K newton h = 6.63 × 10−34 J is 10 A hertz J/K 9 106 s mole 8 10 kg second Prefix Symbol
giga
G Factor m mn = 1.67 × 10−27 kg Avogadro’s number,
Universal gas constant, Symbol 2 Neutron mass,
Electron charge magnitude, PREFIXES T 53 4/5 3/5 4/3 degree
Celsius C 60 3 /2 1/2 3 90 1 0 • electronvolt eV tan θ 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 2006 and 2007
MECHANICS u = u0 + at x = x0 + u0 t + 12
at
2 u 2 = u0 2 + 2a ( x  x0 ) Â F = Fnet = ma
dp
dt F= J = Ú F dt = Dp p = mv
F fric £ m N
W= ÚF K= 12
mu
2 P= dW
dt ∑ dr P=Fv DUg = mgh
ac = a
F
f
h
I
J
K
k =
=
=
=
=
=
=
=
=
L=
m=
N=
P=
p=
r=
r=
T=
t=
U=
u=
W=
x=
m=
q=
t=
w=
a= 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 u
= w2 r
r Fs =  k x Us = Â t = t net = I a Ú r dm = Â mr
2 2 rcm = Â mr Â m L = r ¥ p = Iw
12
Iw
2 T= 12
kx
2 E= F
q ÚE Tp = 2p UG = 12
at
2 r2 Gm1m2
r q Â rii 1
4p 0 V= i UE = qV = 1 q1q2
4p 0 r Q
V C= k C= 0A d Â Ci Cp = i 1
1
=Â
Cs
Ci
i dQ
dt r
A V = IR
Rs =
ˆ
r Â Ri 1
=
Rp 1 ÂR i P = IV FM = qv ¥ B 3 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
distance
time
potential or stored energy
electric potential
velocity or speed
resistivity
magnetic flux
dielectric constant N=
P=
Q=
q=
R=
r=
t=
U=
V=
u=
r=
fm =
k= ÚB ∑ d = m0 I dB = m0 I d ¥ r
4p r3 ÚI d ¥B Bs = m0 nI
fm = Ú B ∑ d A d fm
dt e i i n =
=
=
=
=
=
=
=
=
=
=
= F= I = Neud A g Gm1m2 dV
dr E = rJ m
k Ts = 2 p F
I
J
L 0 E= A
B
C
d
E e Q dA= ∑ R= 2p
1
=
w
f FG =  w = w0 + at
q = q0 + w0 t + 1 q1q2
4p 0 r 2 1
1
Uc = QV = CV 2
2
2 u = rw K= F= I= 2 t=r¥F I= ELECTRICITY AND MAGNETISM = e = L UL = dI
dt 12
LI
2 ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 2006 and 2007
GEOMETRY AND TRIGONOMETRY
Rectangle
A = bh
Triangle A= 1
bh
2 Circle A = pr2 C = 2p r
Parallelepiped
V = wh
Cylinder A=
C=
V=
S=
b=
h=
=
w=
r= CALCULUS area
circumference
volume
surface area
base
height
length
width
radius df
d f du
=
dx
du dx
dn
( x ) = nxn 1
dx
dx
(e ) = e x
dx
d
(1n x ) = 1
dx
x
d
(sin x ) = cos x
dx
d
(cos x ) =  sin x
dx V = pr2 Úx S = 2p r + 2p r 2 Úe Sphere V= 43
pr
3 S = 4p r 2 c Ú a
90° q a
c
b
c tan q = x dx = e x dx
= ln x
x Ú sin x dx =  cos x a 2 + b2 = c2 cos q = dx = Ú cos x dx = sin x b Right Triangle sin q = 1
x n + 1 , n π 1
n +1 n a
b 4 2006 AP® PHYSICS C: MECHANICS FREERESPONSE QUESTIONS
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 the
pink booklet in the spaces provided after each part, NOT in this green insert. Mech 1.
A small block of mass M B = 0.50 kg is placed on a long slab of mass M S = 3.0 kg as shown above. Initially, the
slab is at rest and the block has a speed u0 of 4.0 m/s to the right. The coefficient of kinetic friction between the
block and the slab is 0.20, and there is no friction between the slab and the horizontal surface on which it moves.
(a) On the dots below that represent the block and the slab, draw and label vectors to represent the forces acting on
each as the block slides on the slab. At some moment later, before the block reaches the right end of the slab, both the block and the slab attain identical
speeds u f .
(b) Calculate u f .
(c) Calculate the distance the slab has traveled at the moment it reaches u f .
(d) Calculate the work done by friction on the slab from the beginning of its motion until it reaches u f . © 2006 The College Board. All rights reserved.
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5 2006 AP® PHYSICS C: MECHANICS FREERESPONSE QUESTIONS
Mech 2.
A nonlinear spring is compressed various distances x, and the force F required to compress it is measured for each
distance. The data are shown in the table below.
x (m) F (N) 0.05 4 0.10 17 0.15 38 0.20 68 0.25 106 Assume that the magnitude of the force applied by the spring is of the form F ( x) = Ax 2 .
(a) Which quantities should be graphed in order to yield a straight line whose slope could be used to calculate a
numerical value for A ?
(b) Calculate values for any of the quantities identified in (a) that are not given in the data, and record these values
in the table above. Label the top of the column, including units.
(c) On the axes below, plot the quantities you indicated in (a) . Label the axes with the variables and appropriate
numbers to indicate the scale. (d) Using your graph, calculate A.
The spring is then placed horizontally on the floor. One end of the spring is fixed to a wall. A cart of mass 0.50 kg
moves on the floor with negligible friction and collides headon with the free end of the spring, compressing it a
maximum distance of 0.10 m.
(e) Calculate the work done by the cart in compressing the spring 0.10 m from its equilibrium length.
(f) Calculate the speed of the cart just before it strikes the spring.
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6 2006 AP® PHYSICS C: MECHANICS FREERESPONSE QUESTIONS Mech 3.
A thin hoop of mass M, radius R, and rotational inertia MR 2 is released from rest from the top of the ramp of length
L above. The ramp makes an angle q with respect to a horizontal tabletop to which the ramp is fixed. The table is a
height H above the floor. Assume that the hoop rolls without slipping down the ramp and across the table. Express
all algebraic answers in terms of given quantities and fundamental constants.
(a) Derive an expression for the acceleration of the center of mass of the hoop as it rolls down the ramp.
(b) Derive an expression for the speed of the center of mass of the hoop when it reaches the bottom of the ramp.
(c) Derive an expression for the horizontal distance from the edge of the table to where the hoop lands on the floor.
(d) Suppose that the hoop is now replaced by a disk having the same mass M and radius R. How will the distance
from the edge of the table to where the disk lands on the floor compare with the distance determined in part (c)
for the hoop?
____ Less than ____ The same as ____ Greater than Briefly justify your response. END OF EXAM © 2006 The College Board. All rights reserved.
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 Spring '10
 mr.donald
 Physics, mechanics, Electron, Force, Mass, Electric charge, The College Board

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