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Unformatted text preview: Physics C: Mechanics TABLE OF INFORMATION FOR 2002
UNITS CONSTANTS AND CONVERSION FACTORS
1 unified atomic mass unit, 1 u = 1.66 10 27 = 931 MeV/c
Proton mass, PREFIXES Name Symbol meter
kilogram Factor Prefix Symbol m 10 9 giga G kg 10 6 mega M 10 3 kilo k kg 2 m p = 1.67 × 10 −27 kg Neutron mass, mn = 1.67 × 10 −27 kg second s Electron mass, me = 9.11 × 10 −31 kg ampere A 10 −2 centi c Magnitude of the electron charge, e = 1.60 × 10 −19 C kelvin K 10 −3 milli m micro µ Avogadro’s number, N0 = 6.02 × 10 mol
23 −1 mol hertz Hz 10 −9 nano n 10 −12 pico p 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 Vacuum permittivity,
Coulomb’s law constant,
Vacuum permeability,
Magnetic constant,
Universal gravitational constant,
Acceleration due to gravity
at the Earth’s surface,
1 atmosphere pressure, 0 k = 1 / 4π = 8.85 × 10 C / N⋅m 0 k = µ 0 / 4π = 10 (T ⋅ m ) / A
G = 6.67 10 11 m 3 / kg ¼ s 2 g = 9.8 m / s V
Ω H farad −7 0 henry µ 0 = 4π × 10 −7 (T ⋅ m ) / A C ohm = 9.0 × 10 N ⋅ m 2 / C 2 θ volt 9 W coulomb
2 J watt = 1.24 × 10 3 eV ⋅ nm
2 VALUES OF TRIGONOMETRIC FUNCTIONS
FOR COMMON ANGLES joule hc = 1.99 × 10 −25 J ⋅ m −12 10 mole R = 8.31 J / ( mol ¼ K ) Universal gas constant, −6 F tesla T 45o o = 1.0 × 10 Pa tan θ 0 1 0 3 /2 3 /3 1/2 37o 3/5 degree
Celsius o C 53o eV 60 o
90o 1 atm = 1.0 × 10 5 N / m 2 cos θ 30o electronvolt 2 sin θ 2 /2 4/5 4/5
2 /2 3/4
1 3/5 4/3 3 /2 1/2 3 1 0 ∞ 5 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 2002
MECHANICS
a = acceleration
F = force
1
x = x 0 + u 0 t + at 2
f = frequency
2
h = height
2
u 2 = u 0 + 2a x  x 0
I = rotational inertia
Ê F = Fnet = ma
J = impulse
K = kinetic energy
dp
F=
k = spring constant
dt
l = length
J = F dt = Dp
L = angular momentum
p = mv
m = mass
N = normal force
F fric mN
P = power
W = F dr
p = momentum
1
2
r = radius or distance
K = mu
2
r = position vector
dW
T = period
P=
dt
t = time
P=F v
U = potential energy
u = velocity or speed
DUg = mgh
W = work done on a system
u 2 = w2r
x = position
ac =
r
m = coefficient of friction
t=rF
q = angle
Ê t = t net = Ia
t = torque
2
2
w = angular speed
I = r dm = Ê mr
a = angular acceleration
rcm = Ê mr Ê m
u = rw
L = r p = Iw
1
K = Iw 2
2
w = w0 + at
q = q 0 + w0 t + 1 at 2
2
Fs =  kx
1
Us = kx 2
2
2p
1
T=
=
f
w
m
Ts = 2 p
k
l
Tp = 2 p
g
Gm1m2
$
FG = r
r2
Gm1m2
UG = r u = u 0 + at 0 I I I 5 ELECTRICITY AND MAGNETISM
q1 q 2
A = area
2
B = magnetic field
r
0
C = capacitance
F
d = distance
E=
q
E = electric field
e = emf
Q
E • dA =
F = force
0
I = current
dV
L = inductance
E=−
l = length
dr
n = number of loops of wire per
qi
1
V=
unit length
4 p 0 i ri
P = power
1
F=
4p ∑ UE = qV = 1
4p 0 q1 q 2
r Q
C=
V
kA
C= 0
d
C p = ∑ Ci
i 1
1
=∑
Cs
i Ci
dQ
dt
1
1
Uc = QV = CV 2
2
2
rl
R=
A
V = IR
I= Rs = ∑ Ri
i 1
1
=∑
Rp
i Ri
P = IV
FM = qv × B
B • d ø = m0 I I F = I dø × B
Bs = m0 nI I fm = B • dA dfm
dt
dI
e = −L
dt
12
U L = LI
2 e=− 3 Q=
q=
R=
r=
t=
U=
V=
υ=
r=
fm =
k= 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 2002
GEOMETRY AND TRIGONOMETRY
Rectangle
A = bh
Triangle
1
A = bh
2
Circle
A = pr 2
C = 2 pr
Parallelepiped
V = lwh
Cylinder
V = pr 2 l
S = 2 prl + 2 pr 2
Sphere
4
V = pr 3
3
S = 4 pr 2
Right Triangle
a 2 + b2 = c2
a
sin q =
c
cos q = area
circumference
volume
surface area
base
height
length
width
radius c
q a
90 b b
c tan q = A=
C=
V=
S=
b=
h=
l=
w=
r= a
b CALCULUS
df
d f du
=
dx
du dx 27
27 dn
n 1
x = nx
dx
dx
e = ex
dx
d
1
(1n x) =
dx
x
d
(sin x) = cos x
dx
d
(cos x) =  sin x
dx
1 n +1
xn dx =
x
, n 1
n +1
e x dx = e x I
I I dx
= 1n x
x
cos x dx = sin x I
I sin x dx =  cos x
4 2002 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
pink booklet in the spaces provided after each part, NOT in this green insert.
Mech 1.
A crash test car of mass 1,000 kg moving at constant speed of 12 m/s collides completely inelastically with an
object of mass M at time t = 0. The object was initially at rest. The speed u in m/s of the carobject system
after the collision is given as a function of time t in seconds by the expression u= 8
.
1 + 5t (a) Calculate the mass M of the object.
(b) Assuming an initial position of x = 0, determine an expression for the position of the carobject system after
the collision as a function of time t.
(c) Determine an expression for the resisting force on the carobject system after the collision as a function of
time t.
(d) Determine the impulse delivered to the carobject system from t = 0 to t = 2.0 s. Copyright © 2002 by College Entrance Examination Board. All rights reserved.
Advanced Placement Program and AP are registered trademarks of the College Entrance Examination Board. 5 GO ON TO THE NEXT PAGE. 2002 AP® PHYSICS C: MECHANICS FREERESPONSE QUESTIONS Mech 2.
The cart shown above is made of a block of mass m and four solid rubber tires each of mass m/4 and radius r.
1
ML2 , where M is the mass and L is
Each tire may be considered to be a disk. (A disk has rotational inertia
2
the radius of the disk.) The cart is released from rest and rolls without slipping from the top of an inclined plane
of height h. Express all algebraic answers in terms of the given quantities and fundamental constants.
(a) Determine the total rotational inertia of all four tires.
(b) Determine the speed of the cart when it reaches the bottom of the incline.
(c) After rolling down the incline and across the horizontal surface, the cart collides with a bumper of negligible
mass attached to an ideal spring, which has a spring constant k. Determine the distance x m the spring is
compressed before the cart and bumper come to rest.
(d) Now assume that the bumper has a nonneglible mass. After the collision with the bumper, the spring
is compressed to a maximum distance of about 90% of the value of x m in part (c). Give a reasonable
explanation for this decrease. Copyright © 2002 by College Entrance Examination Board. All rights reserved.
Advanced Placement Program and AP are registered trademarks of the College Entrance Examination Board. 6 GO ON TO THE NEXT PAGE. 2002 AP® PHYSICS C: MECHANICS FREERESPONSE QUESTIONS
Mech 3.
An object of mass 0.5 kg experiences a force that is associated with the potential energy function
4.0
U ( x) =
, where U is in joules and x is in meters.
2.0 + x
(a) On the axes below, sketch the graph of U(x) versus x. (b) Determine the force associated with the potential energy function given above.
(c) Suppose that the object is released from rest at the origin. Determine the speed of the particle at x = 2 m.
In the laboratory, you are given a glider of mass 0.5 kg on an air track. The glider is acted on by the force
determined in part (b). Your goal is to determine experimentally the validity of your theoretical calculation in
part (c).
(d) From the list below, select the additional equipment you will need from the laboratory to do your experiment
by checking the line next to each item. If you need more than one of an item, place the number you need on
the line.
___ Meterstick ___ Stopwatch ___ Photogate timer ___ String ___ Balance ___ Wood block ___ Spring ___ Set of objects of different masses (e) Briefly outline the procedure you will use, being explicit about what measurements you need to make
in order to determine the speed. You may include a labeled diagram of your setup if it will clarify your
procedure. END OF SECTION II, MECHANICS Copyright © 2002 by College Entrance Examination Board. All rights reserved.
Advanced Placement Program and AP are registered trademarks of the College Entrance Examination Board. 7 GO ON TO THE NEXT PAGE. ...
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