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Unformatted text preview: AP® Physics C: Mechanics
2003 FreeResponse Questions The materials included in these files are intended for use by AP teachers
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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 2003
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 m 10 9 giga G kg 10 6 mega M 10 3 kilo k Symbol 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 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 g = 9.8 m / s 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.
IV. For mechanics and thermodynamics equations, W represents the work done on a system. 2 ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 2003
MECHANICS
a = acceleration
u = u 0 + at
F = force
1
x = x 0 + u 0 t + at 2
f = frequency
2
h = height
2
2
u = 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
t = torque
Ê t = t net = Ia
w = angular speed
2
2
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 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
V
k 0A
C=
d
C p = ∑ Ci
C= 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
Ri
i
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
1
U L = LI 2
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 2003
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 a
90 q
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 2003 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.
The 100 kg box shown above is being pulled along the xaxis by a student. The box slides across a rough surface,
and its position x varies with time t according to the equation x = 0.5t 3 + 2t , where x is in meters and t is in
seconds.
(a) Determine the speed of the box at time t = 0.
(b) Determine the following as functions of time t.
i. The kinetic energy of the box
ii. The net force acting on the box
iii. The power being delivered to the box
(c) Calculate the net work done on the box in the interval t = 0 to t = 2 s.
(d) Indicate below whether the work done on the box by the student in the interval t = 0 to t = 2 s would be greater
than, less than, or equal to the answer in part (c).
Greater than Less than Equal to Justify your answer. Copyright © 2003 by College Entrance Examination Board. All rights reserved.
Available to AP professionals at apcentral.collegeboard.com and to
students and parents at www.collegeboard.com/apstudents. GO ON TO THE NEXT PAGE.
5 2003 AP® PHYSICS C: MECHANICS FREERESPONSE QUESTIONS Mech. 2.
An ideal spring is hung from the ceiling and a pan of mass M is suspended from the end of the spring, stretching
it a distance D as shown above. A piece of clay, also of mass M, is then dropped from a height H onto the pan
and sticks to it. Express all algebraic answers in terms of the given quantities and fundamental constants.
(a) Determine the speed of the clay at the instant it hits the pan.
(b) Determine the speed of the pan just after the clay strikes it.
(c) Determine the period of the simple harmonic motion that ensues.
(d) Determine the distance the spring is stretched (from its initial unstretched length) at the moment the speed of
the pan is a maximum. Justify your answer.
(e) The clay is now removed from the pan and the pan is returned to equilibrium at the end of the spring. A rubber
ball, also of mass M, is dropped from the same height H onto the pan, and after the collision is caught in midair
before hitting anything else.
Indicate below whether the period of the resulting simple harmonic motion of the pan is greater than, less than,
or the same as it was in part (c).
_____ Greater than _____ Less than _____ The same as Justify your answer. Copyright © 2003 by College Entrance Examination Board. All rights reserved.
Available to AP professionals at apcentral.collegeboard.com and to
students and parents at www.collegeboard.com/apstudents. GO ON TO THE NEXT PAGE.
6 2003 AP® PHYSICS C: MECHANICS FREERESPONSE QUESTIONS Mech. 3.
Some physics students build a catapult, as shown above. The supporting platform is fixed firmly to the ground.
The projectile, of mass 10 kg, is placed in cup A at one end of the rotating arm. A counterweight bucket B that is to
be loaded with various masses greater than 10 kg is located at the other end of the arm. The arm is released from the
horizontal position, shown in Figure 1, and begins rotating. There is a mechanism (not shown) that stops the arm in
the vertical position, allowing the projectile to be launched with a horizontal velocity as shown in Figure 2.
(a) The students load five different masses in the counterweight bucket, release the catapult, and measure the
resulting distance x traveled by the 10 kg projectile, recording the following data.
Mass (kg)
x (m) 100
18 300
37 500
45 700
48 900
51 i. The data are plotted on the axes below. Sketch a bestfit curve for these data points. ii. Using your bestfit curve, determine the distance x traveled by the projectile if 250 kg is placed in
the counterweight bucket.
Copyright © 2003 by College Entrance Examination Board. All rights reserved.
Available to AP professionals at apcentral.collegeboard.com and to
students and parents at www.collegeboard.com/apstudents. GO ON TO THE NEXT PAGE.
7 2003 AP® PHYSICS C: MECHANICS FREERESPONSE QUESTIONS
(b) The students assume that the mass of the rotating arm, the cup, and the counterweight bucket can be neglected.
With this assumption, they develop a theoretical model for x as a function of the counterweight mass using the
relationship x = u x t , where u x is the horizontal velocity of the projectile as it leaves the cup and t is the time
after launch.
i. How many seconds after leaving the cup will the projectile strike the ground?
ii. Derive the equation that describes the gravitational potential energy of the system relative to the ground
when in the position shown in Figure 1, assuming the mass in the counterweight bucket is M.
iii. Derive the equation for the velocity of the projectile as it leaves the cup, as shown in Figure 2.
(c)
i. Complete the theoretical model by writing the relationship for x as a function of the counterweight mass
using the results from (b)i and (b)iii.
ii. Compare the experimental and theoretical values of x for a counterweight bucket mass of 300 kg. Offer a
reason for any difference. END OF SECTION II, MECHANICS Copyright © 2003 by College Entrance Examination Board. All rights reserved.
Available to AP professionals at apcentral.collegeboard.com and to
students and parents at www.collegeboard.com/apstudents. 8 ...
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This note was uploaded on 08/05/2009 for the course PHYS 101 taught by Professor Reich during the Spring '08 term at Johns Hopkins.
 Spring '08
 Reich
 Physics, mechanics

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