PH2100
FINAL EXAM
Spring 2002
INSTRUCTIONS
1) Write your name, student identification number and recitation section on the appropriate
spaces provided on the answer sheet.
2) With the exception of the included fresh equation sheet, no other equation sheets, papers,
books, handbooks or tables are permitted. If you need an extra blank sheet of paper to
work problems on, raise your hand and ask your exam proctor for a sheet of paper.
3) No materials, including calculators, may be exchanged during the exam. Cell phones may
not be used during the exam; ringers should be turned off.
4) Keep your eyes on your own papers.
5) Units are an important part of numerical answers; be sure to include units on your
answers.
6) Report all numerical answers to three significant figures unless the problem specifically
instructs otherwise.
7) Vectors should be reported using iˆ, ˆj, kˆ unit-vector notation, unless otherwise instructed.
8) Write answers on your answer sheet as you work. Don’t wait until the end to copy your
answers over. All answers have equal weight of 5 points each.
9) There are a total of 160 possible points on the exam. It will be graded out of 150 points
total.
10) At the end of the exam, turn in only your answer sheet.
Recitation Section
R01
R02
R03
R04
R05
R06
R08
R09
R10
R11
R12
R13
R14
R15
R16
Time
TR 0805-0855
TR 0905-0955
TR 0905-0955
TR 1005-1055
TR 1005-1055
TR 1105-1155
TR 1205-1255
TR 1205-1255
TR 1305-1355
TR 1305-1355
TR 1405-1455
TR 1405-1455
TR 1505-1555
TR 1505-1555
TR 1005-1055
Instructor
D. Gao
R. Nemiroff
G. Agin
E. Nadgorny
C. Zhou
U. Hansmann
R. Nemiroff
C. Zhou
G. Agin
Y. Yap
C. Zhou
R. Nemiroff
R. Nemiroff
Y. Yap
R. Vanga
PH2100
page 1
FINAL
5/7/2002
PROBLEMS
1) A sinusoidal transverse wave on a string is described by the displacement
y ( x, t )  (2.00m) cos[15.7 x  8.58t ] ,
where x is in meters, and t is in seconds.
(a) Find the wavelength of the wave.
(b) Find the frequency of the wave.
(c) Find the maximum speed of any infinitesimal segment of the string in its motion.
2)
An experiment requires a sound intensity of 1.23×103 W/m2 at a distance 4.00 m from a
speaker. Assume the speaker radiates uniformly in all directions.
(a) What is the required power output of the speaker?
(b) What is the decibel sound level at a distance 8.00 m from the speaker?
3)
A commuter train approaches a passenger platform at a constant speed of 44.4 m/s. The train horn
is sounded at its characteristic frequency of 320.0 Hz. Take the speed of sound to be 343.0 m/s.
What frequency does a person standing still on the platform as the train approaches hear?
PH2100
4)
page 2
FINAL
5/7/2002
A particle of mass m = 0.195 kg moves with a speed v = 0.454 m/s in a circle of radius
ri = 1.34 m on a frictionless tabletop. The particle is attached to a string that passes through a hole
in the table, as shown in the figure. The string is then slowly pulled downward until the particle
moves in a smaller circle of radius rf = 0.470 m.
v
(a) What is the magnitude of the initial angular momentum of
the mass?
m
r
(b) What is the final tangential speed of the particle while
moving in the circular path of smaller radius?
Applied
Force
(c) How much work was done by the agent pulling on the string in order to change the circular
motion from the large radius to the smaller radius above?
5)
A solid disk of mass 2.44 kg and radius 8.00 cm rolls without slipping up an inclined plane that
makes and angle 36.0º with the horizontal. At the moment the disk is at position x = 2.00 m up
the incline, its center-of-mass speed is 1.80 m/s. The disk continues up the incline some additional
distance x, and then rolls back down. It does not roll off
the top end. Compute x.
vcm
x
PH2100
6)
page 3
FINAL
5/7/2002
A planet (mp = 1.20×1022 kg) moves around the sun (ms = 1.99×1030 kg) in an elliptical orbit.
When the planet is at perihelion, it has a speed 5.00×102 m/s, and is 1.00 ×1015 m from the sun.
(a) What is the magnitude of the gravitational force between the planet and sun at perihelion?
(b) What is the speed of the planet when it is at aphelion, a distance 2.20 ×1015 m from the sun?
(c) What is the ratio of the potential energy at perihelion compared to the potential energy at
aphelion; i.e., what is the ratio Uperihelion/Uaphelion?
TRUE OR FALSE?
Circle T for true or F for false on your answer sheet to describe each of the statements below:
7)
If the pressure amplitude of a sound wave is doubled, its intensity is also doubled.
8)
If the speed of a mass is constant it cannot be accelerating.
9)
The momentum of a system can be conserved even if its total mechanical energy is not
conserved.
10)
Work is the area under the force-versus-time curve.
11)
The change in kinetic energy of a point mass is always equal to its change in potential energy.
12)
All parts of a rotating rigid pulley must have the same angular speed and the same angular
acceleration.
13)
All periodic motion is simple harmonic motion.
14)
When a wave pulse travels from medium A to medium B such that the wave speeds satisfy
vA > vB, the reflected wave pulse is inverted.
PH2100
page 4
FINAL
5/7/2002
MULTIPLE CHOICE (select only one best answer for each problem below):
15)
Ball #1 is released from rest from the top of Fisher Hall. Ball #2 is projected horizontally from
the same height as ball #1 with a non-zero initial speed. Neglecting the effects of air resistance,
which ball has the higher speed as they hit the ground?
(a) They both hit the ground with the same speed.
(b) Ball #1.
(c) Ball #2.
16)
A child ties a rock of mass m to the end of a string and spins it in a circular path in a vertical
plane. The speed of the rock is maintained to be constant. When the rock is at the bottom of the
circle, which of the following statements is true about the tension T in the string?
(a) T = mg
(b) T > mg
(c) T < mg
17)
A standing wave is set up in an organ pipe that is open at one end, but closed at the other. If the
standing wave corresponds to the THIRD HARMONIC (f = 3f1), how many displacement nodes
will there be in the tube, not counting any nodes that may be at the ends of the tube?
(a) 0
(b) 1
(c) 2
(d) 3
(e) 4
18)
A block of mass m is wrapped around a solid disk of radius R and moment of inertia I,
as shown in the figure. The block is accelerating downward as the string unwinds
without slipping. The magnitude of the torque on the solid disk is:
(a) = 0
(b) = mgR
(c) > mgR
(d) < mgR
m
19)
R
I
A yo-yo is initially at rest on a rough, horizontal surface. What happens to the yo-yo if you pull it
via its string with a small force F, which is parallel to the surface in the +x direction, and the
string is tangent to the lower part of axle, as shown in the adjacent figure?
(a) It rolls in the +x direction.
(b) It rolls in the –x direction.
(c) It spins in place.
(d) It does not move.
F
^x
PH2100
page 5
FINAL
5/7/2002
20)
A fisherman is out on the lake gently gliding along in a canoe. The canoeist gets up and moves
from the back of the canoe to the front of the canoe (no paddling). Assuming that the lake acts as
a frictionless surface, which one of the following statements is true?
(a) The position of the center of mass of the canoe-fisherman system remains the same during
the whole motion.
(b) The kinetic energy of the canoe-fisherman system remains constant during the whole
motion.
(c) The momentum of the center of mass of the canoe-fisherman system changes while the
fisherman is moving to the front, but returns to the initial value when the fisherman stops
walking.
(d) The momentum of the center of mass of the canoe-fisherman system remains constant
during the whole motion.
21)
Which one of the following functions can be a wave function representing a wave pulse traveling
in the negative x-direction with a speed 3.0 m/s, where x and y are in meters, and t is in seconds?
(a) y( x, t )  2.50 sin( x  3.0t 2  9.0)
(b) y ( x, t )  2.50 sin( x  3.0t  9.0)
2.50
(c) y ( x, t ) 
( x  1.5t 2  9.0) 2
2.50
(d) y ( x, t ) 
( x  3.0t  9.0) 2
(e) y ( x, t )  2 A(sin kx) cos  t
22)
Three identical, uniform bricks, each of length L, are
placed in a stack over the edge of a horizontal surface
such that the maximum possible overhang without
falling is achieved, as shown in the figure. The
distance x is:
(a) L/2 + L/2 + L/2 = 3L/2
(b) L/2 + L/4 + L/6 = 11L/12
(c) L/2 + L/4 + L/8 = 7L/8
(d) L/2 + L/4 + L/4 = L
23)
L
x
A cello A string vibrates at 220 Hz in its fundamental. If the tension in the string were to be
doubled, and assuming the string didn’t break, what would the fundamental frequency be?
(a) 110 Hz
(b) 220 Hz
(c) 311 Hz
(d) 440 Hz
(e) 880 Hz
PH2100
page 6
FINAL
5/7/2002
24)
A distant planet has two moons. The first moon has an orbit radius 4.00×105 m and a period of
10.0 days. What is the period of the second moon if it has an orbit radius 4.00×105 m?
(a) 28.3 days
(b) 20.0 days
(c) 16.8 days
(d) 10.0 days
(e) 3.54 days
(f) There is not enough information to answer since the masses are not given.
25)
A pendulum is made of a solid sphere of mass M and
radius R with a massless stick of length 2R. If the
pendulum is pivoted at the end of the stick as shown in the
figure, what is the moment if inertia of the pendulum
about the pivot? (Moment of inertia formulae are given
below.)
(a) 9MR 2
(d)
12
MR 2
5
2
MR 2
5
47
MR 2
(e)
5
(b)
R
pivot
L = 2R
17
MR 2
5
22
MR 2
(f)
5
(c)
MOMENT OF INERTIA FORMULAE FOR HOMOGENEOUS RIGID BODIES
1
1
Thin rod: I cm  ML2
Thin rod about one end: I end  ML2
12
3
1
1
2
2
Solid cylinder: I cm  MR 2
Hollow cylinder: I cm  M ( R1  R2 )
2
2
2
Cylindrical shell: I cm  MR
2
2
Solid Sphere: I cm  MR 2
Spherical Shell: I cm  MR 2
5
3
Please sit in seat number:
PH2100
Exam 2
4/4/2002
ANSWER SHEET
Name:
ID#
1.
2.
Recitation Section #
(a)
11.
T
F
(b)
12.
T
F
(c)
13.
T
F
(a)
14.
T
F
(b)
15.
a
b
c
16.
a
b
c
(a)
17.
a
b
c
d
(b)
18.
a
b
c
d
(c)
19.
a
b
c
d
20.
a
b
c
d
(a)
21.
a
b
c
d
(b)
22.
a
b
c
d
(c)
23.
a
b
c
d
e
3.
4.
5.
6.
e
e
7.
T
F
24.
a
b
c
d
e
f
8.
T
F
25.
a
b
c
d
e
f
9.
T
F
10.
T
F
Score: