Download PHYS 1112 Final Exam A Thu. April 29, 2010, 12:00pm-3:00pm

Physics 1112
Spring 2010
University of Georgia
Instructor: HBSchüttler
PHYS 1112 Final Exam A
Thu. April 29, 2010, 12:00pm-3:00pm
This is a closed-book, closed-notes exam, but you are permitted to bring and use a copy
of the official Formula Sheet for this exam, which you should have printed out from the
PHYS1112 web page.
The exam consists of 24 multiple-choice questions. Each question is worth one raw score
point. There will be no penalty for wrong answers. No partial credit will be given. I
recommend that you read all the questions at the start so that you can allocate your time
wisely. (Answer the easy questions first!)
You may use a scientific calculator for arithmetic only; your calculator must be non-graphing,
non-programmable, and non-algebraic. You are not allowed to share your calculator. The
use of cell phones, pagers, PDAs, or any other electronic devices (besides calculators) is
forbidden. All such gadgets must be turned off and put away; distractions caused by these
devices will not be tolerated.
• Do not open the exam until you are told to begin.
• Make sure the scantron sheet has your name and your UGA Card ID (810-...)
number filled in. Make sure you also have entered your name, UGA Card ID number
and signature on the exam cover page (this page!) below.
• At the end of the exam period you must hand in both your scantron sheet and this
entire exam paper, with the cover page signed and with your name and UGA Card ID
(810-...) number filled-in. You may not keep any parts of this exam paper.
• Your exam will not be graded, and you will receive a score of zero, if you do not hand
in both a properly filled in scantron sheet and this entire exam paper, with properly
filled-in and signed exam cover page.
• You promise not to discuss the contents of this exam with anyone before the end of
final exam week (May 10, 2010).
By signing below, you indicate that you understand the instructions for this exam and agree
to abide by them. You also certify that you will personally uphold the university standards
of academic honesty for this exam, and will not tolerate any violations of these standards by
others. Unsigned exams will not be graded.
Name (please print):
UGACard ID (810-...) #:
Signature:
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Physics 1112
Spring 2010
University of Georgia
Instructor: HBSchüttler
WORKSPACE
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Physics 1112
Spring 2010
University of Georgia
Instructor: HBSchüttler
Conceptual Problems
Problem 1: A student runs eastward at 4m/s, towards a vertical plane mirror, while the
mirror, mounted on wheels, also travels eastward at 1 m/s (with both speeds given relative
to the ground). The speed at which the student’s image moves and its direction, relative to
the ground, is
(A)
(B)
(C)
(D)
(E)
2m/s
6m/s
6m/s
7m/s
7m/s
westward
eastward
westward
eastward
westward
Problem 2: Sound waves (including ultrasound) have a speed of wave propagation vAir =
340m/s in air and vWater = 1500m/s in water. Also, sin(Θ) = vAir /vWater when Θ ∼
= 13.10o .
A narrow ultrasound beam striking the flat water surface of your swimming pool
(A) will undergo total internal reflection if incident from below the water surface with
an angle of incidence of 7.7o .
(B) will have an angle of refraction greater than the angle of incidence if the beam is
incident from below the water surface;
(C) will undergo total internal reflection if incident from below the water surface for
any angle of incidence greater than 13.10o ;
(D) will undergo total internal reflection if incident from above the water surface with
an angle of incidence of 7.7o ;
(E) will have an angle of refraction smaller than the angle of incidence if the beam is
incident from below the water surface;
Problem 3: In a two-source interference experiment two sources are oscillating in phase
with the same period. The closest intensity minimum, counted from the central intensity
maximum M and to the left of M, is located at point P, as shown in Fig. 2.01. A wave crest
A from source 1 and a wave trough B from source 2 arrive simultaneously at P. Therefore,
A and B must have departed from their respective sources as follows:
Fig. 2.01
P
Source 1
M
Source 2
(A) A departed 3/2 period before B.
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Physics 1112
Spring 2010
(B)
(C)
(D)
(E)
University of Georgia
Instructor: HBSchüttler
B departed 3/2 period before A.
B departed 1/2 period before A.
A departed 1/2 period before B.
B departed 1 period before A.
Problem 4: Q1 and Q2 in Fig. 2.15 are negative point charges. Assuming Q1 , Q2 and P
are located at three corners of a square, as shown, which arrow drawn at P could correctly
~ generated by Q1 and Q2 at P ?
represent the total electric field vector E
Fig. 2.15
P
(E)
(C)
(D)
(A)
(B)
Q2
Q1
(A)
(B)
(C)
(D)
(E)
Problem 5: Three different circuits, X, Y and Z, are built with the three resistors, R1 > 0,
R2 > 0, and R3 > 0, and a battery of battery voltage E, as shown in Fig. 3.04.
Let Io > 0, I1 > 0, I2 > 0, and I3 > 0 denote the currents through the battery, R1 , R2 , and
R3 , respectively. Let V1 > 0, V2 > 0, and V3 > 0 denote the voltage drops across R1 , R2 ,
and R3 , respectively.
Fig. 3.04
Io
I2
I3
E
I1
Io
R2
R3
I2
Io
R2
I1
E
R1
(X)
I3
R3
(Y)
R1
I3
R3
I1
E
I2
R1
R2
(Z)
Which of the following statements is false ?
(A)
(B)
(C)
(D)
(E)
In
In
In
In
In
circuit
circuit
circuit
circuit
circuit
Z: V1 /R1 = E/(R1 + R2 ).
X: V3 /E = R3 /(R1 + R2 + R3 ).
Y : V1 /R1 = E[1/(R3 + R2 ) + 1/R1 ].
Y : I1 /(R2 + R3 ) = I2 /R1 .
Z: V3 = V1 + V2 .
Problem 6: A molecular ion beam containing four different types of ions, called P , Q, R
and S here, enters a uniform magnetic field, as shown in Fig. 3.15, with B 6= 0 above the
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Physics 1112
Spring 2010
University of Georgia
Instructor: HBSchüttler
~ perpendicular to, and pointing out of, the plane of the drawing.
lower horizontal line, and B
The incident beam, below the lower horizontal line, is in the plane of the drawing.
Fig. 3.15
B (out)
P
Q
R
S
B=0
~
The radii of the semicircular ion trajectories in the B-field,
denoted by rP , rQ , rR and rS ,
respectively are observed to be in a ratio of
rP : rQ : rR : rS = 3 : 2 : 1 : 4 ,
as indicated in Fig. 3.15. Assume all four ion types carry the same amount of charge per
~
ion, |q|, and they all enter the B-field
with the same kinetic energy K. What is the ratio of
the four ion masses, denoted by mP , mQ , mR and mS , respectively ?
(A)
(B)
(C)
(D)
mP
mP
mP
mP
:
:
:
:
mQ
mQ
mQ
mQ
:
:
:
:
mR
mR
mR
mR
:
:
:
:
mS
mS
mS
mS
= 13 : 12 : 11 : 14 .
=3 : 2 : 1 : 4 .
√
√
√
√
= 3 : 2 : 1 : 4 .
= √13 : √12 : √11 : √14 .
(E) mP : mQ : mR : mS = 9 : 4 : 1 : 16 .
Problem 7: In an electric generator, a single metallic wire loop, enclosing an area of 5cm2
~ at 700RPM, produces a maximum induced
and spinning in a uniform magnetic field B
electromotoric force (EMF) of 6mV. What is the maximum induced EMF in a loop of
~
10cm2 area, spinning at 2100RPM in the same B-field?
(A)
(B)
(C)
(D)
(E)
48mV
36mV
9mV
4.5mV
1mV
Problem 8: A beam of unpolarized light of intensity I0 is incident from the left upon a
polarization filter PF1, with vertically oriented transmission axis T1 , followed by a second
polarization filter PF2 with transmission axis T2 , located to the right of P F 1, as shown in
Fig. 4.09. T2 is initially also oriented vertically ( parallel to T1 ); but it is then rotated around
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Physics 1112
Spring 2010
University of Georgia
Instructor: HBSchüttler
the beam axis by 120o .
Fig. 4.09
Before:
After:
T2
I0
I1
T1
I2
T2
Side View: Before
120o Rotation of T2
120o
T2
Frontal View: Before and After
120o Rotation of T2
√
Recall that cos(30o ) = ( 3)/2 and cos(60o ) = 1/2. What is the light intensity I2 of the
beam observed to the right of PF2, before and after the 120o -rotation of T2 ?
(A)
(B)
(C)
(D)
(E)
0 before, 3I0 /8 after
I0 /2 before, 3I0 /8 after
I0 before, 3I0 /4 after
I0 /2 before, I0 /8 after
I0 before, I0 /4 after
Numerical Problems
Problem 9: The vacuum wavelength range of electromagnetic radiation visible to the human
eye is 400nm to 700nm. A beam of monochromatic light with a frequency of 7.142 × 1014 Hz
in air travels from air into water, with indices of refraction nAir = 1.00 and nWater = 4/3,
in air and water, respectively. To an under-water human observer, the light beam while
traveling in water will
(A) have a wavelength of 420nm, have a frequency of 9.523 × 1014 Hz, and be visible to
the human eye;
(B) have a wavelength of 315nm, have the same frequency as in air, and be visible to the
human eye;
(C) have a wavelength of 420nm, have a frequency of 5.366 × 1014 Hz, and be visible to
the human eye;
(D) have a wavelength of 420nm, have the same frequency as in air, and be invisible to
the human eye;
(E) have a wavelength of 315nm, have the same frequency as in air, and be invisible to
the human eye.
Problem 10: The state highway patrol radar gun sends out a frequency of 8.25GHz. You’re
approaching a radar speed trap driving 6.24m/s and the radar gun measures the frequency
of the radar wave reflecting from your car. Assume c = 3.00 × 108 m/s. By what percentage
is the reflected wave’s frequency different from the original frequency sent out by the gun?
Would this percentage change if the radar gun sends out a different frequency, but your
speed is the same ?
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Physics 1112
Spring 2010
(A)
(B)
(C)
(D)
(E)
University of Georgia
Instructor: HBSchüttler
4.16 × 10−6
4.16 × 10−6
4.13 × 10−6
4.13 × 10−6
2.08 × 10−6
%,
%,
%,
%,
%,
will
will
will
will
will
not change with frequency
change with frequency
not change with frequency
change with frequency
not change with frequency
Problem 11: A postage stamp placed 5.00cm to the left of a spherically curved mirror
produces an image 40.0cm to the right of the mirror. What is the focal length of the mirror
and where is its focal point F located ?
(A)
(B)
(C)
(D)
(E)
−5.71cm,
−5.71cm,
+5.71cm,
+4.44cm,
+4.44cm,
F
F
F
F
F
to
to
to
to
to
left of mirror;
right of mirror;
left of mirror;
right of mirror;
left of mirror.
Problem 12: In flint glass, the index of refraction is nR = 1.661 for red light, and nV = 1.696
for violet light, while nAir = 1.000 in air for all wavelengths. A beam of white light enters
a triangular prism of flint glass from air at normal incidence at the front surface and then
stikes the prism’s back surface at an angle of incidence φ = 22.0o as shown here:
φ
Red
Violet
The prism is surrounded by air. What is the angle of divergence, enclosed between the red
and the violet beam after leaving the prism through the back surface ?
(A)
(B)
(C)
(D)
(E)
0.1223o
0.2736o
0.4883o
0.9661o
2.073o
Problem 13: If a diffraction grating with a line spacing of 1550nm is illuminated at normal
incidence by coherent (laser) light with a wavelength of 550nm, at what angles θ, measured
from the central (0th order) intensity maxium, will the 3rd order maxima be observed ?
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Physics 1112
Spring 2010
(A)
(B)
(C)
(D)
(E)
University of Georgia
Instructor: HBSchüttler
3rd order maxima are not observable.
±66.44o
±50.23o
±39.18o
±26.78o
Problem 14: Two identical point charges, spaced 56.2m apart, repel each other with a
force of 160.0N. What is the amount of each point charge?
(A)
(B)
(C)
(D)
(E)
3.5mC
5.5mC
7.5mC
9.5mC
11.5mC
Problem 15: A charge of −18nC is uniformly spread out over a single thin, square-shaped
sheet of aluminum foil with a side length of 1.5m. What is the strength and the direction of
the electric field generated by that charge, very close to the surface and far from the edges of
that foil? (Hint: Think of the aluminum foil as a single, uniformly charged planar surface.)
(A)
(B)
(C)
(D)
(E)
~ pointing towards the foil
5752.0N/C, E
~ pointing away from the foil
5752.0N/C, E
~ pointing towards the foil
27.89N/C, E
~ pointing away from the foil
27.89N/C, E
~ pointing towards the foil
452.0N/C, E
Problem 16: If the electric field strength between the capacitor plates in Fig. 2.13 is
683.V/m, what is the magnitude and the direction of the acceleration ~a of an electron
traveling from A to B between the plates, assuming the electron is subject only to the
electric force between the plates ?
Fig. 2.13
------------------------E
B
A
E
+++++++++++++++++++++++++++
(A) 5.00 × 1013 m/s2 , ~a pointing rightward
(B) 5.00 × 1013 m/s2 , ~a pointing upward
8
Physics 1112
Spring 2010
University of Georgia
Instructor: HBSchüttler
(C) 12.0 × 1013 m/s2 , ~a pointing leftward
(D) 12.0 × 1013 m/s2 , ~a pointing downward
(E) 12.0 × 1013 m/s2 , ~a pointing upward
Problem 17: A wire with a length 350m and a circular cross-section of diameter 0.17mm is
made of dawgium alloy (a very poorly conducting metal!) with a resistivity of 3 × 10−6 Ω · m.
Find the current flowing in this wire when it is connected to a 16V battery. [Hint: The area
of a circle is A = (π/4)D2 .]
(A)
(B)
(C)
(D)
(E)
86.5µA
0.346mA
3.46A
1.84kA
3.11GA
Problem 18: In a Kirchhoff rule analysis, current arrows have been assigned to the I1 -, I2 and I3 -branches of a circuit for which a fragment (i.e., not the whole circuit) is shown in
Fig. 3.10. Also assume that the voltage drop across R is defined as
VR ≡ Va − Vb
where Va and Vb are the electric potential values at points a and b.
I1
I2
Fig. 3.10
a
I3
R
b
Suppose R = 20Ω and VR = −40V and I2 = −6A for the arrow directions shown in Fig.
3.10. What is I1 ? Is the current |I1 | actually flowing towards or away from point a ?
(A)
(B)
(C)
(D)
(E)
I1
I1
I1
I1
I1
= +8A
= −8A
= +4A
= −4A
= −4A
with
with
with
with
with
|I1 |
|I1 |
|I1 |
|I1 |
|I1 |
flowing
flowing
flowing
flowing
flowing
towards a.
away from a.
towards a.
away from a.
towards a.
9
Physics 1112
Spring 2010
University of Georgia
Instructor: HBSchüttler
Problem 19: If a 15A current flows in a thin straight metal rod of length 4m through a
uniform magnetic field of 90T and the direction of the current flow is at an angle of 35o from
the direction of the magnetic field vector, what is the strength of the magnetic force exerted
on the rod ?
(A)
(B)
(C)
(D)
(E)
872N
1908N
3097N
4423N
6770N
Problem 20: A very thin circular metal ring of radius R = 1.0m lies initially in the x − zplane and it is centered at the coordinate origin O ≡ (0, 0, 0), as shown in Fig. 3.21. A
current I = 1.0A flows around the ring in the direction indicated in panel (B) of Fig. 3.21.
(A)
(B)
z
Fig. 3.21
z
I
y
x
z
x
y-z-Plane View
z
y
y
x
x-z-Plane View
This ring (and its magnetic field!) is then rotated by 20o around the x-axis, the rotation
direction being counter-clockwise in the y−z-plane view shown in panel (A) of Fig.
~ ≡ (Bx , By , Bz ) due to I, at the center of the
3.21. The z-component of the magnetic field B
ring, after the rotation, is:
(A)
(B)
(C)
(D)
(E)
Bz
Bz
Bz
Bz
Bz
= +0.590µT
= −0.590µT
= +0.215µT
= −0.215µT
= +0.628µT
Problem 21: A single conducting ring of wire encloses an area of 7.4 × 10−2 m2 and a
resistance of 11.0Ω. Perpendicular to the plane of the loop is a uniform magnetic field,
initially of strength 0.28T. At what rate (in T/s) must this field change if the induced
current in the loop is to be 0.32A?
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Physics 1112
Spring 2010
(A)
(B)
(C)
(D)
(E)
University of Georgia
Instructor: HBSchüttler
2.23µT/s
7.76mT/s
3.87T/s
47.6T/s
68.9T/s
Problem 22: The electric motor in a toy train requires a voltage of 6.0V. Calculate the
number of turns in the secondary coil for a transformer that has 2000 turns in its primary
coil and will transform the 120V household voltage down to 6.0V.
(A)
(B)
(C)
(D)
(E)
100 turns
1000 turns
2000 turns
40000 turns
320000 turns
Problem 23: In the circuit in Fig. 4.03, the battery voltage is EB = 20V, and inductance L
is a long, thin solenoid of length 1.5m, cross-sectional area 7.85 × 10−3 m2 , and 3800 turns.
I
Fig. 4.03
L
EB
Immediately after closing the switch, current I(t) in the circuit rises linearly with time t. At
what rate ∆I/∆t does it rise?
(A)
(B)
(C)
(D)
(E)
6820.A/s
211.A/s
39.3A/s
8.27A/s
0.482A/s
Problem 24: A small 100% absorbing spherical object of mass 90 × 10−15 kg and radius
2.0 × 10−6 m is suspended against gravity (with g = 9.81m/s2 ) by the radiation pressure of
an upward-directed laser beam. What is the intensity of the laser beam ? (Hint: A circle’s
area is πR2 .)
(A)
(B)
(C)
(D)
(E)
1.83W/m2
2.94kW/m2
5.88kW/m2
10.5MW/m2
21.1MW/m2
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