Download PHYS 1112 Final Exam B Wed. May 5, 2010, 7:00pm-10:00pm

Physics 1112
Spring 2010
University of Georgia
Instructor: HBSchüttler
PHYS 1112 Final Exam B
Wed. May 5, 2010, 7:00pm-10:00pm
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 5m/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
3m/s
3m/s
7m/s
7m/s
westward
westward
eastward
westward
eastward
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 have an angle of refraction smaller than the angle of incidence if the beam is
incident from above the water surface;
(D) will undergo total internal reflection if incident from above the water surface with
an angle of incidence of 7.7o ;
(E) will undergo total internal reflection if incident from above the water surface for
any angle of incidence greater than 13.10o ;
Problem 3: In a two-source interference experiment two sources are oscillating in phase
with the same period. The third intensity minimum, counted outward 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 periods before B.
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Physics 1112
Spring 2010
(B)
(C)
(D)
(E)
University of Georgia
Instructor: HBSchüttler
B departed 3/2 periods before A.
B departed 5/2 periods before A.
A departed 5/2 periods before B.
B departed 1 period before A.
Problem 4: In Fig. 4.12, Q1 is a positive and Q2 is a negative point charge. Assuming Q1 ,
Q2 and P are located at three corners of a square, as shown, which arrow drawn at P could
~ generated by Q1 and Q2 at P ?
correctly represent the total electric field vector E
Fig. 4.12
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
(X)
Io
R2
R3
R1
I2
Io
R2
I1
E
I3
R3
(Y)
R1
I3
R3
I1
E
I2
R1
R2
(Z)
Which of the following statements is false ?
(A) In circuit Z: V1 /R1 = E/(R1 + R2 ).
(B) In circuit X: V3 /E = R3 /(R1 + R2 + R3 ).
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Physics 1112
Spring 2010
University of Georgia
Instructor: HBSchüttler
(C) In circuit Y : I3 + V1 /R1 = E[1/(R3 + R2 ) + 1/R1 ].
(D) In circuit Y : I1 /R2 = I2 /R1 .
(E) In circuit Z: V3 = R1 I1 + R2 I2 .
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
~ 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 3cm2
~ at 600RPM, produces a maximum induced
and spinning in a uniform magnetic field B
electromotoric force (EMF) of 5mV. At what rotation speed must a loop of 9cm2 area, be
~
spinning in the same B-field
in order to produce a maximum EMF of 60mV??
(A)
(B)
(C)
(D)
2400RPM
1800RPM
800RPM
200RPM
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Physics 1112
Spring 2010
University of Georgia
Instructor: HBSchüttler
(E) 150RPM
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. 4.10. T2 is initially also oriented vertically ( parallel to T1 ); but it is then rotated around
the beam axis by 150o .
Fig. 4.10
Before:
After:
T2
I0
I1
T1
I2
T2
Side View: Before
150o Rotation of
T2
150o
T2
Frontal View: Before and After
150o 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 150o -rotation of T2 ?
(A)
(B)
(C)
(D)
(E)
I0 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 315nm, have the same frequency as in air, and be invisible to
the human eye.
(B) have a wavelength of 420nm, have a frequency of 5.366 × 1014 Hz, and be visible to
the human eye;
(C) have a wavelength of 315nm, have the same frequency as in air, 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 420nm, have a frequency of 9.523 × 1014 Hz, and be visible to
the human eye;
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Physics 1112
Spring 2010
University of Georgia
Instructor: HBSchüttler
Problem 10: The state highway patrol radar gun sends out a frequency of 8.25GHz. You’re
approaching a radar speed trap driving 6.189m/s and the radar gun measures the frequency
of the radar wave reflecting from your car. Assume c = 3.000 × 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 ?
(A)
(B)
(C)
(D)
(E)
4.136 × 10−6
4.136 × 10−6
4.126 × 10−6
4.126 × 10−6
2.084 × 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 left 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) 0.1223o
(B) 0.2736o
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Physics 1112
Spring 2010
University of Georgia
Instructor: HBSchüttler
(C) 0.4883o
(D) 0.9661o
(E) 2.073o
Problem 13: If a diffraction grating with 6452 lines/cm 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 4th order maxima be observed ?
(A)
(B)
(C)
(D)
(E)
4th order maxima are not observable.
±66.44o
±50.23o
±39.18o
±26.78o
Problem 14: Two identical point charges, spaced 18.8m apart, repel each other with a
force of 160.0N. What is the amount of each point charge?
(A)
(B)
(C)
(D)
(E)
2.5mC
4.5mC
6.5mC
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 6.0m. 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.)
~ pointing towards the foil
(A) 3752.0N/C, E
~ pointing away from the foil
(B) 3752.0N/C, E
~ pointing towards the foil
(C) 28.2N/C, E
~ pointing away from the foil
(D) 28.2N/C, E
~ pointing towards the foil
(E) 452.0N/C, E
Problem 16: If the electric field strength between the capacitor plates in Fig. 2.13 is
1366V/m and the plates are spaced 2.5mm apart, 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 ?
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Physics 1112
Spring 2010
University of Georgia
Instructor: HBSchüttler
Fig. 2.13
------------------------B
E
A
E
+++++++++++++++++++++++++++
(A)
(B)
(C)
(D)
(E)
24.0 × 1013 m/s2 , ~a
24.0 × 1013 m/s2 , ~a
24.0 × 1013 m/s2 , ~a
12.0 × 1013 m/s2 , ~a
12.0 × 1013 m/s2 , ~a
pointing
pointing
pointing
pointing
pointing
downward
upward
leftward
downward
upward
Problem 17: A wire with 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. It carries a
current of 43.23µA when it is connected to a 4V battery. How long is the wire? [Hint: The
area of a circle of radius R is A = πR2 .]
(A)
(B)
(C)
(D)
(E)
28m
70m
175m
700m
2800m
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
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Physics 1112
Spring 2010
University of Georgia
Instructor: HBSchüttler
Suppose R = 20Ω and VR = −80V and I2 = −12A 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 with |I1 | flowing away from a.
= +16A with |I1 | flowing towards a.
= −16A with |I1 | flowing away from a.
= +8A with |I1 | flowing towards a.
= −8A with |I1 | flowing towards a.
Problem 19: If a 5A current flows in a thin straight metal rod of length 4m through a
uniform magnetic field and the direction of the current flow is at an angle of 35o from the
direction of the magnetic field vector, the strength of the magnetic force exerted on the rod
is 1032N. How strong is the magnetic field?
(A)
(B)
(C)
(D)
(E)
6.3T
9.0T
45T
63T
90T
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 y-component of the magnetic field B
ring, after the rotation, is:
(A) By = +0.590µT
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Physics 1112
Spring 2010
(B)
(C)
(D)
(E)
By
By
By
By
University of Georgia
Instructor: HBSchüttler
= −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 has
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?
(A)
(B)
(C)
(D)
(E)
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) 6820.A/s
(B) 211.A/s
(C) 39.3A/s
11
Physics 1112
Spring 2010
University of Georgia
Instructor: HBSchüttler
(D) 8.27A/s
(E) 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
5.25MW/m2
10.5MW/m2
21.1MW/m2
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