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Unformatted text preview: Physics 222, Summer 2009
FINAL EXAM
Friday, August 7, 2009 Name (Printed): fa? /r’t {NW 5
Section Number: Recitation Instructor: INSTRUCTIONS: 1. This is a two hour exam consisting of 30 multiplechoice questions. Questions 101
through 120 are each worth 1 point. Questions 121 through 130 are werth a half point (132
point) each. I will count all y0ur correct answers for a total of up to 25 points. Use your
previous bubble sheet answering questions # 101 through # 130 on the back of your
bubble sheet from the first three exams.. 2. Use a number 2 pencil when marking your bubble sheet. Do not use ink. Ask for a pencil
if you did not bring one. Fill in the appropriate bubble completely. if you need to change any
entry, you must completely erase your previous entry. Also, circle your answer on the
exam. 3. Carefully read each problem and its five possible answers before beginning to work on
the problem. Select only one answer for each problem. Choose the answer that is closest
to the correct one. 4. Before handing in your exam, be sure that your answers on your bubble sheet are what
you intend them to be. You should copy down your answers on a piece of a scratch paper
for comparison with the answer key to be posted later. 5. When you are finished with the exam, place all exams materials, including the bubble
sheet, the exam itself, and scratch paper that you used for the exam, in your folder and
return the folder. Enjoyed working with you this summer and wish you all the best in your future
endeavors. Good Luck!  Art Meyers A resistnncclcss LC circuit consists ofa capacitor and an inductor, as drawn in ﬁgure 101 When the
current ﬁnwi up through on inductor change. a voltage (emf) gets cmalod in the inductor that Opposes
the change in the curran So. inductors have on "inertia" with reattch to changes in current. just Iikc masses have inertia with respect to changes in veiociry. In an LC circuit. charge oscillates back and {on}: between the two capacitor piatcs. just like a pendulum's
position oscillates back and forth between the two endpoints of its staring. For instance. in ﬁgure I I3.
suppose the bottom pinto initially carries negative charge. Excess electrons ﬂow off the bottom plate.
through the inductor. and onto the top plate. 50. the top plate now carries tho negative charge. But then.
the negative charge "sioshos" back onto the bottom plate. In this manner. the charge oscillates. At any given moment. the com? Stored in the capacitor is U: n i where 0 denotes tho net charge
on [ht top plate. and C denotes litc capacitance. Tho cncrgy stored in the inductor is UL k i L12. where 1 denotes the current through the circuiL and L is a constant called the inductance. Since the circuit is
essentially rcsistanccicss. no boat dissipates as Cllﬂ‘cn'l Oscillator back and forth In this circuit. C = (Mil {mods and L = 2.0 heart's. (Farads and hcnrys are both 51 units.) Initially. at
umc t ‘= 0. the bottom plate has charge  H} coulombc. and no current is ﬂowing. 101. Which graph host rcprcscnut the chnrgc on the top platc of the capacitor as a function oftirne'? Intro out:
L 3f CTrottom pint
1 i
Figure 101 time
C. D.
‘1‘ +1
n Eu
'5 0 g o . _
+5 1; Hi?!» E} None of the above graphs rcprcscnt the charge in the top plate of the capacitor as a funcrinn
of time. 102. An ion of mass to and of charge. +e is in circular orbit around a ﬁxed
pornt charge Q, with charge ~8.0 tic. The radius of thc orbit is 0.20 in. and
the speed of the ion in the orbit is 12110‘ m. A uniform external magnetic
ﬁeld. perpendicular to the plane of the orbit, is present. The magnetic force
on the ion is equal to the clcctric force in magnitude and in direction at all
points ofthe orbit. In the ﬁgure. the mass m ofthc ion is closest to: IVI‘IZHDGWS A) 6x10“ kg
B) 53:10“ kg
4x10"‘ kg I[.2 a e.
81:10 "6 kg Net forcczm— = qu+k : 3k (because F = F )
7x10 '2‘ kg r I" r" H E
7 _ 9 49 —t
:m : citric; _ 2x9><10 ><1.6><10 a x8><10 :8X10_mk8
rt" 0.2X(i.2)‘ The correct answer is option D)8x10'1"kg If an electron is accelerated through a potential of 300 V and then enters, from the left, a region with an
electric ﬁeld of 12.00 x 10I3 N/c pointing down [see figure below]: XXﬁK’K 103. What is the election speed leaving the accelerating potential? [in me] A) 1.05 x 10 1“ ‘,
g} 5.25 x 10136 511.2,. a? “a /a/ fsjeg’
10.27 x 10 ' ‘ D) 1.05 x 10’
E) Need more information to solve the problem. 104. What magnetic field pointing into the paper will allow the electron to travel to the right without
being deflected up or down? [See ﬁgure above] A) 0.987 T , . B) 1.05 T ' f (31.5 2: {/2}; zr’r/f'75/CZ
@1168 T J) D) Not enough information given in Problem #103. E) Impossible since fields are in the wrong direction for there to be no deflection. 105. You have a long solenoid which has 1500 turns in 20 cm with an AC current of 3.5 amps flowing
through the coil. This coil has a diameter of4 cm and a resistance of 25 ohms. What is the
magnetic field inside the center of the solenoid? [ in Tesla] A) 6.50x10'3 /
B) 0.3299 I, ._ w / I? H.
@ 3.295;)(10'2 SH... “#1: 2 I a} 5
D) 4.67x10'2 E) 1.549 106. if a coil of 300 turns with a diameter of 1.00 inch was placed in the above solenoid (assume
Brrns = 10 x 10‘“t T) what will be the Erms voltage reading on an AC voltmeter or on a digital scope
(in volts) if the frequency = 5000 Hz? [in Volts] A 45 . ‘ ' '7'
CB? 25 5’66 A 6/124]! Jﬂﬁc’»; c) 21
0) 23.5
E) 30 107. Consider a series R1. circuit consisnng of a battery. a wink. an inductor and a resistor all
connected in series. The switch is closed and the amt and the voltage clung: with time are
measured. noted and plotted in graph #1 and graph #2“ The graphing persons forgot to label the
axes. As a physicist, you will do this for them. These are graphs of current and voltage versus
time. The correct axes labels are as follows; ' #2 A Graph #3] C Gragh H GRAPH #1 B GRAPH #2 D a E Q Ll
A) time current time voltage
3} current time voltage time
C) time voltage lime current
@ voltage lime current time E) None of the above combinations. 108 In the ﬁgure, an insulated wire is bent into a circular loop of radius 6.0 cm
and has two long straight sections. The loop is in the xy plane. with the center
at the origin. The straight sections are parallel to the zaxis. The wire carries a
CLIITBI'II of 8 A. The magnitude of the magnetic ﬁeld at the origin. in 1.1T. is clsest to:
9’0
) 80 C) 110 I
DHOO 5:3 43 :_»‘L,§_#JT
E) a'nll: II'u'e' J
: 45x10'7‘x8; 4EX10_TX8‘_
2x6x10‘‘ zzrxéqu " = —84x10‘f‘i —26.7>< 10h} _—>l 8 I: J84: + 26.72 x 10'“ = 88;:T :~ The closest answer is A) 90,uT. 109. An electron has the same de Broglie wavelength as an 800 nm photon. The speed of the
electron is closest to: [in m/s] A) 500 B) 700 C 800 {66, ﬂ ggﬂd/udy/I/g 2' 6/5
@900 .2 E) 1000 110. An object 8 m high is located 125 m in front of a concave mirror which has a focal length of
200 m. Which of the following set of positions, size, and character of the image is correct? Image Position E Character of Image
A) 500 m +32 m erect virtual
63):) 333 rn +213 rn erect virtual
C) +333 m 21.3 m inverted real
D) +500 m 32 m inverted real E) None of the above. 5/676. (394/ [36534 111. Determine the focal length of a converging lens which will project the image of a lamp magnified
4 diameters, upon a screen 10 m from the lamp (in m). A) 1.25 ' 1.6 5198 if {Kris/Egg}? fat/£7.33
c) 2.0 D) 2.5 E) Not enough information. 112. A narrow beam of light strikes a glass plate in = 1.60) at an angle of 53° to the normal. If the
plate is 20 mm thick, what will be the lateral displacement of the beam after it emerges from
the plate (in mm)? A) 25.5
B) 15.0 I ‘ J P I I
C) 11.5 g (’5 z . (Of @ 9.0 E) Not enough information. 113. 114. 115. 116. Two identical beakers are filled to the same level, one filled with water (n = 1.361) and the other
with mineral oil, {n = 1.47} they are both viewed from directly above. Which beaker appears to
contain the greater depth of liquid? A) same depth water depth greater C) mineral oil depth greater
D) Not enough information. f 03 A {/ulu/Efgéj‘gf An amateur lens grinder wants to grind a converging lens of crown glass (n = 1.52) with the
same curvature on both sides and a focal length of 25 cm. What radius of curvature must he
grind on each face? [in cm] A) 13 B 25
@26
D) 50
E) Not enough information. 5‘56: ($1446 Lﬁa/fﬁff"), The interference pattern of two identical slits separated by a distance d = 0.25 mm is observed
on a screen at a distance of 1 m from the plane of the slits. The slits are illuminated by
monochromatic light of wavelength 589.3 nm (sodium D) traveling perpendicular to the plane of
the slits. Bright bands are observed on each side of the central maximum. Calculate the
separation between adjacent bright bands (in mm). A 1.08 “'1
«1 B 2.35 1 y C) 4.72 3 0) 5.30 “ E) None of the above. ) D =1 m f (36.. xi / "I?! ‘25 The headlights of a distant automobile are 1.4 m apart. If the diameter of the pupil of the eye is
3 mm, what is the maximum distance at which two headlights can be resolved? [in m] Consider
the headlights as point sources of wavelength 500 mm. A) 2030
a) 5700  I
C) 6100 g (is [l— /Ar/a/f"j’(5 @ 6900 E} No enough information. 117. A grating having 15,000 lines per inch produces spectra of a mercury arc. The green line of the
mercury spectrum has a wavelength of 546.1 nm. What is the angular separation between the
1st order green line and the 2"" order green line? é 18.3” 21.4° . _
c) 40.20 5 ‘16 " f7}?
o) 59.00
E) None ofthe above. 118. In an important experiment in 1927, a beam of electerons was scattered off a crystal of nickel.
The intensity of the scattered beam varied with the angle of scattering, and the analysis of
these results lead to the conﬁrmation of A) the particle nature of light. _ B) the Bohr model of the atom. _. , L ' _ I L T,
@he wave nature of light. f a? ‘6 f D) the Rutherford model of the nucleus. E) the quantization of energy levels. 119. You have a biackbody radiator with a maximum intensity at a wavelength of 414.3 nm, what is
the Temperature of the blackbody radiator? [in Kelvin] A) 5000 B} 6500 ‘ . @7000 5'" car} 5: /£jl¢?
D) 7500 E) Not encugh information. 120. The work functions for potassium and cesium are 2.25 and 2.14 eV, respectively. Will the photoelectric effect occur for either or both of these elements with an incident light of
wavelength 565 nm? A) neither cesium nor potassium "3
@cesium only {Cm "’5
C) potassium only D) both E) Not énough information. PHYSICS 222 — Summer, 2009
Laboratory Final NOTE: Each of these questions are worth V: a point. 121. In the electron beam experiment, the electron d
tube contained two electrodes: r‘ ano e a. a straight, glowing ﬁlament narrow sit
(perpendicular to the page in the ﬁgure on the right);
b. a cylindrical anode that surrounded the k electro n beam
ﬁlament. filament On the side of the anode was slit through which a
beam of electrons emerged. What was the primary cause of the kinetic energy of the emerging electrons? A) The magnetic ﬁeld generated by the currents in the two large Helmholtz coils;
B) The high temperature of the glowing ﬁlament;
The potential difference between the two ends of the glowing ﬁlament;
The potential difference between the ﬁlament and the cylindrical anode;
1 None of the above. I #1 122. Consider two conducting Spheres mounted on insulating rods and
located (with the relative positions shewn) in a region of large
electric ﬁeld, near a negatively charged rod as shown. #2 Assume that both of the spheres are initially uncharged. Then one
of the two spheres is displaced slightly so that the two spheres
touch each other briefly. Assume that neither touches the rod, and
that their relative positions always are as shown. Which of following are possible values for the resulting charge on
each sphere, #1 and #2, reSpectively, after the sequence of events described? 123. In laboratory, the EMF produced within a small coil (by a sinusoidal magnetic ﬁeld within a
solenoid) can be measured with an AC voltmeter. This EMF can be measured for coils of various
design, such as those whose main features are listed in the table below. Other conditions being
equal, how would your expect the reading of the voltmeter when using coil #6 (in place within the
solenoid) to be related to the reading observed when using coil #1? Coil #of turns Diameter EMF
(inches) Volts
(RMS) —
m A) The readings with #6 should be about twice that obtained with #1. B) The readings with #1 and #6 should be approximately the same. C) The readings with #6 should be about 4 times that obtained with #1. D) The readings with #6 should be about U4 that obtained with #1.
® The readings with #6 should be about li’2 that obtained with #1. 124. A laser beam strikes a Plexiglas block (such as you used in lab) that is lying on a table. Which of
the paths shown is a possible path for the beam? (Choose E if none of the paths shown is appropriate.) 125. In the Polarization lab, you measured the
intensity of the light (in lux) transmitted ‘
through two polarizers, as a function of the :
angle of rotation of one of the polarizers. Data .
from such an experiment is shown at the right. I
For these data, which of the following
theoretical forms best represents the data. A) 200 cos (8) ' B) 200 cos2 (8) @ 160 cos2 (a) + 40 D) 80 cos (8) + 40 g E) None of the above represents the data i
very well. Intenmty {qu)   ‘ 0 90 180 270 360
 i Theta (degrees) I 126. You have an incandescent light bulb and you would like to determine the energy it consumes m for various applied potential differences. You have available DC power supplies (PS) and high quality voltmeters (V) and ammeters (A). Which m . m instruments would you place in the positions
shown in the ﬁgure to make the necessary
measurements? 127. In laboratory, the EMF
produced within a small
coil (located within a
solenoid powered by the
sine function output of a
function generator
operating at 5000 Hz)
was measured with an
AC voltmeter; a typical
result is shown in the
table below for one of
the coils. tunction
generator test coil  small col
wound on rod Digital llﬂl— Snap: N
voftrneter solenoid (15 cm long} Diameter EMF
(inches) (RMS Ili .51! If the signal from the small coil was connected instead to an OSCilloscope (rather than to an AC
voltmeter), which of the following best describes the waveform that would be observed? (Assume
that the 0 volt level is centered in the middle of the screen, and that the scope is operated in the
“sweep” or “triggered” mode, with the horizontal axis corresponding to time.) A) A sine function, with its vertical peaks at i 0.30 volts. B) A horizontal line, displaced upward from 0 at +0.30 volts. C) A horizontal line, displaced upward from 0 at +0.42 volts.
A horizontal line, at the middle of the screen. é? A sine function, with its vertical peaks at i 0.42 volts. 128. 129. 130. As you read this exam, which of the following best describes some aspect of the light reaching
your eye from the page?
A) Light is emitted by the page.
B) Light from various places suffers diffuse reﬂection from the page, a process in which the
_ angle of reﬂection equals the angle of incidence.
@ Light from various places suffers diffuse reﬂection from the page, a process in which the
direction of the reﬂected light has little relation to the direction of the incident rays.
D) Light from various places suffers specular reﬂection from the page, a process which is
described by Snell’s Law.
E) Light from various places suffers specular reﬂection from the page, a process in which the
angle of reﬂection equals the angle of incidence. Assume that you are focusing your eyes on an upright Cy Cyclone. If someone could look inside
your eyeball, what would they see when they examined the retina of your eye?
a little upsidedown picture of Cy on your retina; A) Q a little rightsideup picture of Cy on your retina;
C) nothing, because the image of Cy is virtual. However, you see an upsidedown Cy;
D) nothing, because the image of Cy is virtual. However, you see a rightsideup Cy;
E) None of the above descriptions is correct. In laboratory, you had access to a precision vertical adjustable slit. Assume there is a laser beam
passing through the slit, and that you can see a bright spot (with a diameter of a few rnrn) where this
beam impinges on a distant wall. Which of the following best describes how that spot is affected as
you slowly close the slit. A) The spot remains about the same size, but gradually gets dimmer.
B) The spot gradually gets smalier in the vertical dimension, eventually disappearing entirely.
C The spot gradually gets smaller in the horizontal dimension, eventually disappearing entirely.
@ The spot gradually gets dimer, and horizontally wider, with considerable spatial variation in
intensity.
E) No matter how slowly you close the slit, the spot suddenly disappears, because it is laser light. Hm f/W'I/é—ey (51“; A} — m
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I: #7“, ,2. g, A narrow beam of light strikes a glass plate (:1 = 1.60) at an angle of 53° to the normal. If the plate is 20 mm
thick, what will be the lateral displacement of the beam after it emerges from the plate? The situation is described by Fig. 3415, with CE the lateral displacement; E = 20 mm. sin 53°
1.60 EB = 26.5 — 11.5 =15.o sinr= r=30° E=2ozan 53°=26.5 R= 20 tan 30° =11.5 ﬁ=C—Dc0553°=9.0mm ® f/ 3. W. (n = 1.361) and the other ﬁlled with mineral oil (it = 1.47), are viewed from directly above. Which beaker appears to contain the greater depth of liquid, and what is the ratio of the apparent depths? Figure indicates the bottom of a beaker b
image of P, labeled 1", will be determined in y point P. For an observer looking in the —Y direction, the
and :92 are small, Snell‘s law gives y a vertical ray 1 and the nearly vertical ray 3 (or 2). Since 91 n191==n262 or $23 92 “.1
But E=ytan81=y’:an32 or tan 61=ﬂ=g
tan 92 82 y Consequently, for given y and n2, y’ is inversely proportional to n . The waterﬁlled b k
by a factor of 1.47.11.361 = i._o_s. 1 ea er appears deeper, X (exaggerated scale) C59 An amateur lens grinder wants to grind a converging lens of crown glass (it = 1.52) with the same curvature
on both sides and a focal length of 25 cm. What radius of curvature must he grind on each face?
@3 Use the lensmaker‘s equation. 1 1 2 , . ) = (053(3) and R1 = 25(0.52)(2) = 26 cm radius of curvature for each side
I . i_‘
R. R2 f (n—1)( with R‘ = —R2 or 1 1 1
3—(1.52—1)(JR:—“RI The interference pattern of two identical slits separated by a distance d = 0.25 mm is observed on a screen at
a distance of 1 m from the plane of the slits. The slits are illuminated by monochromatic light of wavelength 589.3 nm (sodium D) traveling perpendicular to the plane of the slits. Bright bands are observed on each side
of the central maximum. Calculate the separation between adjacent bright bands. The situation is shown in Fig. 364. For the ﬁrst bright band it = 1. The path diﬁerence is one wavelength. 025 x 10—33: _ 5893 x 10‘1"
Fr ca 5893X10"°= =2.36b<10'3m=2.36rnm 1 y ‘ 0.25 x 103 separation of adjacent bright fringes. The headlights of a distant automobile are 1.4 in apart. If the diameter of the pupil of the eye is 3 mm, what
is the maximum distance at which the two headlights can be resolved? Consider the headlights as point sources of wavelength 500 mm. D :: ﬁg“; )3 aﬂ'gfgncé rem/yd Using the Rayleigh criterion for resolution of two point sources 0 erved through a circular
aperture of radius 13' and the equation for diffraction by a circular opening, we have —'!
minimum angle that can be resolved = e = sin a = 1.223 =1—'2—:—(:—:0E—?—) = 2.03 x 10—“ rad @ Then setting 6' = 1.4,lttwe get 3: 1.4!6 = 1.4f(2.03 X 10") = 6900 rn. A grating having 15 000 lines per inch produces spectra of a mercury arc. The green line of the mercury
n ? Spectrum has a wavelength of 5461 A. What is the angular separation between the ﬁrstorder green line and
C the secondeorder green line? 1__) 5’4, 6. ‘ l Xyp“ 9m
Use the grating formula and solve for 9 for both n = 1 and n = 2, with distances in meters: ml = of sin 8 5461 X ll]—10 — —1~ sin 9. or 0.3225 = sin 61 and 6'; =18.8° ﬁrst order ' (39.3m15 000) Next, for n = 2, 2(5461 x 10“”) = 1— sin 62 or 0.6449 = sin 6'; and 62 = 402" second order {39.37)(15 000)
Finally 92 — 6. = 40.2“ — 18.8“ = 21.4“ separation. @ . In an important expenment in £927 a beam at electrons was scattered or! a casts] of
I I 8 : nickel. The intensity of the scattered beam varied with the angle of scattering. and
analysis of these results lead to continuation of A) the paniele nature oflight. B} the Bohr model of the atom. the wave name of electrons
_} the Rutherford model ofthe nucleus. E) the quantization nl’ energy levels. _{ }(d. __ :— 2206)‘/
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