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Unformatted text preview: Final Exam — Physics 221 — Spring 2006 You may record your answers here and take this page with you to compare with the
posted answers. 59 5 69 6 79 D 60 D 70 c, 80 E 61 c 71 p 81 D 62 E 72 A 82 Q 63 C W 33 p 64 p T? T?
65 D Z 75 C 85 g 66 g 76 C, 86 3 67 C 77 F E 87 a 68 x2 78 A 88 C, 16 PHYSICS 221  Spring 2006  FINAL EXAM: Solutions The situation below refers to the next two questions: A bob of mass m = 1.0 kg is attached at the bottom of a massless, ideal string of length 80 cm to make a pendulum. When the string makes an angle of 15° with the
vertical, the speed of the bob is 1.2 m/s. i 59. What is the tension on the string at the position described? A. 1.8N ‘ {L
B, 4.6N T’ L ‘= ‘7:
C. 7.7N L 60. How long does the bob take to go through a complete oscillation cycle? 2 E.____.
A. 0.65  .2.
: i
B. 0.95 T 'g
C. 1.25
1.85 _
. 2.2s “ l'gs 61. A block of mass m is being pulled at an angle by a force F on a horizontal
surface as shown in the ﬁgure. The block moves to the right at constant s eed Let f be the friction between the block and the surface and N be the normal
force on the block by the surface. N I:
Q) Q um‘é
Which of the following relations between magnitudes is true? A. f=F; N=mg ><z <13f=F ; N<mg C f<F ; N<mg ’1 :m S F
D.f<F ; N=mg F <
E.f<F ; N>mg pa; N+%9*mﬁso
Naming “F808 C W? Final Exam — Physics 221 — Spring 2006 62. A 2.0kg block is pressed against an ideal spring so it compresses the spring
4.5 cm from its relaxed length. When released, the block slides on a rough, horizontal surface with ,uk = 0.2 and comes to a stop due to friction 85 cm from
its initial position. Determine the spring constant. A. 9.2 N/m 3’6 = Wm om m A C. l74N/m 2, ‘ D. 1450N/m L x __ mm d {3&2 3290 N/msmx O ‘ 3‘“ T f 3 d
t. Hts“ a“ f (Tinnitus): ; k z 8030 a . ._ KL ,
l ’. a m. w.~...»wmuwmwmr ~t...«.......y . n. M. m . Newt. The situation below refers to the next two questions: Two identical capacitors C1 = C2 = 3.0 til: are connected as shown to a battery that
provides a potential difference V0 = 10 V 63. What is the total electric energy stored by the circuit? A. 75a] C]
B 150m
gmow
. 450 to
E. 500m
QT 1 0‘ +0;
’2, 7/ C2
zgec+ggw
. V
2 0 64. If a dielectric is inserted between the plates of C1, what happens to the charges
on each capacitor (as compared to before the dielectric was inserted)? v ‘ ' arena, 06%?) 6a.:
A. Both charges increase. m . m ..
B. Both charges decrease. 3’ fLmCUOS > W . . Q1 increases, Q2 decreases ,, k at
é Q1 increases, Q2 remains the same % (“’6' Cl Claw m W l
E. Q1 decreases, Q2 remains the same remains ’llxe .
C2, 10W?) Ave. +0 ALE/ltcﬁb / 50 <92. : 935 mch GU) 2 Final Exam — Physics 221 — Spring 2006 65. When a resistor R = 90 Q is connected to a given battery, a current of 1.0 A
runs through the wires. The resistor is then placed over a ﬂame so its temperature increases by 50°C. If the temperature coefﬁcient of resistivity a of
the resistor is 0.005 (°C)_l, what is the current through the circuit after the heating? _ ‘ I
m a" new remiéuce Que; me. “imvfraEi A. 1.3A WWW
B. 1.0A 1,: n {3 gram}?  {govmfim’} «; HQYJL . “till
1', 5—,: Eagle» __—— « 089
‘ Q ' HQA’JL 66. Four identical bulbs are connected in a circuit with an ideal battery as shown
below. Rank the brightness B of bulbs 1, 2 and 3: @B}>Bz>B3 87) i LS M
B. BJ>B2=B3 ‘ C. BI>JB3>B2 bﬂﬁkiGSi‘_ D. Bl=Bz>B3 /__ t E. Bl=BZ<B3 //_ (if; RM M Final Exam — Physics 221 — Spring 2006 67. A neutron star has a radius of 10 km and a mass of 2.8><1030 kg (about 1.4
times that of the Sun). If you (somehow!) dropped a coin 1 m above the surface
of such a star, how fast would it be moving by the time it hits the surface? A. 280km/s A (3M \ I
B. 14001qu ‘ f. O” M SUVIF"; at M
@IQOOKm/s 3W . 8500km/s
E. 13000km/s !
Ugmro CmWVﬂhm UL “RAW +0») 5» "lief; 17446;
"L 7"“ mm — 420‘s?" ——~v C= y M14 \J v 16M?
r TI“ " ___,_..___—— A 0"
1V aka/35 u x Q: ‘ 19x10 /3 A 68. A charge Q1 = 4.0 HC is kept fixed at the origin. Another charge Q2 = —2.0 uC
is ﬁxed on the xaxis, at x1 = 3.0 Hi. What is ycomponent of the electric ﬁeld at (Xay) = (0, 30) m 7 a
A. E,.,=2000 N/C , "’
B. Eg=2600 N/C x
. 553000 N/C 1W \ all
@553300 N/C at E. Ey=47OON/C 9 ‘ ‘~ Q73
Mum “Em” 6 “
a z (a l — lei m» w
<31 Ck). \E
2 [L A __ _____ A
07' 203‘ z Final Exam — Physics 221 — Spring 2006 69. A lSOg toy car rolling on a horizontal table at 0.80 m/s comes to the edge of
the table and lands on the ﬂoor 40 cm away from the edge of the table in the
horizontal direction. At what angle with the horizontal does it strike the ﬂoor? e. O\
A. 16° 08 B. 24° C. 62° @D. 72° 81° MWMW.,..i...._...w__.mw;
C; (DHm
X : CEm'E T = : O VS
0804/; 70. Consider the system depicted below. A block of mass m = 1.0 kg is resting on a
wedge of mass M =1 0 kg and angle 6:30". The wedge is in turn resting on an
incline of angle 6 as shown so that the surface on which the block rests is level.
Initially the block and wedge are at rest. Assume that there is no friction
between the block and wedge and likewise no friction between the wedge and incline. If the block and wedge are released, which of the arrows most correctly
indicates the direction of the acceleration of the block? Final Exam — Physics 221 — Spring 2006 71. Rigid bodies P, Q, R and S are each rotating about an axle parallel to the z—axis.
The angular momenta and rotational kinetic energies of these rigid bodies are given in the table below. Which is the correct ranking of the z—components of
the angular velocities of these rigid bodies? A. aiR>coS>wP>co0 1C: JRIw : ,(z) :3 w L
“ A B. wR>wP>COS>wQ 7 C. aiQ>wS>aip>wR LZICO @ wQ>coP=wS>cax E. None of the above 72. As shown below, a 13rn beam with a mass of 10 kg where the mass is
distributed uniformly is attached to the ceiling with a hinge on one end and a 5m massless string at the other. What is the tension in the string if the system is
in equilibrium? O
B. 82N
C. 196N (“a D. 470N ITan my m, twinge ; E. 510N Final Exam — Physics 221 — Spring 2006 73. In the three systems below, the inclines have the same angle with the
horizontal and the objects are released from the same height h. l. A solid sphere of uniform
density, mass M and radius R
rolling down without slipping. 2. Hollow cylinder of mass
M and radius R rolling
down Without slipping. 3. Hollow cylinder of mass
M and radius 2R rolling
down Without slipping. ~ How do their speeds at the bottom of the incline compare? A. v1<v2=v3
B v1<V2<V3
V1>V3>V2 C:
D.
@ v1> V2 =V3 74:;thmﬂlmmmlmﬁﬁ COWS“. £0 lam l) as U W p 7 {(a\:LL® e? m maixb m‘l‘b KEN” M 51 >62, l Final Exam — Physics 221 — Spring 2006 74. A projectile is fired from the Moon’s surface at exactly the escape velocity in a
horizontal direction as shown. It passes points P and Q where R P and RQ are the distances between each point and the center of the Moon. Likewise, vP and v0 are the velocities of the projectile as it passes points P and Q respectively. lfRQ = 2RP , what is the ratio vQ :vP ? RQ = 212,: 75. Which of the following statements about equipotential surfaces (EPS) is false? A. The electric ﬁeld is always perpendicular to the EPSs.
B. The electric ﬁeld lines are always perpendicular to the EPSs.
The electric ﬂux through an EPS is always zero.
. The surface of a conductor in equilibrium is an EPS
E. The EPSs of a point charge are concentric spheres. m CMwa Clleﬁ} f: £33 #0 Final Exam — Physics 221 — Spring 2006 The situation below refers to the next two questions:
Four point charges of charge Q are arranged in a square of sidelength L as shown. 76. What is the magnitude of the electrostatic force on one of the charges due to
the other three? A' +Q L +Q  > 1
B WW] i mi 2
L2 ‘ Ls ii a
3 : $3
k 2 l r ' ‘ ' ' ' ' ’ ” 0 )
@ E [7”] +Q‘ i Q “I3 a
5 M ¢
k 2 (t F i
D 1% USVBM S‘t‘mm‘; f l.) 1 6
A x f if 6%") a
B 3kQ2 E ‘ ﬂ (:1 *2 @2357; ~ kg“ L+ﬁ>
L : LL 2 ’ L3 2. / 77. Find the electric potential at the center of the square if V(oo) = 0. 4kQ T— A. T w j W W LCQMAVYA' #5 Q V 1 la 5‘51?
c m a m: l mm +<> m
D. g 2 ‘ Walg(\ L y
E Final Exam — Physics 221 — Spring 2006 78. A point charge Q is at the center of a hollow symmetric spherical shell made
out of an insulating material with inner radius 2R and outer radius 4R as
shown. The material has a uniform charge density and a total charge Q. What
is the magnitude of the electric field at a point at distance R from the center of the shell?
r/CQ E= "9
R
B. E22129—
R4
C. Ezk—Q2
2R
1) £2.12
4R2 §>=€g l 79. Each of the ﬁve capacitors in the circuit below has a capacitance of 1.0 pF.
What is the equivalent capacitance of this circuit? lpF
A. 0.25 pF I B. 050 pF @ 2.0 pF 1?}: 11’}: p
. 4.0 pF ___l_ :
7m ,Camciibji in W: I
.L... Ci: O.Y_FF~ lpF \. Final Exam — Physics 221 — Spring 2006 80. A rock is thrown straight downwards at a speed of 29.4 m/s from a bridge over
a river of height 784 Hi. What is the speed of the rock the instant before the
rock strikes the river? Neglect air resistance. kg 83.7 111/5
43/} 49.0 m/s
C. 40.4 m/s
D. 25.9 m/s E. Cannot be determined without knowing the mass of the rock.
(WU Wm ( 6;. or m \
= \n L q. ,1 = .4. am I 
“3+2‘7 0 2i \¢€®:Q%Ao M
tar: Vial”, * Gil : 4401/! 81. The ﬁgure below is the energy diagram for a particle that can move along the x axis. Compare the magnitude of the force acting on the particle and the kinetic
energy of the particle at x1 and X2. Um A. F1 > F2 KE1> K52 F —_ — gage
B. W > w KE1< K52 r; t stage ’2 \& wees?” .
 lFil<lel KE1>KE2 F11<1th KE1<KE2 W *‘Ll WW
' . It is not possible to answer the question without knowing the initial position and velocity of the particle. 11 Final Exam  Physics 221 — Spring 2006 82. A 1.5 kg rock at rest undergoes an explosion into three fragments of mass 0.5
kg each. Fragment #1 has a kinetic energy of 100 J; Fragment #2 has a kinetic energy of 36 J and fragment #3 has a kinetic energy of 25 J. What is the angle
between the velocity vectors of fragment #1 and fragment #2? "' 1‘ 13' A. 71°
B. 138°
@ 158°
D. There is not enough information given to determine this angle
E. The scenario described is not physically possible. I .“L ,_.;’;.L; a. m re "" ..
Kﬂim‘ “3 “‘E‘S‘F; =5 “1' 90 5 “’9 .5 U3 " low/J Wangmawl‘Un .
x...) J
(3:; =~l \W 4‘67} or 1 0'3 = we: «Mar ——> 8: 63 83. (Extra credit) In the circuit below, each of the capacitors has a capacitance of 2.0 F and the resistor has a resistance of 4.0 Q. Initially, at t = 0, capacitor C1 has charge of 2.0 C while capacitor C2 has no charge. Which of the following
is the best estimate of the total amount of energy dissipated by the resistor
during the subsequent 60 s? A. 1/16] B. 1/8J R=4Q C. 1/4J C,=2.0F C2=2.0F
@1/21 Q1(t=0)= . E. H )
. / le v
(hibiscus! ~eﬁ€ﬁm Q‘Oc‘ﬂé'l/ou‘ag UL :42 ?! 1 1.03
i l'L ,
an w w. 1+: of: :gL Jig: mm qua... LOC ( W XSO Qt : 0T1 ‘ m”m15§io\”€ﬁ€fs W3}? ' 01,— Up : of? V) Final Exam — Physics 221 — Spring 2006 PHYSICS 221  Spring, 2006
Laboratory Final 84. As you did in lab, consider the motion of a cart which is given an initial velocity up an inclined track toward a "motion
detector ". Assume the cart goes part of the way up, and then
returns back down the track. (As was done in lab, assume the ci\>x Which of the following best graphs illustrates the velocity, Vx , of the cart (after
leaving your hand) versus time? km: ﬂ‘vt a? St) (ml be men} (himer yqdcmm ’ (ta : .V 85. The reading of the left load cell and left protractor used in the Forces and Vectors
lab are given in the table below. — Protractor
reading Using the coordinate system shown, what is the X component of the force exerted by the left (— ﬂ _ Fg g:
load cell ON the suspended system (student, W ' [m seat, etc.) (in 1b.)? sensor gives positions relative to the X axis illustrated above). 0 (Note: cos (55°) = sin (35°) and sin (55°) = cos (35°) )
A. 125 cos (55°)
125 sin (55°)
C. 125 sin (55°)
D. —125 cos (55°) E. O (The total force must be zero, since nothing is accelerating.) l3 Final Exam — Physics 221 — Spring 2006 86. As in the Collision in Two Dimensions lab,
consider two air pucks sliding with little friction
on a smooth, level surface. Assume they are
each moving with some velocity, collide, and then one subsequently rebounds from the edge of
the table. Consider the total vector momentum, P, of the
two pucks (only). Let P1 be its value before the / . .
I
O . \ “ \\\\ “x collision of the pucks, P2 its value after
collision, and P3 its value after one of the pucks O
)7
\\\\\\\\\ e {W\\ hits the edge of the table. ° . Which of the following most accurately . o describes the relationship between these uantities? , .
q The ﬁsh» involm‘iﬂ unieer *OFL’LD) KO
. P1 = P2 = P3 "“ _ .5
® P1 = P2 i P3 ?L ’ P1
C. P1 i P2 = P3 {dial QXQF‘i 5 am (Lb/Lit $13112 , :0
D. P1 i P2 i P3 L ~— ﬂ,
E. Without knowing whether the collisions are elastic, one cannot say. Pg 3.57 87. Using the rotating wheel apparatus such as you used in lab, a second disk is dropped
concentrically upon the wheel as it is rotating freely. Which of the following graphs best represents the total angular momentum, L, (wheel plus disk) versus time
before, during, and after the disk is dropped? LA LB LC LD [email protected] hm («Widow (PM omt imgm’icwl bfw 0mg,
tirlemaQ (it teem di'dz M mite/ell / so 174%,
+22% mme R: , I
OV/Emﬂ}vﬂw%h) ’lbeh 8‘ka 50% Slow gown elm,
4CD +5521“; ED L. is nol’ was?)er EMY deCKWE/D a (Lille; . l4 Final Exam — Physics 221 — Spring 2006 88. Consider two metal cans, each perched atop an
electroscope. Assume that the right one is charged, and that
the left one is not. By what procedure, say by moving an
electroscope, or by using a conducting ball mounted on an
insulated rod, can one move essentially the entire net
charge from the can on the right to the one on the left? A. Move one electroscope so that one can touches the other
can. B. Place the ball so that it touches one can, then move the
other electroscope so that the second can touches the ball. Move the ball about so that it repeatedly touches the outside of the right can
and then the inside of the left can. D. Move the ball about so that it repeatedly touches the outside of the right can
and then the outside of the left can. E. None of the above since the best one can do by simple mechanical means is
to equalize the charge on the cans (it’s like trying to remove wallpaper paste by simply touching or rubbing it; eventually everything gets covered equally
with paste.) 4 A "l
CLAW asth 55W v V L 15 Final Exam — Physics 221 — Spring 2006 You may record your answers here and take this page with you to compare with the
posted answers. 59 5 69 6 79 D 60 D 70 c, 80 E 61 c 71 p 81 D 62 E 72 A 82 Q 63 C W 33 p 64 p T? T?
65 D Z 75 C 85 g 66 g 76 C, 86 3 67 C 77 F E 87 a 68 x2 78 A 88 C, 16 ...
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