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Unformatted text preview: Physics 1710
Fall 2008
Examination 3 .‘*1Na1ﬁe: LL T _KEY—A— Student ID: . irIn‘structor(circlesone); , ,0 ,VKobe‘é, . ,Lukic—Zniic ' Weathers This test consists of 8 multiple—choice questions and 4 free—response problems, for a total ,, ofllO points ‘(so that 10 points of extra credit are possible). To receive credit for the freeresponse problems, you must show all of your work on the pages provided. Don’t
hand in any extra sheets or other paper. You may also earn partial credit for the some of
the multiple choice problems if you show your work. Suggested procedure for solving the problems: 1. > Read each problem carefully and make sure you know what IS being asked
' ' before starting the problem. ~ Draw a ﬁgure for the problem. ' List the parameters given. Write down the equations to be used. Solve for the answer symbolically. Substitute numbers into you ﬁnal equation and circle your answer. aweaw* WORK THE EASY PROBLEMS FIRST” 1. (7 points) What fraction of the period does it take for a simple harmonic oscillator (e. g., a
pendulum undergoing small oscillations) to go from maximum displacement to a
displacement at which its potential and kinetic energies are equal? 1:; ii? W'AWO‘WSSWaf/gﬁnﬂ win/re w= K =>k=w2m
c) 1/4 Displacement K ('0sz ng mi {:0 (Wd’sﬂ)
C2? iiis ”that a: imam ?0(:W)ﬁax Wm: Marina 2%” HM =2mu2 => :me/iaswt zwazm/ismawt
=> Coswt = swat or ”€th =( :1: gr ifﬂwg if
. 2. (7 points) A particle located at the position vector f = (4.00i + 5.005) III has a force
.. A A N i
= (2.00i + 3.00 j)Aacting on it. The torque about the origin is @Eiiiﬁm i J k 4 5 . .m M a c) (—2k)Nm =4.“ 5.« 2n 3“ k (4mm numb ZNmk
d) (—5k)N  m 2” SN e) (2i+3j)N  m 3. (7 points) Two disks of identical mass but different radii (r and 21') are spinning about the
same axis on frictionless bearings and at the same angular speed coo, but in opposite
directions. Initially, they are not touching; then the disks are brought slowly together. The
resulting frictional force between the surfaces eventually brings them to a common
angular velocity. What is the magnitude of the ﬁnal angular speed, 60f, in terms of coo? a) COf=COO/4 ‘3’ u b) COf=2600/5 _ J
c) _a;f=5wo/9 @
.COf=3a)0/5 ‘13:, e) (Of: 600  1’ Baku. A“?! Use Wmafmaa’ulatmmwim‘ Ibefafq " Inna “ [rug * Izruo = Ur" Ilr)°’¥ .. 1 V, 211 “3.9?" 4l 3
g. u; a 12.: Ion : 2W1(2r amrwb .. ”w = .. (0o
lzrtL émarY+ﬁmrt 4+1 6 5 4. (7 points) A piano's middle C string vibrates at its fundamental frequency of 261 .6 Hz.
On one piano the total mass of the string is 0.0100 kg and the length of the string is 64.0
cm. What is the tension in the string? Recall that 1/2 wavelength ﬁts on the string for the
fundamental vibration. PMLté ”w'd’l 11:1; = 2L"? a) 9.8N ._..
b) 122N <:>"7 wal U;f; => 2146:]; c) 385N : , 1 4 . ‘ 2. :4vuLl‘z = 4 cola; 0.64... (26145"); =7§Z N 5. "‘(6 points) You are standing between two speakers. The speaker on the left IS emitting a
tone with frequency 306 Hz. The speaker on the right 18 emitting a tone with frequency
295 Hz. Irritated by the beats, you try to eliminate them by Doppler shiftng the
frequencies so you hear them as the same. The speed of sound is 343 m/s. In which
direction would you have to run to eliminate the beats? a) left, towards the speaker with 306 Hz
b) right, towards the speaker with 295 Hz 6 strai ht ahead I You M +11 move. so W the higkw
di not nz2:0“? at all i: {(2%) is shifted (W Go (Mama 19m 306 He Sam) M
SOWW {W as 501‘}fo h'WGO’
W5 2959(250wm / .,
nil) r (W
306th ° 295M: 2%: 6. (7 points) Standing 5.00 in from a jackhammer in operation, the sound level is llOﬁdB.
How far away from the jackhammer would you have to be for the sound level to be at 70
dB? Treat the jackhammer as a point source. a) 45m. f . Iyv
b) 50 m ‘ q “0115‘ [010% T:
(3 388m 0" Wism‘a‘é
m r *1 ‘0 i
. A: L I
d) 50km 40d3' 0(]%_10% °)=I0ieﬁﬁ=l0iﬁ f3. 9%" 42—40%:9
~ '$ ,04. .r, 1741'? (gy
I2 War: r.
$ :I_ .. [02 '> (‘HOOVX
I
=I00'5M 3 500m 7. (6 points) Kepler’s 2nd law states that «a line drawn from the Sun to a planet will sweep .
out equal areas in equal times. This law follows from
a) conservation of energy.
b) conservation of linear momentum.
@ conservation of angular momentum. ,
) the nonzero torque exerted on the planet by the Sun.
e) the l/r2 nature of the gravitational force. I Remtlder‘wwim‘ m
, , .5. a ‘ _. 4  rx A é __ ‘ a L
1‘ dr dAélrxdrtglr voltl => 3.? élrwi;$ﬁlr”m‘7l‘ﬁ
ﬁnals MAILSO exertsmforinmapw'aual Iowa. 32 :f:o
=3>~li=cauw
~“ d—é:(‘m'&ant 8. (7 points) A solid sphere of mass M and radius R is released from rest on an inclined
plane with an angle of 6 . What is the smallest value of #5 needed to ensure that it rolls
without slipping? ‘ a) tanB b) (2/5)sin6
(1/5)cose
(2/7)tan6 e) (Mg/R)sm9 ZS Sphere. Pivots about cwlncl POM 1’ when r! rolls wdﬁml‘ dipping . so 273?: IP“' IP2 R
“ ~ $> masme ~=R (3&th “119%
=> 0, = — ggs'me ' N Shallow ‘ 2ij .ma‘ =>. ”sue 4‘ we. a» f: wgsynélwa m: gwn Wu“ we Mwewéwee e/us: $1M 9. (14 points) A uniform solid cylinder of radius R = 0.100 m and mass M = 5.00 kg is
supported on a frictionless axle at the top of a ramp that makes an angle of 0 = 30° to the
horizontal, as shown in the ﬁgure. A cord of negligible mass is wrapped around
ci1cumference of the cylinder, and the free end IS attached to a block of mass m  2. 00 kg
that slides without friction on the ramp.
The cord does not stretch. a) Find the acceleration of the
block down the ramp when it is
released from rest. . b) Find the tension in the cord. . ‘1‘‘
N
P g .1
l2.
1:.
a:
Add NeWiIIM M (an! foam block' 252‘ WLO.,, ._ ‘> wussme —T= ma, (1) 12.15221242222192224224122212 22312221222 21,1 1.2 => T1251“ ~sz ‘12 ';4>;"T=gMa (z) Solve ()aMd(2)§w 0. MT' , , . p
‘ 3'3 98151/53 5m3o° EV ‘ :2 ’SMG =’ W 311 =,.—————————— =2J3m a. ”l “"1““ =1“ “MT “LN; 22.. . 2. 922.22., , ; b)T— 1311104? 551:3 218mg: I 10. (14 points) A student stands on the center of a rotating platform that has frictionless
bearings. He has a 2. 00 kg object 1n each hand, held 1. 00 m from the axis of rotation of
the system. Assume that the moment of Inertia of the platform + student remains
constant at 1.00 kgm 2. The system is initially rotating at 10.0 rpm. Determine a) the initial angular velocity in radians per second,
b) the angular velocity of the system in radians per second after the objects are
brought to a distance of 0.200 m from the axis of rotation, and c) the change in the rotational kinetic energy of the system as the objects are pulled
closer to the center of rotation. left—4 >' rd:— 1 ‘ 2 J" ,_ I‘ ‘1} g y I '_ 2: . 4, a ma.
Iiw;:I‘wa $ w¥=w;.ﬁ=wi‘M1;IO$‘@ W/ LL22 0 z, n
m L » lWl‘s“? ”21$an c)4§Kr‘;'il<¢K4= gig. 41144: :3—4 5[(;§W+zmq)n (1Wt2m2)w] ﬂats“ 422159 42..) X4554) (H44 422440») )0 ml 1! II 11. (14 points) A spaceship of mass In: 5.00 X 104 kg moves around a planet 1n a circular orbit with a period of T= 3.00 hours at a distance of 122.00 X105 m from the planet’ 3
center a) Find the mass of the planet. b) Find the kinetic energy K of the spaceship. c) The spaceship’s engines are ﬁred brieﬂy (so that the distance the spaceship moves
away from the planet while they’re on is negligible). What minimum additional kinetic energy AK must the spaceship’s engines impart to the spaceship for it to
escape from the planet? , , 7:, . r;  4&3; ‘ 47(2R3 ~ 4112 (ZXIQTMf r
. . , 2  W.” .
a) WTPTK’T’T’M“ T EMT T‘“ “ T T M 6T1 saltwater3%? b) Emil?“ Swieﬂtle' [I E=é . 111103 GT?“ ‘7 (22% W V‘= o.= R kr‘clrwlm‘ orlax‘t have. u = ,W cm GMM' = 667YIOT'N‘K‘431'4WTOITE3‘5‘10T5
2Kn—T 2K Zanotm = C) To escaea’fiw Spaccétarl‘tls 15050} E? W W lMi WW'EO EI~ O' ‘ . ”e K'Tz‘v“ ZR
E": ETAK O =E>AK= E=%’%—Ti3.39xww§' (I a other wardsfffm. Line‘ﬁcw afﬁx: shtp mud IN. douMwL) 12. (14 points) A mass m = 3.00 kg is suspended by a vertical spring, and is displaced
downward a distance d = 5.00 cm from its equilibrium position before being released
from rest at t = 0. When it passes through its equilibrium position, it is observed to have speed v = 7.00 m/s.
a) Find the spring constant k of the spring. b) Find the period Tof oscillation.
c) Write an expression that gives the distance of the mass f1 om its equ111b11um position at any time t > 0. .. , L , é)/iffh€£ﬂMt ibﬁmrwmmaadf‘ﬂe 515%»: is [(012110 dimmdokfw,
,. ' , aﬂéiﬁjwzis 1%,;th ”Winklemw' sW,so ~ 4 30 05M); ”$231“ AF ’3‘ 5:8,WNAN=(w=F=14om¢mA) e) y= Ashtédtw whu A=at ml y(f~o)=~'al=> 4:43.34; 33942: 3 y. com 57414611147, t it) a was... 095(l40mJ/5 t) Physics 1710
Fall 2008
Examination 3 Name: KEY B (See KEY A —For detailed 501mm)
Student ID:
Instructor (circle one): Kobe LukicZrnic Weathers This test consists of 8 multiple—choice questions and 4 freeresponse problems, for a total
of 110 points (so that 10 points of extra credit are possible). To receive credit for the
free—response problems, you must Show all of your work on the pages provided. Don’t
hand in any extra sheets or other paper. You may also earn partial credit for the some of
the multiple choice problems if you show your work. Suggested procedure for solving the problems: 1. Read each problem carefully and make sure you know What is being asked / i ,
before starting the problem. Draw a ﬁgure for the problem. List the parameters given. Write down the equations to be used. Solve for the answer symbolically. Substitute numbers into you ﬁnal equation and circle your answer. aweww WORK THE EASY PROBLEMS FIRST” . ,vs..,dm_..4.us._m. . . ..... ..... .. .. .. . . l. (6 points) You are standing between two speakers. The speaker on the left is emitting a
tone with frequency 306 Hz. The speakeron the right is emitting atone with frequency
295 Hz. Irritated by the beats, you try to eliminate them by Doppler shifting the
frequencies so you hear them as the same. The speed of sound is 343 m/s. In which
direction would you have to run to eliminate the beats? & .» a)~ straightahead r’  r '
b) not move at all
@ right, towards the speaker with 295 Hz
(1) left, towards the speaker with 306 Hz 2. (7 points) A piano's middle C string vibrates at its fundamental frequency of 261.6 Hz.
On one piano the total mass of the string is 0.0100 kg and the length of the string is64.0
cm. What is the tension in the string? Recall that 1A; wavelength ﬁts on the string for the
fundamental vibration. @ 1752N‘
b) 980N
c) 385N
d) 122N
e) 9.8N 3. (7 points) Standing 5.00 m from a jackhammer in operation, the sound level is 110 dB.
How far away from the jackhammer would you have to be for the sound level to be at 70 dB? Treat the jackhammer as a point source.
a) 50 m 4. (7 points) A solid sphere of mass M and radius R is released from rest on an inclined
plane with an angle of 6 .’ What is the smallest value of ,us needed to ensure that it rolls
Without slipping? ' a) (2/ 5)sin6 b) (1/5)cosG
@ (2/7)tane d) tanB e) (Mg/R)[email protected] 5. (6 points) Kepler’s 2nd law states that a line drawn from the Sun to a planet will sweep
out equal areas in equal times. This law follows from
a) the nonzero torque exerted on the planet by the Sun.
b) conservation of energy.
0) conservation of linear momentum.
@ conservation of angular momentum.
e) the l/r2 nature of the gravitational force. 6. (7 points) What fraction of the period does it take for a simple harmonic oscillator (e.g., a
pendulum undergoing small oscillations) to go from maximum displacement to a
displacement at which its potential and kinetic energies are equal? a) 1/16
(E) 1/8
c) 1/4
d) 1/3
e) 1/2 7. (7 points) A particle located at the position vector i" = (4.00i + 5.00;) m has a force
F = (2.00i + 3.003) acting on it. The torque about the origin is a) (5k)Nm
b) (—2k)Nm
@ (2k)N  m
d) (—5k)N'm
e) (2i+3j)N'm 8. (7 points) Two disks of identical mass but different radii (r and Zr) are spinning about the
same axis on frictionless bearings and at the same angular speed am, but in opposite
directions. Initially, they are not touching; then the disks are brought slowly together. The
resulting frictional force between the surfaces eventually brings them to a common
angular velocity. What is the magnitude of the ﬁnal angular speed, 60f; in terms of am? a 60f: coo / 4
® wf= 3 £00 / 5
c) 60f: 5 coo / 9
d) 60f: 2 £00 / 5
e) CUf= €00 9. (14 points) A uniform solid cylinder of radius R = 0.100 m and mass M = 4.00 kg is
supported on a frictionless axle at the top of a ramp that makes an angle of 6 = 30° to the
horizontal, as shown in the ﬁgure. A cord of negligible mass is wrapped around
circumference of the cylinder, and the free end is attached to a block of mass m = 3.00 kg
that slides without friction on the ramp.
The cord does not stretch. a) Find the acceleration of the
block down the ramp when it is
released from rest. b) Find the tension in the cord. _ 5M0 , ollc'ir/sf :mSOD' _ . y b) T: ﬁlm: 541.3. 2.54%; = 10. (14 points) A student stands on the center of a rotating platform that has frictionless
bearings. He has a 3. 00 kg object in each hand, held 1. 00 m from the axis of rotation of
the system. Assume that the moment of 1nertia of the platform + student remains
constant at 1.00 kgmz. The system is initially rotating at 12.0 rpm. Determine a) the initial angular velocity 1n radians per second, b) the angular velocity of the system in radians per second after the objects are
brought to a distance of 0.200 m from the axis of rotation, and c) the change in the rotational kinetic energy of the system as the objects are pulled
closer to the center of rotation. a1». 12% em 17,—; ms =m I ZWGa “+23 (ilk)
1:, w ww: (26ml M— J .
) ‘ IWwZM / lav“+23% (714‘ C)AK “HUWQWM; (15w +ZW‘)w.] [(1W123H(Zm)allm4/) (“saw 423%{1M\)(I.26w#)] ' ll. (14 points) A spaceship of mass m — 6.00 X 104 kg moves around a planet 1n a circular
orbit with a period of T: 4.00 hours at a distance of R 2.00 ><106 m from the planet’s
center. a) Find the mass of the planet. b) Find the kinetic energy K of the spaceship. c) The spaceship’s engines are ﬁred brieﬂy (so that the distance the spaceship moves
away from the planet while they’re on is negligible). What minimum additional kinetic energy AK must the spaceship’s engines impart to the spaceship for it to
escape from the planet? 4“ R3 (2.106“ 3
GT‘ Zinnia; (it 36% MK _ GM“: 667xlo“Na£1228i103 (W 04%; " ' 2 2mm 12. (14 points) A mass 'm = 4.00 kg is suspended by a vertical spring, and is displaced
downward a distance d = 3.00 Cm from its equilibrium position before being released
from rest at z‘ = 0. When it passes through its equilibrium position, it is observed to have speed v = 7.00 m/s.
a) Find the spring constant k of the spring.
b) Find the period T of oscillation.
c) Write an expression that gives the distance of the mass from its equilibrium
position at any time t > 0. am ":72— 4%?
OM b) "2“"2“F,aom m an [Tow/s) =Asin[w+*€P) = o 03m'5m(233ml/5 t 1g): — 003m 605(233raJ/s t) ...
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