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Unformatted text preview: PHY 31?K
1 May Elli}? NAME: Exam 3 — PHYEITK Instructions: . I , I Take alternate seats if possible. e No notes. textbooks1 calculators or similar aids are permitted. You may only use the
sheet with formulas as provided. I Use the scantron answer sheet to provide the answers. Follow exactlyr the directions how
to mark it. Write your name, course number, unique number. Sign and date it. Mark solutions for all problems. Mark your answer sheet using #2 pencil. Ir Any questions you may have about the test have to be directed to the instructor — no
conversations andfor collaborative work are permitted. i The next page contains some equations and other information that may be useful on
this exam. You may not ask questions about this sheet, however. I A blank page is attached at the end for scratch paper. You may use both sides of all
pages. Some Useful Equations 4 Newton‘sLaw of Universal Gravitation: F = HGE‘EEH where G = (id? x lil“”§i1n"ﬂ’kg”.
Gravitational potential energy: U = 4:29:52“. 4! Kepler’s Law of Periods: T2 = %r3 I Pressure as a function of height in a ﬂuid of densityr p: 'p = pm  pgh. I Archimedm‘ Principle: The buoyant force on an object equals the weight of fluid it displaces. I Equation of Continuity: pAu = constant. e Bernoulli’s Equation: 13 + in)? + pph = constant. I if F = ﬂies. Utes} = ﬁlm2, and E = K + U = irkiefn, where mm is the amplitude. I For various aimple'hlarinonie osdillators. the period T is given by:
Mass and spring : T = ﬂex/"1:5 Simple pendulum : T = ﬂux/E
Toreionalpendulum'. T: EFﬁ Physical pendulum . T = 211' allﬂ Recall j' =1;'Tand w = 21rf= ‘2sz. I Sinusoidal traveling 1ivave: yfz. t} = ymsin [ks—wt—qb} = ymsin 27" [sei—e'r']. pm is amplitude1 A
is wavelength, k is wave number [it = wal}, 1.I is phase velocity {tr = aika a! is angular frequency [to = 2T" = 2n)“ = 27's}, and at is the phase constant. {I is frequents.r and T is the period.) I Wave velocitv on a string: e = ar'Tfp {T is tensionI p: is the mass per unit length]. I Allowed wavelengths on a string clamped at both ends: Jr = ELfn {n = 1.2.3....1. Allowed
wavelengths in a column of air with one end open. one closed: J. = 4Li’f2n — l]: e For sound: intensityr in decibels {dB}: 43 = Wingi, where IO = 10—12 'me2. Relative intensities
of f1 and I; in dB: 1D logE.  Beat frequency: as = If: — er. I Doppler eﬁeet: f’ = ffv :I: name 2121.5]. where e is the wave speed, vs the speed 0f the source,
and 1),, the speed of the observer. Upper,“ lower signs refer to approachingfreseding. I Speed oflight {in vacuum}; 3 x 10“ mfe.
I Tirne dilation: t = "ft; = err; length oontraction: L = Luff; 7 = 3,117 if! = ufe. I Relativistic transformation of veloeitim {for velocity u in the zdireetion in frame 5 and velocity
u‘ in. frame 3', where 5" moves with speed it along the +edirection with respect to 5'): a i d .u _ E.
u _l—1.I'u:fe2 an  1+1.I"u,l"r:2
. ax“ = e, (a; + ear}; ear = 1; {eat +ufﬁzjfc] II Total energy: E = vmoz = K + mcz, where K is kinetic ailing].r and me:E is the rest energy.
Momentum: p = vﬁmc. E2 = lips)” + [turgid The invariant in all frames is mils“ = E2 — ripe]? Answer the following queﬁiuns: 1. The mass of a hypothetical planet is 1f100 that of Earth and its radius is 1,34 that of
Earth. If a person weighs 000 N on Earth, what would she weigh on this planet? {new a GMM {h} 48 N T; W“ .
q 192M 12 Man Th“ _.L_ l we: t“ ' II
is) see N I em
2. An object released at rest inﬁnitely far from the Earth falls in and crashes to the Earth at a speed of approximately 3 krnfsee. Using G e: i x 10‘11 ngg’kga, and using the
fast that the Earth’s radius is approximately 'i'000 [on1 deduce the mass of the Earth. ﬂuse conservation of energy1 and assume U = 0 infinitely far away}. .2x1024 kg = +
{h} BAXinset“ Ea ’ a M“ K. E5 = (fluI I9 {e} 3.2x1013kg E]? : ém‘ 3 5M“
{a} 0.21.):1015 kg ' R
is] 22.4mm” kg .1174? .. Grit ‘2‘ Bus EMF. Cfﬁlﬂbmygm “5&3: fishers»!h
2c} ‘ ' W's 3. A sphere of uniform density ﬂoats in 1water so that exactly 1 5' 10th of the spheres volume is above the surface. Assuming the dity of the water is 1000 kgfma. what is the
density of the sphere? a sooaggmﬂ {puff} are uM‘LIJ' «whiffuni =we~3£+5£ kg} 1113 E'P'In u: u.
KID e 1000 kglr’m3 (d) 110mgme G93 Waxy...» a ’ ﬂimsy?
{e} 1200 kgftna ' ’
fzfiun : (01%,; 4. An incompressible ﬂuid is ﬂowing through a. eiroulsr pipe of radius R st s velocity of U.
Then the pipe widens to s rsdius 2R. If the pressure in the smaller section of the pipe
is p, what is the pressure in the larger section? The pipe is horizontal. Take the ﬂuid‘s 1':lensit;llr to be p.
s 2 r ,1
{a}? 2r?“ : T 4‘ If)“
Ehls+gsv2
i l __j_ 1
03' “rev” Jed1:133 +— c” ma me: “P a? 1’ 21°C 3
(elsi'gsvﬂ “39R Pr}: 4dr r i I It _ .L.
. H ' 'P*'F+ZPU("M
AdoAd _U="""P' I? '1
. . . . . ~"" "" PM!
32
5. A rock weighs 1400 N in air but has an apparent weight of Elﬂﬂ N when submerged in
water (density,r lﬂEIﬂ kgfrnﬂ}. The volume of the rook is what? Use 9 = 10 m 3' s2. 4. F
II
(a) 0.14 m3
{b} 43.601113 mé‘ffﬂﬁs " w " (Ova : LU
(r: {191) m3 I
.05 1113 (D = M ‘ ej 0.1111113 u.  u; gm “
\I = ——_fr. .1: " 0.515" p a. (I oouyte‘) _ E. A psrtiole moves in simple harmonic motion scording to :1: = 2 oos{5llltj, with s." in meters
and t in seconds. Its maximum velocity is: (a) lﬂﬂsinﬁﬁﬂt}
{b} lﬂﬂeosﬁﬂr) ﬂ“ d
{sheet} .5 s  2(ﬁ)3;.(§of) (e) none of the shove =  [so stuGﬁt} 'F. A traveling were is described by y[:r,t} = 2.0 ElnEélJE — 101:), where m is in meters, 3: is in
centimeters and t is in seconds. The wave number is: 3. Jrcm (its wt) 7 4 8. A standing wave has developed on a. string which is ﬁxed at its two ends! so that the
ends of the string are not free to move. The length of the string is L. Which of the
following sets of positions1 measured from one end of the string1 may be e list of all the onﬁnodes of the standing wave? U1 L 2, L ,
{all x r, \ {b} Lysssgs ml. L “4‘
4, ELM ‘  r” {e} Lfﬁ,Lf31Lf2,2Lf3,ﬁLjﬁ T (e) Lli'irl ELJHT _ m 9. The intensityr of is sound wave is ll] me2. What is the sound level of this wave in
decibels {dB} '3' {e} is en * E\ = l”
Eb} IEdB  l0 (It, la (JDﬂ ﬁnes
d} see 1 m lub( {012) [e] 3 dB '= in (133 = i'So it). An organ pipe is 11.75 rn long. It is closed one end and open on the other. 1flu"hat is
frequency of the 3"; harmonic? [Recall the 151 harmonic, or fundamental, is the lowest
possible frequency, so it has the longest possible wavelength.) Use 1: = 35f} 1113's for the speed of sound. The answer is closest to one of the following: la} him H: A if: 4L 4 L = g— melt—7‘; dogma inn. " Zia—i  g
c TDDHZ [djﬂflﬂHz rU—z Aha, .C: All“ 1—“: (e) 901] Hz 45." M Q S; {Om)3: I": 5510551 11. As an airplane approaches and then recedes from a stationary source of sound, the pilot
measures a frequency dr'ﬁerence (i.e., between approaching and receding) of EDD Hz. If
the speed of the airplane is If“) mfs and the speed of sound in the air is 300 mfs, what is the frequency of t e sou he‘ g rnad hy the stationary source?
43— (“M3 an (W
{a} 225 Hz '— 0 T a”.
{bjﬂﬂﬂ'Hz “w __U+U 2U
_ . z
{c}4f}UHs ﬂl‘r1_¥b(—a——T"— ‘4‘?) 1: 3
ﬁg: EDoHe=%(% 12. Two protons of mass mp collide headon to make a new particle1 called the 11", which
has a mass M a: 3m,,. When we View this collision in the centerof—momcnturn frame,
with what {equal} speed must the two colliding protons approach one another in order
to have just enough energy to create the III? __ z,
ETGT :—  2 E11? Er! “P
I'M—F +——ue eh .aHx
E, F: s e3 A
C!"
U
loltn Ena who
' h 13. in stationary observer in frame 5' notices that e clock which is moving with respect to
3 runs slow by a factor cf exsetly 2;“ The speed of the clock in frame 3 is: tam99c 'i’='~‘ut/nr = ltd/Vs {1:} es c ' {dues .
(ejcflﬂ __ _J_ ._.. a“...__ .E .. ._L
#1” r / *r . 1 141. An unstable particle is created in my experith with speed 1.: = gc. It traveled mm
in my laboratory befere decaying. What is the particles lifetime [according to the particle)?
in lath :i' 'iH‘ﬂﬂll' d: Uh“ = g8ﬁ)’tm' ? x 10—11 5 bd John. . Vii Cele“: d:lﬂ'i§ll¢n‘) d1. Tfsﬁt’e—ai ¥M=¥¢tr _ i
3 . 4
in! l_ 1* 5 3*“ r in .3be H. :jbls 21' 1
a. may 9:
'3' " 1175'
15. A particle of mass m has kinetic energy 4mg. It‘s speed is:
{a} r .
use heme0y”: M
(c) %c
6:5723:19 C" I 3" 4'
(a) 3:35 Y: Q
_____L_—#—— r— 6
I "' lye.“ ‘ 16. A. [1.21] kg object atttaohed to a spring with l: = 500 N! m executes simple harmonic
motion with amplitude 13.14] m. Its maximum speed is 51115 = _ a ﬁ?« 6 f. F 1" 0,”,1‘3 " 12.549 )4;
{d} 15.8 mfs = 5bit]!
[s] 13.2 mfs 11'. The sketch helou'r shows the potential and kinetic energy of a pendulum as a function '
of time. I start the pendulum in motion at t = {1. Which statement best describes situation? (a) I draw the pendulum to the side and release it1 initially at rest. and it goes into
simple harmonic motion. {h} Starting with the pendulum hanging down at its lowest point, I whack the pen—
dulum so it starts moving to the side, and “it thereafter executes simple harmonic motion. in) I draw the pendulum to the side, and at t = [l I ping it. downward {back toward
the hanging down position), and it thereafter goes into simple harmonic motion. draw pendulum to the side, and at t = [1 I give it a ping upward, away from the
. equilibrium point. {e} None of these descriptions is consistent with the sketch time I) gin£ gacksamt. idealit... 4; Sam
> punMm gun'11 Lnrl' lasﬂli’ﬁﬁn'é, hm.
manta},
Z) Huts; altarﬂ dtmc aim: 3 3) Peta/Hm W tomcatt 18. The low edge of your hearing is about 2U Ha. What is the wavelength of such a wave?
The speed of sound is about 340 rn ,3 s We“!
Zﬂﬂaqeﬁﬁ'};
geese”? my (a) BEEN] In is] 1.? m
{d} 1.? on:
to] none of these 5 III?!" 19. The largest number of beats per second will be heard from which pairs of tuning' forks? (a) 2m) and rolls: {sfg; _. I
(b) are and see Hz ' I = q.
{o} 534 and 540 He 3 {9
(e) 3420 and 3422 Hz : a 2D. III am about 1 year older than my spouse. I would like to blast oﬁ in a space ship for
what I judge to he 1 year {13.5 years away from earth, [11.5 years haech1 and have her be
1 year older than me upon my return. How fast must my ship be moving? (note: these things matter when you‘re pushing alﬂl}. lair: x {EEC yarns45%;? Xtl
C EC
“is: For an (rel«Hg
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