w04FinalSoln - Physics Department University of Michigan...

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Unformatted text preview: Physics Department, University of Michigan Physics 140, General Physics I— Winter 2004, Final Exam FORM 1 April 23, 2004 Please print your NAME: 5 f 8“ ' (Last) (First) Your SECTION NUMBER or TA NAME: INSTRUCTIONS AND INFO: 1. Fill in your name above ‘ 2. FILL IN YOUR NAME, SECTION NUMBER and the EXAM VERSION NUMBER ON THE MACHINE-SCAN SHEETS: 19,22,23 , - 3. RECORD YOUR ANSWERS ON THE SCANTRON SHEETS. PREFERABLY WITH A #2 PENCIL SIGN AND DATE THE SCANTRON SHEET. Turn in the exam copy with your machine scan answer sheet. This is a two hour (120-minute) exam. This is a closed book exam. You may, however, refer to up to four 3” by 5” notecards loaded with material of your choosing. You may use a calculator but you may not share calculators. All cellphones and other communication devices must be shutoff and out of sight. 10. This exam has 24 multiple choice questions. Check NOW that your exam has ALL its questions. 11. For each question mark one answer only which is the most correct. 12. For problems marked with (P) at the beginning there is a secondag answer which will receive half-credit. l3. Bold face letters are VECTORS. ‘ 14. Useful information: g = 9.8 m/s2 = 32 fi/s2 unless stated otherwise in the problem. #999 9w Physics 140 Winter 2004 FINAL EXAM 1. , Three packages of salamis with masses m1: 0.5kg, m2: 1.5kg and m3: 3.0kg are being pulled to the right across a horizontal, frictionless surface using the light connecting strings shown. If T3: 12.0N, what is the magnitude of the net force acting on mass m2? a 1.2N 3.6N c) 7.8N d) 10.5N e) 12.0N 2. Three position versus time curves for the one-dimensional motion of a single particle are shown below. Rank the curves according to the net work done on the particle between times t1 and t2, greatest to least. X Physics 140 Winter 2004 FINAL EXAM 3. (P) A Spring hung vertically in a lecture hall is observed to stretch 1.5cm from its rest length when a ball of mass m is connected to it and allowed to reach static equilibrium. If the ball is given a small upward push and let go, what will be the frequency f of the resultant oscillations of the spring-mass system? ' “fl” fife/V1 = 0, am (II) } 0(0/f M .... T; 31‘ 1E ;,_,-.r-'-m :w/f’Ay A q__ 5 ‘4' 5 3/ j. mjmg ézmg/M/f WIZ’WC: W: W @4.1Hz =5” _ (EFF/If] f: l/g/am? b) 13.7 Hz P33 (“Mam/r” 6/! 44/ ' f i ni d d e) more 1n ormato s nee e . m 477 .p ) 4. (P) A bat navigates a cave using ultrasonic chirps emitted at a frequency of 41.0 kHz. If the bat is moving directly toward a wall at a speed of 0.12 times the speed of sound in the air of the cave, what is the frequency of the reflected chirp heard by the bat? U flrf‘f 4 mama 50W ..—r _ fr9¢g£_€k'(7l :3 gig: 3,55% mm 1; a. WWW génger; fa flee-Ar- p c) 45.9w: gawk Jag/M44 {hf : a) 48.9kI—Iz - 52.2kHz .; 4f+75 :- //_:,/n 9/01.. ] 7”; jig/2% Physics 140 Winter 2004 FINAL EXAM 5. A large tin drum, open at the top, is filled with olive oil to a height of 1.6m. A small . hole is punched at a height 0.4m below the oil’s surface, and a stream flows out of the hole horizontally. From the moment the hole is punched, how much time elapses before the oil hits the ground at the base of the container? : . MW apemvt ,: M230 2 , t, M new J i v 7A! I. a ’lémf 044M Va) 0.12s @0.49s t/ c.s 'émw‘. digs ‘ aim Camel! Ulla e) 4.8s M .wwomeew | erxf<<vmde 'L. ' .— ~ .. : k "' 3'5 N mimwwew WW”- 0 laid!" '3 zh‘ ," f: V "it: V7§hl V2“: : ' m M £9 &¢ S 6. The curves‘lglow Show 4gdisp’lace nts over ti)r(ne of two systems undergoing ’3 (‘0 «\N m simple harmonic motion. How large is the phase difference between them? w \% kw» n x displacement 69min r‘. l“ 17% b) 76/3 rad c) m2 rad d) 313 rad e) 3311/2 rad Physics 140 Winter 2004 FINAL EXAM 7. You place a small rubber ball of density pb at a distance d below the surface of a pool of water with density pw. Released from rest, the ball accelerates upward because pb<pw. Ignoring the effects of drag, to what height above the water’s surface will the ball rise after it emerges from @ter? a i- f ‘- ' ) ) ' a V 7“”? M’E‘ZFEEW’VJ W f” 9* a F g ,_ ——-....._/ ' 0' (Pw/Pb'l) d(pw/pb+1) c) d/(Pb/Pw-l) d) d/(pw/PbH) e) d(pw-pb'.1) ' 8.» (P) A block of mass m slides with velocity v on a frictionless, horizontal surface . toward a second block of mass m2 that is initially at rest on a Spring with spring constant k.' The blocks collide in an elastic fashion, and the second mass and spring oscillate after the collision. Which properties of the oscillator depend on the initial velocityl of the first block? ‘ , I ‘ l a) maximum displacement V (UP—9 K ) 3%vafif b) frequency C) Ir)na)1(1imumdvelocity ‘ l I d y alcitofai)?lb):31d c) {3 W9 down if)?“ . Ml Physics 140 Winter 2004 FINAL EXAM 9. A sirane pendulum composed of a small piece of salami of mass m hung from a string of length L, oscillates around pivot point 0. At the instant that the mass has maximum kinetic energy, what is the time rate of change of its angular momentum? 0 a) 3mgL/4 ' l L .3 b) 3mgL/2 Y c) 3gL/4 d) mgL ‘ e) 0 I A D A a” e A T: {XFcazdL/fi: :0 10. In the video game Snideley’s Challenge, the 70kg villain makes an elusive maneuver by running across the screen according to the trajectory r = (800—3t —8t2+4t3)i + (920 + 2t + 6t2 -—5t3)j in pixel units. If each screen pixel represents 0.2m in the world of the villain and t is time in seconds, what is the i -component of the villain’s acceleration at t=25? ' ‘ b) 2.4 m/s2 6.4 m/s2 12 m/s2 e) 24m/52 a =11 I A a) 1.2rn/s2 A IL . Physics 140 Winter 2004 FINAL EXAM 11. A 2.0kg body moving along the x-axis is subject to a fOrce F (x) = —6x N, with x the position in meters. If the velocity of the body at x=3.0m is 8.0m/s, what is the velocity of the body at x=4.0m? 4 . K:W=~ /\ >. 2352:3118 f. 1’34qu 2,, L '5 . 2:4‘“ img'v") I: f—éx 4K: ‘2‘!“ 6.6 m/s 2 ‘l. a _, .- jaw—8) : ,3pe)+3(q):.yg.z7j..-2: I e) 13.2m/s V Bvfi—Na-w: Ln :> WW? if"? . [#3 Me a, Win} fiance > 12. At the sight of a yo-yo resting on a (horizontal, an ordinarily frictional) table, you can’t resist performing a small physics experiment. You unwind a bit of string and give a gentle pull straight upward, "as shown below; What will be the outcome of your experiment? a) The yo-yo rolls to the right. b) The yo-yo spins clockwise in place. @ The yo-yo rolls to the left. 4 d) The yo-yo spins counterclockwise in place. e) It’s impossible to tell how the yo-yo will move. Piaf) W??? {S D .. Oxauvxol PNdfi- (f) 5 3. 30—39 vols Left 6 Physics 140 Winter 2004 FINAL EXAM 13. A middle school student is standardizing the concentration of a salt~water solution by slowly adding salt to a beaker of water until an (uncooked) egg will just float in it. The procedure is based on the assumption that 8 r41 624} f . 'a) all eggs have the same volume. b) all eggs have the Same weight. , 3 m 3 Va 5) é all eggs have the same shape. «2 ' n 6} ‘ ? all eggs have the same density. ' l . r / o ’ fig “fie/n e salted eggs taste better than unsalted eggs. {Adam a n 2 file: Ca /: I, realm; ) abje (if é/ lemme/n f 14. Two identical billiard balls are placed on a‘pool table. One of the balls is at rest while the other is hit toward the first ball with velocity 31 m/s. After the collision, the first ball is moving at 30° to the x-axis and the second is moving at —14.5° to the x—axis. What are the final speeds of the balls, vl ; v2? a) 0.90 m/s; 1.80 m/s b) 3.04 m/s; 1.52 m/s c) 0.55 m/s; 1.10 m/s d 2.12 m/s;2.12 m/s 1.07 m/s; 2.14 m/s 2 h : Cons evveJ ‘ :' z ‘1 +9 5 pa :1 o 2 I i; re. MW ’30 3 M(5 -: 18:7 1;. + .97 V2 tom” 37(20- %"Is:7.9lv. $V.= Lo? ml; V1:’2..MM/{ Physics 140 Winter 2004 FINAL EXAM 15. A cold water line enters my house 1.5m below the ground. Heading to bed late at night, I turn on the tap in the upstairs bathroom located about 6m above ground. It’s the only water source in use at the time. Having (quite handily) borrowed a pair of flow meters from Warren, I measure the flow velocity in the ground pipe to be 1.4m/s while the velocity in the second story pipe is 4.5m/s. Which one of the following ‘ statements about this situation is false? 3 The pipe diameter upstairs is smaller than that in the ground. T The water pressure upstairs is greater than that in the ground. F c Along the sections of pipe carrying the flow, the mass flow rate is constant. T' d) The gravitational potential energy of the water upstairs is greater than that in the ground. T e) The density of the water is the same upstairs as in the ground. 1' 9/»an > (Adam/n) 16. At a private school in a swank Cleveland suburb, high school students learn . dimensional analysis by playing a computer game where they must zap the one expression from a list of expressions whose dimension differs from the others. If m is mass, F force, p linear momentum, t time, d distance, and L angular momentum, which would you 2E in the following list? p " dele‘iz \l a) Fd a“? b) pZ/m c) mdz/t2 3 @ Lz/mt2 M", 'V e) LZ/mdzf 2 M. mil/VYM? “’1 Physics 140 Winter 2004 FINAL EXAM 17. (P) By blowing air over the top of an empty bottle, you excite a spectrum of standing sound waves that produces an audible hum. If the tube of the bottle is 12cm, and the speed of sound in the room is 340 m/s, what is the spacing of adjacent harmonic frequencies produced in the bottle? :3 F213;; baa/“W P199 OJiM M P@)1.41<sz ' f: V’3wm/f f-i- 212»- (Jig-W 2 i ' d) 7.1kHz e) 17 kHz '= W7 H3 41.41”; 18. An Atwoods machine is set up with a frictionless, massless pulley and string from which two unequal masses are suspended. ‘After the masses are released from rest, which of the following statements about the two-mass system is true? a) The location of the center of mass of the system is not changing with time. F _ . ® The tension in the string does no work on the system. T _ I ‘ 624;“; e I 5‘ bud J c) The total momentum of the system is constant in timeF d) The system’s kinetic energy is decreasing in time. F- e) The mechanical energy of the two mass + Earth system is increasing in time. F Physics 140 Winter 2004 FINAL EXAM 19. (P) The figure below shows an 18.0kg crate of salami sliding down a ramp on a ’ (massless) rope that is wrapped around a uniform disk of radius 0.25m and mass 6.0kg. The coefficient of kinetic friction between the crate and ramp is uk=0.24. What is the magnitude of the crate’s linear acceleration? (Recall that the moment of _ inertia of a uniform disk is I=mr2/2.) 20. (P) When a resonant driving force is applied to a harmonic oscillator, a) the driving frequency matches the natural frequency. , b) the power absorbed by the oscillator is maximized. ’ c) the mechanical energy of the oscillator decreases. both a) and b) e both a) and c) Physics 140 Winter 2004 FINAL EXAM 21. The dominant water waves in a particular patch of sea are observed to be sinusoidal with wavelength 1000 ft, frequency 0.07 Hz and amplitude 10 ft. For this region, what is the ratio of the wave speed to the maximum vertical velocity of water caused b he waves? . yt _ ' ' r 1f; .23 =21:(M7)/m 23/“ W :440M/‘rtl’4 33m . RM WW?) J W flea/M'- more information is needed ‘9 :gm 3M ( Rx— (‘1’ V} 1' 43M 3 Wyn-m ” WM“ wm‘ Ram 2.ng 22. (P) A small ring is rolling toward a loop-the-loop with velocity more than sufficient to successfully execute the loop. The ring rolls withoutslipping. When it ascends to the top’ of the loop, its vertical acceleration is zero. there is no normal force acting on it. the net force acting on it is zero. _ the magnitude of its vertical acceleration is less than g. the static friction force acting on it is zero. Physics 140 Winter 2004 FINAL EXAM 23. A wave reflected from a hard boundary (a node) will undergo +3? wow:- a) a phase shift of 912/2. @ a phase shift of at. c) no shift inphase. ‘ d) an increase in wave amplitude. e) a doubling of the wave velocity. ' 24. (P) You toss two eggs (W and Z) from the same location in the trajectories shown “A N , below. The initial velocity of egg W is directed at an angle 75° above horizontal ¢=A/=7r while that of egg Z is 30°. If the ratio of their ranges is RW/RZ =5/8, what is the ratio 2 of their initial speeds vw/vz? F 32:: my :[QWQQa‘A W, 6,- PM: 1’3) a (63/53,,th e/ 0 . G e) 3.33 N K» 5 vii/.40;on , ‘1 '0’; ...
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This note was uploaded on 04/04/2008 for the course PHYSICS 140 taught by Professor Evrard during the Fall '07 term at University of Michigan.

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w04FinalSoln - Physics Department University of Michigan...

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