MidTerm_Solutions_W08

MidTerm_Solutions_W08 - Date: February 13, 2008 NAME...

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Unformatted text preview: Date: February 13, 2008 NAME (Print): LD. #: PROFESSOR: SECTION #: UNIVERSITY OF WATERLOO DEPARTMENT OF PHYSICS PHYSICS 1251 WINTER 20081 I MIDTERM EXAMINATION Time: 7:00 — 9:00 pm \G‘M” SIGNATURE: _\I IMPORTANT INSTRUCTIONS - READ CAREFULLY TO AVOID PENALTY Use PENCIL. Mark your ID# and three digit “Section number”. Check that you have not missed, or put double marks in any row in the answer field. (Keep sheet face down when not in use.) Fill in name, etc., at upper right on computer sheet and on this page. HAND IN SHEET AND BOOKLET SEPARATELY. Booklets will be returned later. Check that your exam has 12 questions. All questions are of equal value, so don’t get hung up and miss the easy ones. Formula sheet should be attached There is no penalty marking for incorrect answers; However, in the event that the computer sheet cannot be completely read, credit will be given to correct answers only if work is shown in the space below the questions in this booklet. If you need more space for your calculations, use the back of the previous page and label it with the question number. Good luck!! g = 9.8 m/sz, I0 =10'1ZW/m2 . . . 1 Moment of Inertia for a c1rcular disk through center of mass [m = — ml?2 2 . . 1 Moment of Inertla for a Circular rod through center of mass [m = —m€2 12 Circle your Professor: Lecture Section Lecture Section Lecture Section 001 F. Wilhelm—Mauch (Elec.) 002 R. J ayasundera (Mech) 003 R. J ayasundera (MGTE) Winter 2008 Midterm Page 2 of 9 1. A mass attached to a spring produces simple harmonic motion in a horizontal frictionless plane. It is found that at a certain time t, it has a displacement of half its amplitude in positive x direction and its motion is toward the negative x direction. Four seconds later the mass arrives for the first time at a position of half the amplitude in positive x direction and its motion is ' toward the positive x direction. Calculate the periodiof oscillation. Answer in sec. (a) 2 (b) 3 (c) 4 (d) 5 6 9< (6):» «=4me Vte) 3...;999 Slhfbéffi‘fio) W) 9/1”" ’ ” ‘_ 1s Md ’l/‘(6J40 fi/Q- ’ n (60 (w c P) -Aw Crusoe-{WAD //,_ m/ v 6%) = C” (W =16“ m1 Mrwt+’)>o =3) 0’(¢\96*¢) cue-W = 7’73 "‘03 lav/w Iféwfily’) -_-. A/z WOC Ma‘- (w (cm 1'4!) 40 ‘1’ Cl: - ’— )=”/g_ =3 wCé-MJ-I‘s’: 277-7173 _ 5-7773 (9 Coo ( can-w) 4 40) 77/ A) w .2 777’ 1. L7]- ' ® —-® =7 6’10 = 9 3 — 7. i i 7' = 5' 9c. 2. A simple harmonic oscillator consists of a block attached to a spring. The block slides on a frictionless surface, with equilibrium point x = 0 andiamplitude 0.20 m. A graph of the block’s velocity v as a function of time t is shown in diagram. What is its acceleration at t = 0.12 sec? Answer in m/sz. (b)-190.0 (c) —280.0 (d) 499.0 (C) -640.0 1 ] 1 / fl:a.Q_m %u:1fi l(m/S) M: M; =-> 2% =3 74(0) = fitmcqt) quay-.3 Cw Coot-W?) O .. __ ‘ =0 fwmwé we)” —3 'MM‘”) —27r{——~———— JAM-=0 =9 ‘P = a”? If . a «UNA-’0 .au’flq Ibqg-fi‘w .,w.r=fif6!{m' 7gth 40 MM’ 19“" i 90 :77 sum-my <0 mac m 4m and are):.-Aw Cw (we-+an ) etc n”) ~ — (0'2)C/077)LC°3 C row (12.) +17 _— - was? 34"” M/Ih- (“’1- ———- 4(6) Winter 2008 Midterm Page 3 of 9 3. In diagram, a 2.50 kg disk of diameter D = 42.0 cm supported by a rod of length L = 76.0 cm and negligible mass that is pivoted at its end. Without the torsion spring it would have a period of oscillation of “T” sec. However, when a torsion spring is connected the period reduces by 0.500 seconds. Calculate the torsion spring constant. Answer in N.m/rad. (a) m 23.2 (d) 30.6 (e) . Wt‘flwt 72“ 75V 1 v , ‘af 1?...“ k, WNW“ 5A '1. , o 1‘, = .Lmnwmll-‘I‘N " 7"“? 7’37! ’1 (a..r)(-u)" 2‘ l'rq'vw‘wt 2. — ' .. 2.9/90!“ Tia-'03“ . ‘n ._ 6119' «9.712201 9 gr. - To an. 0 -—"-’-—h gt},- = .. mjawehfla‘Q "’53 I. —[/”j[Lf-R) +k)9‘ ‘-' I 3,449: -'(m2(c+n) +"-) e~ —-—.--® 041‘: To ' 60:13.77: #277 =0 T' [2-0") , "‘3 M w= 1911:1512 fr?“ m 1" D 7": 43.5" H'- 4. A spring has one end attached to a mass and the other to a wall and is free to oscillate in SHM on a frictionless horizontal plane. When the displacemeht is x = 30 cm in the positive x direction its speed is half the maximum speed and is positive. Find the position where the kinetic energy will be 1/: of the total energy. Answer in m. ‘ (b) 0.54 (c) 0.62 (d)0.71. (6) 0,84 fwa Mags '5 Mid} “his”? 6 w: W ‘01—: M06 51%}“4”: k€+l°6 W", 72...; ah/WMWA»; Ummcfiw ilfiz': §m(¢£o}L+g~_ Ax" gm"? if" A?" +/{ #:0327- flr= waft?” + [(3) 1/9203)” 9.2/9 :0 3:9.d‘m W Mské Winter 2008 Midterm : Page 4 of9 5. Two sinusoidal waves of the same period, with amplitudes of 5.0 and 7.0 mm, travel 111 the same direction along a stretched string; they produce a resultant wave with an amplitude of 9.0 mm. The phase constant of the 5.0 mm wave is 0. What is the phase constant of the 7.0 mm wave? Answer in degrees. ( ) 90 (b) 84 (c) 70 (d) 66 (e) 53 a W flu mm A» Ct: Q‘— f-g‘l- zaé (a: a. 97- : 5' 4 7‘“- 2(7)“?(076 .:(c,9-= - 7/7-0g —'/ _ O 9 = 9; .79 9 -‘¢1 :~ 1 8?. 2' «89° / ’- The following two waves are sent in opposite directions on a horizontal string so as to create a standing wave in a vertical plane: 321(x,t) = (6.00171m)sin(4.007zx — 400m) y2 (x, t) = (6.00mm) sin(4.007rx + 400m) , with x in meters and t in seconds. An antinode is located at point A. In the time interval that . . . l . . p01nt takes to move from max1mum upward dlsplacernent to maxrmum downward d1splacement, how far does each wave move along the string? Answer in m. (a)0.4ll (b)0.372 (0)0.310 (e)0.127 A ,_ ‘1' ’- l Wag 7WW U ’ho/A - M537” =/oo;/ni/5 —, ,+ -. 1#%(A%)Cw(ufie) V V ;1 ’2[‘.ao)v¢d(9'fl= 3) Cw (i90077‘6) —L 7.9.77: ~ (“p—QM” 7? .47: J-Su. -,,I.. ma. 37.24» 9c: :06“ = /°\°>0'2r M' Winter 2008 Midterm Page 5 of 9 7. Two identical speakers emit identical sound waves of frequency 170 Hz uniformly in all directions in space. Each speaker has a power of 1 mW (10'3 W). A point P is 2.00 m from one speaker and 3.00 m from the other. If the speakers are driven in phase and the speed of sound is 340 m/s, find the total intensity due to the two speakers in point P. Answer in uW/m2@ ((a) 2.2. (b) 3.3 (c) 4.4 (d) 5.5 (e) 6.6 V 3 9m¢mhi1~ti0mi°91=It ‘5?" "Ma/i! i H u M ii )\SL-'I1_ )\ I J) )1 AL. ML; WIMILW AA=/’9/'fl‘l L ._-—- 1“ = ’0— ' ,I,=tfil ’ 977(2)‘- 2._ ,0—3 Igor/h" ’9); ' "f 97731.... A‘ 2. ‘..£"_ ?=&L unfit/=2: :5) ’41-:3—29/ j." -— 7 ’9‘; a. or a, .-. M'Aa. gnaw M 29/ =/~M' .'. fl) "Ha. 36“” :- A/e' ‘-. I70! 9‘ fi/ifi’ _ /o 3) . Ifef_fi‘/g=_/. 217214592-“31’9779 1’2. 291-: 9 = 2.2.on "7/ML@ 8. A sinusoidal wave travels on a stretched string with an amplitude of 5 cm, wavelength 4 m and velocity 8 m/s. For the string element at x = 0 its displacement is zero at t = 0 and its transverse speed is directed upward, also at t = 0. (up is considered positive). Which of the equati 3 below describes correctly, the travelling wave. (a) y(x,t) = .05sin(.57rx—47rt+7r/4) ' ‘: 0.057”- (b) y(x,t)=.0531n(.57rx~47rt+—7§) f '- 9’” H‘ k s E3. = 0.; 7/... (C y(x,t) = .05 Sin(.57z'x— 4m) I 9 97; y(x,t) =.058in(.57rx—47rt+7r) ’U‘ 2‘ f: N/k ~ - LO : en? — (e) None of the above. Winter 2008 Midterm Page 6 of 9 9. A wave travelling on a string is of the form y(x,t) = 2x2 —16xt —121'+ 3x + 321‘2 + 4 . If the linear density of the string is 2 kg/m find the tension of the String. Answer in N. (a) (6)1]0neofthese ’ y(7(,0)=%(9(/ p490: 29411.3“.‘9 10. A point source emits 100W of sound isotropically. A small microphone intercepts the sound in an area of 1 cm2, 500 m away from the source. Calculate the power intercepted by the microphone. (b) 30 nW (c) 300 nW (d) 3 uW (e) 30 uW 1, I’ Wkwgwéfla foam. r ('- WY 1'. . ‘ _ [00 _ z (2, MAC“ AM 4"9 ._ .- / 9/7010)“ Winter 2008 Midterm ‘ Page 7 of 9 11. The sum of two sinusoidal traveling waves is always Kexcept for complete destructive interference) a travelling wave only if: (a) Their amplitudes are the same and they travel} in the same direction. (b) Their amplitudes are the same and they travel[ in opposite directions. ?/ @ Their frequencies are the same and they travel in the same direction. l (d) I Their frequencies are the same and they travel in opposite directions. (e) Their frequencies and amplitudes are the same. 0%“ 12. Professor Wilhelm—Mauch is standing at the rear of a ferry which is travelling south at 5.0 m/s. A speedboat travelling north at a speed of 10 m/s has just passed the ferry. The two vessels are moving directly away from each other when the speedboat sounds its whistle at a frequency of 1000 Hz. In response, the ferry sounds its whistle with a frequency of 952 Hz. In this question assume that the speed of sound in air is 340 m/s. Wllat is the difference of the two frequencies heard by Professor Wilhelm-Mauch while the two whistles are sounding? (Answer in Hz) (a) 2.0 (b) 4.5 (d) 6.5 (e) 8.0 ,qu «4:24) u;’\/r' <.._——-u L— qzlohls U=§M(,r l 5:" -: loco swirl" '3 [00° 1 9y7o/ 5‘9 ‘.. 5%,” “ rfir') 76"“91‘2- = 3.0,Hb‘ 2’: ...
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This note was uploaded on 02/05/2011 for the course PHYSICS 125 taught by Professor Jaysundera during the Spring '10 term at Waterloo.

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MidTerm_Solutions_W08 - Date: February 13, 2008 NAME...

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