Winter_2007_Midterm

Winter_2007_Midterm - Date: February 7, 2007 NAME (Print):...

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Unformatted text preview: Date: February 7, 2007 NAME (Print): UNIVERSITY OF \VATERLOO DEPARTMENT OF PHYSICS PHYSICS 125 WINTER 2007 MIDTERM EXAMINATION Time: 7:00 —~ 9:00 pm ID. #2 W5 PROFESSOR: . SECTION #: SIGNATURE: IMPORTANT INSTRUCTIONS - READ CAREFULLY TO AVOID PENALTY 1. 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.) 2. Fill in name, etc, at upper right on computer sheet and on this page. 3. HAND IN SHEET AND BOOKLET SEPARATELY. Booklets will be returned later. 4. 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 5. 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. 6. If you need more space for your calculations, use the back of the previous page and label it with the question number. 7. Good luck! ! g : 9.8 m/s2, 10 = 10'”W/m2 1 7 =-—mR‘ 2 1 7 ~mC' 12 Moment of Inertia for a circular disk through center of mass It”, Moment of Inertia for a circular rod through center of mass [m 2 Circle your Professor: Lecture Section 001 R. Jayasundera (Eleo) Winter 2007 Midterm Page 3 01‘8 l. The diagram shows the position ofa 20 g block oscillating in SHM on the end ofa spring. What is the maximum kinetic energy ofthe block? Answer in Joules. (a) 4.2 (b) 3.1 (c) 2.7 (e) 1.3 (£€)m% = fiMI/MZ; = é/m'” ,9... “10",” M you/4' 7 -, 90 xiv—3 5“ Wle/c/I/fl; 7- 3 7. ‘K- a771,» = 2/7 (20))”0 3 993’: '7’” ' ('r" 7‘ . .‘l (7x/o“) .‘ ékflzr O. ,' /.’2.J v..- nan—fit ll 2. An object in SHM has its initial position to be 1/3 ofthe amplitude (x = + 1/3 A) and its initial velocity to be negative. Four seconds later it is at a position of 1/2 the amplitude (x = + 1/2 A) and its velocity is positive. From the information provided calculate the angular frequency of the object. Answer in Rad/sec._ (a) 0.38 (b) 0.67 (a) 2.64 (e) 4.00 ea 7U“: Ate“ (we-+59). ¢I9 (99(“‘14¢)= a” A (6): ’/’9 =7 3 M ( ’X— I .3 V..(wcw6;_f’fl)://3 nae/+10: #13 0" 5'05. Vgg)1—Aqu («Myra/l We» 40 flawefipl 70 W /*‘/ no”, “1 61 (q .ra an) 5, = yam—é ce ) - fi/ - Ac“ (49 6;”) = “’4 Q t" W 06 2. ' 9- " V052) >0 Mat 44,; (caéL-f'll) <0 @ "Q (43 (5134”): 9 éa’e/ ’ 99C. 44) = ‘1‘ a) = / I" Winter 2007 Midterm Page 3 01‘7 Two students each of mass 75 kg are on a flat circular platform of mass 100 kg. The platform is attached to one end ofa giant slinky and the other end ofthe slinky to a tall crane. The systems oscillates in a vertical plane beside a tall building with an amplitude of 20 m in SHM. When the slinky is fully stretched and at a momentary stop the platform just touches the ground. At this instant one student steps off the platform. The second student continues to oscillate for a while and then decides to step off the platform when it reaches the highest point which also happens to be the roof top of the building. If the slinky has a force constant of 73.5 N/m. Find the height ofthe building. Answer in m. b) (a) 40 (b) 50 (c) (d) 70 (e) 80 0.5 a 0M J’W‘é'éfi‘“ ' A7 :2 7:17 ALE 9-) Ne“) flw‘A-LM/W~ ‘1 c7 =(7r)(?.f)__ [OM . 734‘ . 1 = 10 frozzam. :9 d O 4. A horizontal lank of mass m and len th L is ivoted at one end. , a iv: 3 p g p i. 3255'", g} The plank other end is supported by a spring of force constant k ~-"“~*$~—‘* and is in equilibrium when the plank is horizontal. When displaced a (3 M7 small angle as shown the plank produces SHM. Which expressions ‘7‘ gives its angular frequency. The moment ofinertia ofthe plank about the pivot is 1/3 mLZ. V “\ (a) 3km; (b) 5g— (c) \/k/m (d) X (e) Wg \ __ "M/ 3m 2 g \ u 5"? a} zzm'd'gfizm We... Irz'njww WWW/y. M to» {Wakq’ . mm) 52‘, = 0 (4/6 (W‘Z‘év'wj _ ,4 , Mae/2% “M” =7 “"4" V . @9244- awA/ed and C24, W 9 -—«6«. °\<-<:¢o Q) 09w 9h.“ 2 zfifiméfi‘ + ([k/Vo‘yjj) 1" 14' (:5? ... efifl!‘ Winter 2007 Midterm 3, When the solid object is pivoted at P1 and at P3 it produces SHM for small angles with same period of oscillation T sec. P3 is directly below P1. lfll] + h: : 14 in find the period ofoscillation. Answer in sec. r- - """""" flér'o/ M 1. Pa. 7/117; l. .124 .. :771' Mjé’ ' £2 5 1.2.? :27 h, h. Tm. AL + Mhlté“ = iemclyfl)‘ M‘ILLCVA’) -, 1cm .. M 4 AL : Page 4 of 8 6. A particle executes simple harmonic motion with an amplitude of3.0 cm. From energy considerations, determine its displacement from equilibrium when its speed equals one halfofits maximum speed. Answer in cm. \Q m v» (a) 0.6 (b) 1.1 (c) 1.6 (d) 2.1 (e) 2.6 m m 'V 2. 1. mm: 1 A A J/é(3x<o‘) 2* 32"”(‘Cm‘9 +41%“1 "‘5" 2 4“ 02 2.. z 1. :imrt/‘Zl “we —: 1‘ .Lfimc“ :k(sxlp./: évh(33‘lo ) 4'" -1 ’L. 9L1. (3xt0') “ 4/ 2. - 3(3x’o‘l) . 9L 4]. r Winter 2007 Midterm (a) (b) (C) y(x,f) : 0.55in(.57rx —4m + 7:) (e) Page 5 of8 A sinusoidal wave travels on a stretched string with am amplitude of 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 equations below describes correctly, the travelling wave. I) ‘ z _. _ U:- 9M/5‘ )(.\,I) 0.3s1n(.57rx 4m+7r/4) 7 : ’7 ‘ k: g = 0 Sn. . 7r ._ y(X,l)=0.5$1U(.57IX+47Tl+—£) U: Q/k =7( 8)(0.577) : w .. 9” y(x,l) = 0.5 sin(.57rx — 4m) gage): fivdu'. Clex~ coé +911.) um,“ = - x9e? Cw (ka—WGNP). None of the above QCCWAQJf 5Q“- ffl/wmalm 91m. yam): o = Am(¢j=a ~“¢= 0W7? —- Oar J 70 fi(o,o) 70 :3 6w ’9‘" r,” Cwqfl4o W s 77 444% A01‘ 0 a-rfix — 9/76 +77.) 7(306): j 8. y(x,l) = 20 sin(47rr + 7r/2) sin(67rx) (x in meters, t sec) describes a standing wave pattern on a string ofmass 1 kg fixed at both ends. lfthis string is oscillating at its 4Ih harmonic calculate the tension ofthe string. Answer in N. (a) 4/9 (b) 27/8 (c) 36/4 (d) 15/12 (@523 4—. ,Q ..__.__> 2?:6 4.41M éwcu'lm ,é: (77 :17? '3' Q=§M €=%M' 6.2:?” U“: 317:2 m 4 / 3 1673/ mw max. :23: "=/a. M‘ if; /A e 3/3 Winter 2007 Midterm Page 6 of7 9. An organ pipe A (one end closed) and organ pipe B (both ends open) have lengths in the ratio LA ' L3 = 0.5. The first harmonic is set up in pipe A and the fourth harmonic is set up in pipe B. What is the ratio of the frequencies fA / f8? \ (a) 1/2 (b) 1/8 (c) 8 1—H La, , L P/ “(D 303 3,!1 P/ “C9 ’ "(Lg f 3L“ 2.9-3 :6 1: 'L 9359:1‘ IlaLn Lo 2' LA at» - 3:. 2 a -L f ' l‘ LI. in ,fl, 10. Two strings of equal length but of unequal mass (the second string has four times the density ofthe first string) are joined and their ends tied to supports. With a tension of 1080 N, the first string is Vibrating in the first harmonic and the second string is Vibrating in the second harmonic. For what tension will the first string vibrate in the third harmonic and the second string Vibrate in the sixth harmonic, if the frequency of Vibration remains the same as before the tension was changed. Answer in Newtons. (a) 30 (b) 60 (c) 90 123) (e) 240 \w‘M Winter 2007 Midterm Page 7 ot‘7 l 1. Two loud speakers emit sound in phase at a frequency of 220 Hz. A listener sits at a location which is 8 m from one speaker and l l m from the other. The sound level at the listener from either loudspeaker acting alone is 35 dB. Calculate the sound level when both loudspeakers are on. Assume speed of sound is 330 m/s. Answer in dB‘s. (b) 46 (c) 66 (d) 70 (e) none ofthcse a .a- A ,4 /o 71,, 35 3( 3M P jmkflg4‘qa/é PALESJ‘Yzw/q“ $W’ 1,=I,.=z M. 1,454 7’5 ' Clio/1‘} 02-430 "W " " . ,. , 'm . 4m fig-4’ ' .90” [/K's 11/:3M =39 '0"; “c A = ' - - 2/) M/ «1/- AK am 0‘27):— r_.___.73+ 3 if“: 7 . 'E z ’ we? - My + my? D 2' Mo 4 35’ 94—1/6 1 VVU DIJMHAULD on» Ullvull U)“ llle baulv UDUllluLUJ U1 LlyLiLtVALVJ auu LLLA. J 11v utJvquvlu “1v Auvutvv on a vertical pole a distance 4.00 m from each other. A Biology student whose ears are in line with the bottom speaker walks away from the pole in a direction perpendicular to the pole. How far away from the pole will the student be when she hears a “minimum” sound for the second time? Assume the speed of sound is 330 m/s. Answer in m. 2.43 (c) 8.41615 9.28) (6) 15.4 (a) 1.99 (b) T 41w l __p ///////, ...
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Winter_2007_Midterm - Date: February 7, 2007 NAME (Print):...

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