Exam1_Solution

Exam1_Solution - Exam 1. Wednesday, February 13‘“, 2008...

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Unformatted text preview: Exam 1. Wednesday, February 13‘“, 2008 PHY 252 Name; Sowmom Each question is worth 25 points. Answer all three questions. Be careful to justify your answers — most of the credit will be for clear explanations of the physics. Do not leave questions unanswered. Even if you cannot get the final answer, show me clearly what you know. 1. A string of length L that has a mass per unit length of p, is under tension F and is clamped at both ends so that the ends cannot move. A transverse standing wave of type y(x,t) = Asin(kx — wt)+ Bsin(kx + cut) is set up on the string. (a) Which wave is traveling in the -x direction? Asin (kx — wt) or (Circle one.) (b) Give an expression for B in terms of A. At ec=o Collagen.) we reclaim 3(a,:t)=o .‘. AvatC—wx) + es'utawe) :— o nfis‘méwi) +Bs'm (nut) 20 => 8 =9 —'—_ X. (c) What possible values can k have? Ail: oer-L, we “2M {'ju-J‘e) =‘9- “ (Salim-“mg +5L4£”L*w13) ': o o-r- lfls'mk’Lcoeui =0 = [r = _ = it? c Shay-H3) Efmfiagssibmmaclm whav: L m .5 K L ‘4: '17-:3 - ‘1‘ vmflv=dfz=%e> w=J§ng a4 (e) What is the velocity of the string along the y direction at point x at time t? Velocié-j ‘»=. 35 : AwicoeCKx-rwt) ~m¢Kx~wflj VY‘ (i) What is the acceleration of the string along the y direction at point x at time t? - 2 n s Accelerai'wualau a = 3 a = __ ,4 “)1. [sm( Kan -th) + SmfiKx~wi~fl 81‘- 2 . _ | . . = _wfl L2 (144. sMWosallaJ‘o-rl (g) What is the velocity of the wave along the x direction at pointx at time t? Utgw 22F (h) What is the acceleration of the wave along the x direction at point x at time t? “M5” “1°51: 2—3" 2'" «amassed! "’5 % DOM ‘Lo and“ 'TL-L mum's Plume MW aid. Idea-4% Exam 1. Wednesday, February 13'“, 2008 PHY 252 2. A deep-sea diver is suspended beneath the surface of Loch Ness by a 100—m-long cable that is attached to a boat on the surface. The diver and his suit have a total mass of 120 kg and a volume of 0.0800 m3. The cable has a diameter of 2.00 cm and a linear mass density of p:1.10 kg/m. The diver thinks he sees something moving in the murky depths and jerks the end of the cable back and forth horizoutally to send transverse waves up the cable as a signal to his companions on the boat. How lon does it take for the si nal to reach the boat at the surface? (Hint: This is similar to the dangling-rope homework problem, except here you need to include the buoyant forces on the diver and on the cable when calculating the tension as a function of height along the rope. Density of water = 1000 kg/m3.) Fl'rst’ m M to .ua REL-c 41PM QC. "reunion ad” or. = Me‘fiLto-fi-M + mead” sales-Jalabe _ magma claim— - 10W spatula Wm. F62) 2: mg + ptch -- pwvnj - Pw(TFD’I-./a)o¢j Fox) = (m ~Pon)j +3(/4c‘7TPaP:/‘r) 0“ 5 (Li-ho; Mamet»dede ‘2 U'Cx) = = )3;th Tim to mutt 7&0? 01+ ac: n (=l00m) LA k h LL 1: 1: $5533 ‘“ II—af‘ox do: 2 JEEJ(Q+bag-_)]o O O 7t— : {LEE/(Mm — J3] =7 (M — PanLq' = (not:1 — woo kfllfixaoaooHK) xfi-eowls‘) = 3(uC—‘IT'QJDE/4) = cl-SDx<lJo nrwoaoxézmfilzr) CL CL = 391.000” lo 5 = enrol; HIM (Keep 524.5135.) 'I .‘ 7!: = 1 Llo ‘ . , _ .l 7 - lawn-C i “[V(392000 +9 Rialzxzao) Sqaj t: 3.851 sec 35tj.jt§5 h)“. C Cream: is given for flood 911113153. 1 calculi care, too Much about {she answer. Exam 1. Wednesday, February 13'1', 2008 PHY 252 3. Two very large open tanks A and F contain the same liquid. A horizontal pipe BCD, having a constriction at C and open to the air at D, leads out of the bottom of tank A, and a vertical pipe E opens into the constriction at C and dips into the liquid in tank F. Assume streamline flow and no viscosity. If the cross-sectional area at C is one-half the area at D, and if D is a distance in below the level of the liquid in A, to what height h; will liquid rise in pipe E? Express your answer in terms of h. Appid BQFHOUL'ILLI'IS eiurtiau. to the top tank_ 53% dflzflczan :0 A ‘2. Po +33%; + o : F’3 +0 +301): L: Pc +0 +4391): .2 P°+o+1i~pvo .-_- P°+o+lipya L_____.__.___.__1 \___________J 1 To? O£ A At 3 Ai‘ C. Ai- n oPe"———-Jntoq..rdo Since EMA. D Luau; 2914.1 5M JIM-fer, we:vn).'_!p3=Pn=Pei ® 50, Shame PD+P3L1I = Pls+§Pv$ 2 Po +359"; => ——-—> ® ...
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This note was uploaded on 05/11/2008 for the course PHY 252 taught by Professor Treacy during the Spring '08 term at ASU.

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Exam1_Solution - Exam 1. Wednesday, February 13‘“, 2008...

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