8AFinalExamSolutions - University of California at Berkeley...

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Unformatted text preview: University of California at Berkeley Department of Physics Physics 8A, Fall 2007 Final Exam December 15, 2006 12:30 PM @ QLJLeJ; “x/ You will be given 170 minutes to woyL this exam. No books, but you may use a handwritten note sheet no larger than an 8 1/2 by 11 sheet of paper. No electronics of any kind (calculator, cell phone, iPod, etc) without explicit permission. Your description of the physics involved in a problem is worth significantly more than any numerical answer. Show all work, and take particular care to explain what you are doing. Write your answers directly on the exam, and if you have to use the back of a sheet make sure to put a note on the front. Do not use a blue book or scratch paper. Each part is worth the number of points indicated. These should sum to 100 points. Setup and explanation are worth almost all of the points. Clearly state what you are doing and why. In particular, make sure that you explain what principles and conservation rules you are applying, and how they relate. There are two pages of info at the back. You can tear them off and keep them separate if you’d like. SID NUMBER: DISCUSSION SECTION NUMBER: DISCUSSION SECTION DATE/TIME: Read the problems carefully. Try to do all the problems. If you get stuck, go on to the next problem. Don't give up! Try to remain relaxed and work steadily. Problem 1: Ski Jump (15 points) A skier goes down a makeshift ski jump, see figure. She first goes down a slope of length L at an angle 0, G" then leaves horizontally from the top of a cliff of height H, flying (well, plummeting, really; who would do this?) for a short while before landing on level ground. 4 Ignore friction of all types. a) How fast is she going when she leaves the ground? 1)) How fast is she going when she lands? H c) How far does she go? 5) Cam rfifl tun. snowy? (U? row-Io! fl": (9., wflflswafil)‘ 43“” 1“” (“"133 {marl \l-I- 2—3 CLffiB‘lH) gm H- 6:1er {M‘Hfi T: [0 R946, M} as: minute fiuohm‘élm lf-vewetlicf: 53ft: H T: W 11%;”‘542 MW tit/60%;; oqflw- (0) 'l! MAG/I26.” W drama; «r W W = Zrlktme' Problem 2: Traffic Accident (15 points) A small car with mu : 1000kg collides with a large truck with mt = 7000 kg. They hit and stick together, with much tending of metal. Just before the collision, the car is moving to the right with speed vC : ZSm/s and the truck is moving to the left with speed v‘ = 3 mfsec. If you need it, the coefficient of static friction is as = 0.15 and the coefficient of kinetic friction is uk = 0.10 for tires on this surface. (Note thatI would like you to do each part of this problem symbolically, putting in numbers only at the end; you need to insert the numbers, but you need not do the arithmetic) a) How fast is the clump of two vehicles moving after the collision? b) They slide to a stop after the collision. How far do they slide? c) How much energy went into the collision itself, i.e. bending metal, breaking glass, etc? -—‘v' If . - 2.1 we \iat = ids—Haw: IE t: L“ i - qua: :-" Q§W%te WM: gm fierce JriCmgurt) v: = oi F = d Mr V It'd’tnéfl- (tgfl‘ofwfi ’fla. Milli-raj 9%: H We” Miw @c+mft)j é—[Mciwfl V: :oi Mk (mumflq = Vat .. _0_-_5j__. : l at 214,4 .. 2.4.1:!" /3 Mfi/ a) .540; Mmfi 3.4!. 5,57%: £04? : Kéb+fi kg, = Jiwfiv‘I-«f-Ewtv: -4: (Mciflt)ufll = 5's. rm(:r‘)+i MG.) “1L (Emmy-g1) :— 5” [”11” 7-?13-3- (V011 (we) a) = W(€Z§_+63‘ZI) T m {(2. WM} 4:0 awa (3“ L3. {92:46] 5: Wfégé) ‘2 _'5‘f’§m—¢ (‘17-!- WE‘M mggwé‘c 447; are. air mm Problem 3: The Fountain (15 points) A fountain has a pump deep underground that pumps F liters/second of water into a long vertical pipe of area A and length L. See figure. Ignore friction and other energy loses; this fountain is at Disneyland, where imperfections like that are not allowed. Consider two points: (1) is at the bottom of the long pipe, and (2) is at the very top where the fountain opens to the atmosphere. at) b) C) at) 5’th How much water (litersisecond) flows past points (I) and (2)? Why? What is the velocity of the water at points (1) and (2)? Why? What is the pressure at points (1) and (2)? If it’s important, you can use Palrn for atmospheric pressure. Be sure to specify what type of pressure you are describing. You probably found that the pressures are not the same. If we need them to be for some reason, we can achieve that by using a specially shaped pipe. Which of the pipes shown at the right would have equal pressure at the two points? w #7 7 ("(1) [2in L W15) 94.!) ("(1) 6(2) c—o) 4—0) i&ZM%M{ gamellr‘aoufi’xf” Problem 4: Waves on a pond (20 points) A cylindrical cork of mass M, density pc’ height H and radius R is floating upright in the center of a pond. It bobs up and down with a period T, which causes waves to spread out in a circle from the cork. The speed of waves on the surface of the water is v5. ignore any energy loses, etc; this is a simple, perfect pond. a) What is the wavelength A of the resulting waves? b) Assume the waves have amplitude A at some distance d from the cork. Use energy conservation to figure out what their amplitude is at a distance 4d from the cork. c) Now assume that there are two corks, exactly 2 wavelengths apart. Make a series of sketches that shows how the water between the two corks moves. d) In terms of the other variables in the first paragraph (Le. do not use A. or A), what is the period T of the bobbing motion? )WAM Wtaflwgfi? wit”- 4a) 6M“: MICE W47, WM gwmgc J- ami/#5 mag Ufa/o MW/eT/Z-v m: _—_.____I-‘ W W fun-«refit: / Problem 5: Cooling a burn (15 points) While cooking, you accidentally hold your hand over a pot of boiling water, and m5 = 18 grams of steam condenses on your hand.‘ (Note thatl would like you to do each part of this problem symbolically, putting in numbers only at the end; you need to insert the numbers, but you need not do the arithmetic) a) How much thermal energy Q was deposited in your hand? b) You want to put ice at DC on your hand to cool it back down. What is the mass mi of ice needed to exactly remove Q? If needed, you can consider your hand to be at Tb = 37C. 0) To try to understand the magnitudes here, let’s think about how big Q really is. If instead of transferring that much energy to your hand thermally, we did it by dropping a 2kg brick on your hand, from What height would we need to drop it? (Yes, this is why a steam burn hurts) Hi E ““3. VJ us] via .1- ‘9 3.x“ Problem 6: Different ways to expand (20 points) Consider an ideal gas at initial conditions N, V0, PD,T0. We want to think about two different ways to expand it to a larger volume V): A) Adiabatically B) Isothermally a) On 3 PV plot, show how both of these go, clearly labeling which curve is which process. b) Which process ends up at the lower temperature? Why? 0) During that expansion, which process does the greater amount of work on the outside world? Why? d) During that expansion, which process(es) leave the entropy of the gas unchanged? Why? Which leave the entropy of the rest of the universe unchanged? Why? ...
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