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Unformatted text preview: Problem #1: A set of glass connected glass tubes contain water, cooking oil (which is less
dense than water) and air, arranged as shown below. Six different points in the
system are labeled A through F. You may assume the air has essentially zero density compared to the two liquids. Rank the six points according to the pressure of the fluid at each point, from highest
pressure to lowest pressure. Jr,
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,___._ﬁ* Fﬁ‘ﬁ Problem #2: TruelFalse
Mark each statement as true or false. it a staement is taise. then correct it, by adding, deieting, or changing a few words,
so that it becomes true. Email'1‘ tr eutr?7
1) In an ideal gas, the average‘epeﬁd of a mo ecule depends on the temperature,
but not on the molecular weight. 124'” 'Fhr 1:55 ‘H’W'ﬁ
2) There are My one mole of people living on the Earth right now. £4 (pf Questions 3—6 refer to the toiiowing diagram, showing a nonviscous,
incompressibie ﬂuid moving through a giass tube: ———:7 ' H7 “’7
——9
E A "‘ 3 7
gkt’w 66w a 2‘5"” a ire*7
re H7 «a j i
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hint, 3) The fluid at point B is moving three times faster than the fluid at point A. ﬁrst“ time
4) The pressure at point B is Mr than the pressure at point A. we {Qatari +0
5) The pressure at point C is When the pressure at point A. {slug 6) if the fluid had nonnegligible viscosity, then the pressure at point A would be be
Ibmer than the pressure at point 0. “gift”
Mu, Problem #3: Sanity Check As always on sanity check problems, do not try to solve this problem directly
(unless you want to try for extra credit at the end.) Instead, think about the physical
situation, examine the six equations given as possible answers, and try to reason
out why at least five of the equations are impossible or physically absurd. The problem: A large concrete—walled aquarium has a triangular plexiglass viewing window in it.
The top vertex of the triangle is right at water level as shown below; the height of
the window is h, and the width of its base is w. Assume that the pressure of the air at the water's surface and the pressure of the air on the outside of the window are both Farm. Wmtl‘ff’; (baa+7 :3, f) . ' W:
a) What units should the answer have? New—l?”  £3.1— Q Which eguation(s), if any, does this eliminate? ' whlcln 157,»,
a] ( b) lithe width wof the triangular window were increased, while its height it
remained the same, how should the force change? (Should it increase, decrease,
or stay the same?) “9 Nancyragga I: Ska“ Nrvi‘iate't‘ltiS—é’ Which equationis), if any, does this eliminate? Briefly justify your answer. "Tints New} as W?) FL c) if the height h of the window were increased, with its width w remained
unchanged, how should the force change? as L “:hcrmseg P 5”?“er lawagi Which equation(s), if any, close this eliminate? Brieny justify your answer. i if MA Lemmge LE h“? ({QhamlnalLof,
waskt F¢r d) If you still have two or more equations remaining, see if you can find a logical
flaw in at least one of them. Explain why this equation(s) cannot be the correct
answer. FEW on 1’}; whch Muﬁ— on 'l": Wain? cgnsﬂ] F iiiwt! To (harvest been £9 M4 36, waits. a Janie
amok variable ﬂoat! Mama“ I" W” W 71¢ 43m 014’ on in i—‘orJM, $941M“ Wagons: “(9W L [cacti "to lager average
weirv 3mm»: anti alga n larsrr’ winclut/ arm JPar +13 WNHerO J Pure» an. 50 ‘}wu Pact0r; o? k “ink 9"“93} ELL/7‘ is La‘Hff 4Mn 41:6: e) Which equation(s), it any, might be the correct answer to this problem? 9 Extra Credit: Derive the answer to this probiem “for rest”, from first principies. (Try using iogic
simiiar to the same o'am probiem from your homework, with a few important detaiis
changed.) Does your answer match the equation(s), ii any, that you seiected in part (e)? Probtem #4:
A spring of spring constant it = 5000 Him is attached to the bottom of a tank
containing an unknown liquid (not water). A wooden cube, with density ’53,: 400 kgi'rn3 and length L = 0.5 m on each side,is
attached to the spring. As a result, the spring stretches a distance 2 = 0.4 meters as
shown below. Eczmitxﬁrhml a) Calculate the weight of the wooden cube b} Calculate the buoyant force which the liquid exerts on the cube. (Remember:
the iiguid is not water, and you do not yet know its density.) WM; “it”; ’th “that Fb: V3, we Jon/’4 79+ knits/:1”
g0 Winstam! WE CL’Ji«Gt Ldajanf gfw ,Fram Aéwrfomr; quy'.
.', : ma 9:; . , 4‘ F H L3 H kii‘: O
film]; F it : kl} [Lfi‘lﬁ c) Calculate the density of the liquid}, PH in NW Mfr“; Cﬁtkﬁuhiﬁié Ft?! Mcqﬂ Raﬁ; PM”? III.
— d) If the cube were cut loose from the spring and allowed to float on the surface of
the liquid, what fraction of the cube's volume would be above the surface? Ft Problem #5: A sealed box of dimensions 2 meters by 3 meters by 5 meters is filled with an
unknown monatornic ideal gas. The temperature of the gas T: 2? degrees
Celsius, and its pressure P is one atmosphere, the same as the air outside the box. a) How many atoms does the box contains? (You may either give the actual
number of atoms, which is probably ver  or the number of moles of atoms.) ﬁO‘E‘ot‘l'omy ti 0% WIPE,
PVT “kgif VVJ hlZT
M: BL n, fl , timquﬂgowa ' 1:31”
._, [toome PQBO mt : Um , 1,5131 in? {250 moles ‘ b)
(You mayr answer either in kg or in atom mass units, whichever is more
convenient.) (Extra Credit: what eiement is this gas on e of?) 'W’tﬁtgg 0’6; Gin at"ch a ‘3
Wink“? ' There is a window in the side of the box, of dimensions x = 20 om by y: 50 em.
The manufacturer has warned you that it the net force (inward or outward) on the
window ever exceeds F =20,0DU Newtons, then the window wilt break. ‘S‘L‘JW ii l/ lwindwaren/A:X_kjf 0:2[M1 o) What is the highest pressure Pmax that the gas inside the box could have,
before the window breaks? d} if you increase the temperature 0 t e gas inside the box, white the air outside the box remains unchanged, what is the highest temperature Tmax that the gas can reach before the window breaks? You may answer in either Kelvin or Celsius,
whichever you find more convenient. 6i,“ w'ny: [Di/“Fork WYHJOW} M “Ix/big Extra credit: if instead of heating the gas, you oooi it to absoiute zero temperature,
wiii the window break? Why or why not? ...
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 Winter '08
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