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6b_sample_mt1

6b_sample_mt1 - Problem#1 A set of glass connected glass...

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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. -_--—_— Malai— gx-ﬁ‘a [0“9‘3+ Vega/25” @rt’ﬁﬁwﬂ, Problem #2: Truer’False lvlark each statement as true or false. if a staement is false, then correct it, by adding, deleting, or changing a few words, so that it becomes true. 1) In an ideal gas, the average speed of a molecule depends on the temperature, but not on the molecular weight. 2) There are approximately one mole of people living on the Earth right now. Questions 3—6 refer to the ioiiowing diagram, showing a non-viscous, inoompressibie ﬂuid moving through a glass tube: ____ a “"7 a . H7 ___7 , A ,1 i ‘ 8 "“7 “RD”! grow a 2‘?” a ..——-7 F7 3) The fluid at point B is moving three times faster than the fluid at point A. 4) The pressure at point B is higher than the pressure at point A. 5) The pressure at point C is higher than the pressure at point A. 6) It the fluid had non-negligible viscosity, then the pressure at point A would be be lower than the pressure at point C. 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 tpp 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 Parnr Wad-er”; Jaw-,3? 1;? [3 Which equation(s), if any, does this eliminate? b) If the width w of the triangular window were increased, while its height h remained the same, how should the force change? (Should it increase, decrease, or stay the same?) Which equation(s), if any, does this eliminate? Briefly justify your answer. c) if the height h of the window were increased, with its width w remained unchanged, how should the force change? Which equation(s), if any, does this eliminate? Briefly justify your answer. 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. e) Which equation(s), if any, might be the correct answer to this problem? Extra Credit: Derive the answer to this prohtem ”for rear", from first principies. ( Try using iogic simiiar to the dame {tam problem from your homework, with a few important detaits changed.) Does your answer match the equation(s), it any, that you seiected in part (9) ? Problem #4: A spring of spring constant k: 5000 Nim is attached to the bottom of a tank containing an unknown liquid (notwater). A wooden cube, with density #2,: 400 kgirn3 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. CMNE {Dc-HVQCLQ‘f +0 a) Calculate the weight of the wooden cube b) Calculate the buoyant force which the liquid exerts on the cube. (Remember: the iiquid is not water, and you do not yet know its density.) 0) Calculate the density of the liquid}. PH . d) lithe 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? Problem #5: A sealed box of dimensions 2 meters by 3 meters by 5 meters is filled with an unknown monatomic ideal gas. The temperature of the gas T: 27 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 very large, or the number of moles of atoms.) b) If the total mass of the gas in the box is 4.8 kg, what is the mass of each atom? (You may answer either in kg or in atom mass units, whichever is more ' convenient.) (Extra Credit: what eiement is this gas made of?) There is a window in the side of the box, of dimensions X = 20 cm by y: 50 cm. The manufacturer has warned you that if the net force (inward or outward) on the window ever exceeds F =20,00U Newtons, then the window will break. 3 winéw // c) What is the highest pressure Pmax that the gas inside the box could have, before the window breaks? d) If you increase the temperature of the gas inside the box, while the air outside the box remains unchanged what is the highest temperature Tina Xthat the gas can reach before the window breaks? You may answer in either Kelvin or Celsius whichever you find more convenient. Extra credit: if instead of heating the gas, you tree! it to absoiute zero temperature, wiii the wrhdow break? Why or why not? ...
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6b_sample_mt1 - Problem#1 A set of glass connected glass...

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