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Unformatted text preview: HW15.1 Due: 11:00pm on Friday, October 1, 2010 Note: To understand how points are awarded, read your instructor's Grading Policy . [ Switch to Standard Assignment View] Relating Pressure and Height in a Container Learning Goal: To understand the derivation of the law relating height and pressure in a container. In this problem, you will derive the law relating pressure to height in a container by analyzing a particular system. A container of uniform crosssectional area is filled with liquid of uniform density . Consider a thin horizontal layer of liquid (thickness ) at a height as measured from the bottom of the container. Let the pressure exerted upward on the bottom of the layer be and the pressure exerted downward on the top be . Assume throughout the problem that the system is in equilibrium (the container has not been recently shaken or moved, etc.). Part A What is , the magnitude of the force exerted upward on the bottom of the liquid? Hint A.1 Formula for the force Hint not displayed ANSWER: = Correct Part B What is , the magnitude of the force exerted downward on the top of the liquid? Hint B.1 Formula for the force Hint not displayed ANSWER: [ Print ] ANSWER: = Correct Part C What is the weight of the thin layer of liquid? Hint C.1 How to approach the problem The weight of the layer is given by the formula , where is the mass of the layer and is the magnitude of the acceleration due to gravity. Hint C.2 Mass of the layer Use the definition of density to write the mass of the layer of liquid in terms of its density and its volume (express volume in terms of physical dimensions given in the problem introduction). Hint C.2.1 Definition of density The density of an object is equal to its mass divided by its volume. Hint C.2.2 Volume of the layer What is the volume of the thin layer of liquid? Express your answer in terms of quantities given in the problem introduction. ANSWER: = Correct Express your answer in terms of quantities given in the problem introduction. ANSWER: = Correct Express your answer in terms of quantities given in the problem introduction and , the magnitude of the acceleration due to gravity. ANSWER: = Correct Part D Since the liquid is in equilibrium, the net force on the thin layer of liquid is zero. Complete the force equation for the sum of the vertical forces acting on the liquid layer described in the problem introduction. Hint D.1 How to approach the problem ANSWER: = Correct Part C What is the weight of the thin layer of liquid? Hint C.1 How to approach the problem The weight of the layer is given by the formula , where is the mass of the layer and is the magnitude of the acceleration due to gravity. Hint C.2 Mass of the layer Use the definition of density to write the mass of the layer of liquid in terms of its density and its volume (express volume in terms of physical dimensions given in the problem introduction)....
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 Fall '07
 Rainey
 Physics

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