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Mastering Physics 2

Mastering Physics 2 - Course PHYSICS260 Assignment 2 Due...

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Course PHYSICS260 Assignment 2 Due at 11:00pm on Wednesday, February 13, 2008 Relating Pressure and Height in a Container Description: Walks the student through a derivation of the law relating height and pressure in a container by analyzing the forces on a thin layer of fluid. 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 cross-sectional 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 Force is equal to pressure times area. ANSWER: =

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Part B What is , the magnitude of the force exerted downward on the top of the liquid? Hint B.1 Formula for the force Force is equal to pressure times area. ANSWER: = 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. Part 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.a Definition of density The density of an object is equal to its mass divided by its volume. Part C.2.b 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: Express your answer in terms of quantities given in the problem introduction. ANSWER: = Express your answer in terms of quantities given in the problem introduction and , the magnitude of the acceleration due to gravity. ANSWER: = 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 If you have completed the previous parts, you have already done most of the work needed to answer this part. Just add together the forces that you found in the previous three parts. All three of the forces act along the y axis; some are directed
upward, and others are directed downward. Those that act downward should appear

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Mastering Physics 2 - Course PHYSICS260 Assignment 2 Due...

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