PHYS 1443 – Section 003 Lecture #22AnnouncementsFluid and PressureVariation of Pressure and DepthPascal’s Law and HydraulicsAbsolute and Relative PressureBuoyant Forces and Archimedes’ PrincipleMore Archimedes’ PrincipleSlide 9Example 15.5Example 15.6Superposition and InterferenceSpeed of Waves on StringsSpeed of Waves on Strings cont’dExample 16.2Reflection and TransmissionSinusoidal WavesExample 16.3Sinusoidal Waves on StringsExample 16.4Rate of Energy Transfer by Sinusoidal Waves on StringsRate of Energy Transfer by Sinusoidal Waves cont’dExample 16.5Monday, Dec. 2, 2002 PHYS 1443-003, Fall 2002Dr. Jaehoon Yu1PHYS 1443 – Section 003Lecture #22Monday, Dec. 2, 2002Dr. Jaehoon Yu1. Absolute and Relative Pressure2. Buoyant Force and Archimedes’ Principle3. Traveling Waves: Superposition and Interference4. Speed of Waves on Strings5. Reflection and Transmission6. Sinusoidal WavesNo Homework Today!!Monday, Dec. 2, 2002 PHYS 1443-003, Fall 2002Dr. Jaehoon Yu2Announcements•Homework Due date extensions–Homework # 20: Due noon, tomorrow, Dec. 3–Homework # 21: Due 6pm, Friday, Dec. 6•Final Term Exam –Monday, Dec. 9, between 11:00am – 1:30pm for 1.5 hours–Covers chapters 11 – 15–Review Wednesday, Dec. 4Monday, Dec. 2, 2002 PHYS 1443-003, Fall 2002Dr. Jaehoon Yu3Fluid and PressureWhat are the three states of matter? Solid, Liquid, and GasFluid cannot exert shearing or tensile stress. Thus, the only force the fluid exerts on an object immersed in it is the forces perpendicular to the surfaces of the object.AFP How do you distinguish them?By the time it takes for a particular substance to change its shape in reaction to external forces.What is a fluid?A collection of molecules that are randomly arranged and loosely bound by forces between them or by the external container.We will first learn about mechanics of fluid at rest, fluid statics. In what way do you think fluid exerts stress on the object submerged in it?This force by the fluid on an object usually is expressed in the form of the force on a unit area at the given depth, the pressure, defined asNote that pressure is a scalar quantity because it’s the magnitude of the force on a surface area A.What is the unit and dimension of pressure?Expression of pressure for an infinitesimal area dA by the force dF isdAdFP Unit:N/m2Dim.: [M][L-1][T-2]Special SI unit for pressure is Pascal2/11 mNPa Monday, Dec. 2, 2002 PHYS 1443-003, Fall 2002Dr. Jaehoon Yu4Variation of Pressure and DepthWater pressure increases as a function of depth, and the air pressure decreases as a function of altitude. Why?If the liquid in the cylinder is the same substance as the fluid, the mass of the liquid in the cylinder is MgAPPA 0It seems that the pressure has a lot to do with the total mass of the fluid above the object that puts weight on the object.Let’s consider a liquid contained in a cylinder with height h and cross sectional area A immersed in a fluid of density at rest, as shown in the figure, and the system is in its equilibrium.The pressure at the depth h below the surface of a fluid open to the atmosphere is greater than atmospheric pressure by gh.Therefore, we obtainAtmospheric pressure P0 isPaatm510013.100.1 P0APAMghMSince the system is in its equilibriumPWhat else can you learn from this?VAhAhgAPPA00ghP0Monday, Dec. 2, 2002 PHYS 1443-003, Fall 2002Dr. Jaehoon Yu5Pascal’s Law and HydraulicsA change in the pressure applied to a fluid is transmitted undiminished to every point of the fluid and to the walls of the container.The resultant pressure P at any given depth h increases as much as the change in P0. This is the principle behind hydraulic pressure. How?Therefore, the resultant force F2 isWhat happens if P0is changed?2211AFAFP Since the pressure change caused by the the force F1 applied on to the area A1 is transmitted to the F2 on an area A2.ghPP0This seems to violate some kind of conservation law, doesn’t it?d1d2F1A1A2F21122FAAF In other words, the force get multiplied by the ratio of the areas A2/A1 is transmitted to the F2 on an area.No, the actual displaced volume of the fluid is the same. And the work done by the forces are still the same.1212FddF Monday, Dec. 2, 2002 PHYS 1443-003, Fall 2002Dr. Jaehoon Yu6Absolute and Relative PressureHow can one measure pressure?One can measure pressure using an open-tube manometer, where one end is connected to the system with unknown pressure P and the other open to air with pressure P0.This is called the absolute pressure, because it is the actual value of the system’s pressure.In many cases we measure pressure difference with respect to atmospheric pressure due to changes in P0 depending on the environment. This is called gauge or relative pressure.PThe common barometer which consists of a mercury column with one end closed at vacuum and the other open to the atmosphere was invented by Evangelista Torricelli.Since the closed end is at vacuum, it does not exert any force. 1 atm is0PThe measured pressure of the system ishPP00PP ghP0ghgh)7600.0)(/80665.9)(/10595.13(233msmmkgatmPa 110013.15Monday, Dec. 2, 2002 PHYS 1443-003, Fall 2002Dr. Jaehoon Yu7Buoyant Forces and Archimedes’ PrincipleWhy is it so hard to put a beach ball under water while a piece of small steel sinks in the water?The water exerts force on an object immersed in the water. This force is called Buoyant force.How does the Buoyant force work?Let‘s consider a cube whose height is h and is filled with fluid and at its equilibrium. Then the weight Mg is balanced by the buoyant force B.This is called, Archimedes’ principle. What does this mean?The magnitude of the buoyant force always equals the weight of the fluid in the volume displaced by the submerged object.BBMghAnd the pressure at the bottom of the cube is larger than the top by gh.PTherefore,Where Mg is the weight of the fluid.gFMgAB /ghB PAghAVgBgFVgMgMonday, Dec. 2, 2002 PHYS 1443-003, Fall 2002Dr. Jaehoon Yu8More Archimedes’ PrincipleLet’s consider buoyant forces in two special cases. Let’s consider an object of mass M, with density 0, is immersed in the fluid with density f .Case 1: Totally submerged objectThe total force applies to different directions, depending on the difference of the density between the object and the fluid.1. If
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