PHYS 1441 – Section 002 Lecture #24AnnouncementsYoung’s ModulusBulk ModulusExample for Solid’s Elastic PropertyDensity and Specific GravityFluid and PressureExample for PressureVariation of Pressure and DepthAbsolute and Relative PressurePascal’s Principle and HydraulicsExample for Pascal’s PrincipleSlide 13Wednesday, Dec. 8, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu1PHYS 1441 – Section 002Lecture #24Wednesday, Dec. 8, 2010Dr. Jaehoon Yu•Elastic Properties of Solids•Density and Specific Gravity•Fluid and Pressure•Depth Dependence of Pressure•Absolute and Relative Pressure•Pascal’s Principle and Hydraulics•Buoyant Forces and Archimedes’ PrincipleAnnouncements•The Final Exam–Date and time: 11am – 1:30pm, Monday Dec. 13–Place: SH103–Comprehensive exam•Covers from CH1.1 – CH10.7•Plus appendices A.1 – A.8•Combination of multiple choice and free response problems •Submit your Planetarium extra credit sheetWednesday, Dec. 8, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu2Wednesday, Dec. 8, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu3Young’s ModulusAFexStress TensileLet’s consider a long bar with cross sectional area A and initial length Li. Fex=FinYoung’s Modulus is defined asWhat is the unit of Young’s Modulus?Experimental Observations1. For a fixed external force, the change in length is proportional to the original length2. The necessary force to produce the given strain is proportional to the cross sectional areaLiA:cross sectional areaTensile stressLf=Li+LFexAfter the stretchFexFinTensile strainiLLStrain TensileYForce per unit areaUsed to characterize a rod or wire stressed under tension or compressionElastic limit: Maximum stress that can be applied to the substance before it becomes permanently deformedStrain TensileStress TensileiexLLAFWednesday, Dec. 8, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu4Strain VolumeStress VolumeB iVVAFiVVPBulk ModulusAFapplies force theArea SurfaceForce NormalPressureBulk Modulus characterizes the response of a substance to uniform squeezing or reduction of pressure.Bulk Modulus is defined asVolume stress =pressureAfter the pressure changeIf the pressure on an object changes by ΔP=ΔF/A, the object will undergo a volume change ΔV.VV’FFFFCompressibility is the reciprocal of Bulk Modulus Because the change of volume is reverse to change of pressure.Wednesday, Dec. 8, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu5Example for Solid’s Elastic PropertyA solid brass sphere is initially under normal atmospheric pressure of 1.0x105N/m2. The sphere is lowered into the ocean to a depth at which the pressures is 2.0x107N/m2. The volume of the sphere in air is 0.5m3. By how much its volume change once the sphere is submerged? The bulk modulus of brass is 6.1x1010 N/m2The pressure change ΔP isSince bulk modulus isiVVPBThe amount of volume change isBiPVV757100.2100.1100.2 ifPPPTherefore the resulting volume change ΔV is34107106.1106.15.0100.2mVVVifThe volume has decreased.Wednesday, Dec. 8, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu6Density and Specific GravityDensity,ρ(rho), of an object is defined as mass per unit volume r �Unit? Dimension? 3/ mkg][3MLSpecific Gravity of a substance is defined as the ratio of the density of the substance to that of water at 4.0 oC (ρH2O=1.00g/cm3).SG �Unit? Dimension? None None What do you think would happen of a substance in the water dependent on SG?1SG1SGSink in the waterFloat on the surface2substanceH OrrM VWednesday, Dec. 8, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu7Fluid 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 force perpendicular to the surface of the object.AFP How do you distinguish them?Using the time it takes for the 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 an external container.We will first learn about mechanics of fluid at rest, fluid statics. In what ways 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 per 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 the dimension of pressure?Expression of pressure for an infinitesimal area δA by the force δF is P =δFδAUnit:N/m2Dim.: [M][L-1][T-2]Special SI unit for pressure is Pascal2/11 mNPa Wednesday, Dec. 8, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu8Example for PressureThe mattress of a water bed is 2.00m long by 2.00m wide and 30.0cm deep. a) Find the weight of the water in the mattress. The volume density of water at the normal condition (0oC and 1 atm) is 1000kg/m3. So the total mass of the water in the mattress is Since the surface area of the mattress is 4.00 m2, the pressure exerted on the floor ismPTherefore the weight of the water in the mattress is Wb) Find the pressure exerted by the water on the floor when the bed rests in its normal position, assuming the entire lower surface of the mattress makes contact with the floor.MWVρkg31020.1300.000.200.21000 mgN431018.18.91020.1 AFAmg341095.200.41018.1Wednesday, Dec. 8, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu9Variation 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 imagine the liquid contained in a cylinder with height h and the cross sectional area A immersed in a fluid of density ρ at rest, as shown in the figure, and the system is in its equilibrium.The pressure at the depth h below the surface of the fluid open to the atmosphere is greater than the atmospheric pressure by ρgh.Therefore, we obtainAtmospheric pressure P0 isPaatm510013.100.1
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