UT Arlington PHYS 1441  Lecture Notes (13 pages)
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 Phys 1441  General College Physics I
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PHYS 1441 Section 002 Lecture 24 Wednesday Dec 8 2010 Dr 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 Principle Wednesday Dec 8 2010 PHYS 1441 002 Fall 2010 Dr Jaehoon Yu 1 Announcements 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 sheet Wednesday Dec 8 2010 PHYS 1441 002 Fall 2010 Dr Jaehoon Yu 2 Young s Modulus Let s consider a long bar with cross sectional area A and initial length Li Li Fex After the stretch A cross sectional area F Tensile Stress ex A Tensile stress Young s Modulus is defined as Y Lf Li L Fin Fex Fin Tensile strain Tensile Strain F ex Tensile Stress A Tensile Strain L L Fex L Li Used to characterize a rod or wire stressed under tension or compression i What is the unit of Young s Modulus Experimental Observations 1 2 Force per unit area For a fixed external force the change in length is proportional to the original length The necessary force to produce the given strain is proportional to the cross sectional area Elastic limit Maximum stress that can be applied to the substance before becomes permanently Wednesday Dec 8 it 2010 PHYS 1441 002 deformed Fall 2010 Dr Jaehoon Yu 3 Bulk Modulus F Bulk Modulus characterizes the response of a substance to uniform squeezing or reduction of pressure V After the pressure change F V F F Normal Force F Volume stress Pressure Surface Area the force applies A pressure If the pressure on an object changes by P F A the object will undergo a volume change V F Bulk Modulus is defined as Because the change of volume is reverse to change of pressure Wednesday Dec 8 2010 P Volume Stress A B V V Volume Strain Vi Vi Compressibility is the reciprocal of Bulk Modulus PHYS 1441 002 Fall 2010 Dr Jaehoon Yu 4 Example for Solid s Elastic Property A 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 m2 Since bulk modulus is P B V Vi The amount of volume change is The pressure change P is PVi V B P Pf Pi 2 0 107 1 0 105 2 0 107 Therefore the resulting 2 0 107 0 5 4 3 V V V 1 6 10 m f i volume change V is 6 1 1010 The volume has decreased Wednesday Dec 8 2010 PHYS 1441 002 Fall 2010 Dr Jaehoon Yu 5 Density and Specific Gravity Density rho of an object is defined as mass per unit volume M r V 3 kg m Unit 3 Dimension ML Specific Gravity of a substance is defined as the ratio of the density of the substance to that of water at 4 0 oC H2O 1 00g cm3 r substance SG r H 2O What do you think would happen of a substance in the water dependent on SG Wednesday Dec 8 2010 Unit None Dimension None SG 1 Sink in the water SG 1 Float on the surface PHYS 1441 002 Fall 2010 Dr Jaehoon Yu 6 Fluid and Pressure What are the three states of matter Solid Liquid and Gas Using the time it takes for the particular substance How do you distinguish them to change its shape in reaction to external forces A collection of molecules that are randomly arranged and loosely What is a fluid 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 Fluid 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 This force by the fluid on an object usually is expressed in the form of P F A the force per unit area at the given depth the pressure defined as F Note that pressure is a scalar quantity because it s Expression of pressure for an P infinitesimal area A by the force F is A the magnitude of the force on a surface area A What is the unit and the dimension of pressure Wednesday Dec 8 2010 Unit N m2 Dim M L 1 T 2 Special SI unit for pressure is Pascal PHYS 1441 002 Fall 2010 Dr Jaehoon Yu 1Pa 1N m 7 2 Example for Pressure The 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 m W VM 1000 2 00 2 00 0 300 1 20 103 kg Therefore the weight of the water in the mattress is W mg 1 20 103 9 8 1 18 10 4 N b 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 Since the surface area of the mattress is 4 00 m2 the pressure exerted on the floor is Wednesday Dec 8 2010 F mg 1 18 10 4 3 2 95 10 P A A 4 00 PHYS 1441 002 Fall 2010 Dr Jaehoon Yu 8 Variation of Pressure and Depth Water pressure increases as a function of depth and the air pressure decreases as a function of altitude Why It 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 P0A Let s imagine the liquid contained in a cylinder with height h and the cross sectional area A immersed in a fluid of density at rest as shown in the figure and the system is in its equilibrium h Mg PA If the liquid in the cylinder is the same substance as the fluid the mass of the liquid in the cylinder is M V Ah Since the system is in its equilibrium Therefore we obtain P P0 gh Atmospheric pressure P0 is 1 00atm 1 013 105 Pa Wednesday Dec 8 2010 PA P0 A Mg PA P0 A Ahg 0 The pressure at the depth h below the surface of the fluid open to the atmosphere is greater than the atmospheric pressure by gh PHYS 1441 002 Fall 2010 …
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