PHYSICS 231 Lecture 21 Buoyancy and Fluid Motion PHY 231 1 Review Solids FL0 F A Y L L0 A L Young s modulus F A Fh Shear modulus S x h A x F A P Bulk modulus B V V0 Also fluids V V 0 P pressure General M V kg m3 P F A N m2 Pa Fpressure difference pressure difference P A PHY 231 density pressure 2 quiz extra credit A block of mass M is lying on the floor The contact surface between the block and the floor is A A second block of mass 2M but with a contact surface of only 0 25A is also placed on the floor What is the ratio of the pressure exerted on the floor by block 1 to the pressure exerted on the floor by block 2 I e P1 P2 a b c d e 1 8 1 2 P1 F1 A1 Mg A P2 F2 A2 2Mg 0 25A 8Mg A P1 P2 Mg A 8Mg A 1 8 Mg A 8Mg A 1 8 PHY 231 3 Pascal s principle Pascal s principle a change in pressure applied t a fl to fluid id th thatt iis enclosed l d is i ttransmitted itt d tto th the whole h l fluid and all the walls of the container that hold the fluid HOLDS FOR A FLUID FULLY ENCLOSED ONLY PHY 231 4 Pascal s principle In other words then before a change in pressure applied to a fluid that is enclosed in transmitted to the whole fluid and all the walls of the container that hold the fluid fluid P F1 A1 F2 A2 If A2 A A1 then th F2 F1 So if we apply a small force F1 we can exert a very large Force F2 Hydraulic press demo PHY 231 5 Pressure vs Depth Horizontal direction P1 F1 A P2 F2 A F1 F2 no net force So P1 P2 Vertical direction Ftop PatmA Fbottom P PbottomA Mg P A M PbottomA gAh A Ah Since the column of water is not moving g Ftop Fbottom 0 PatmA PbottomA gAh Pbottom Patm b tt P t gh PHY 231 6 Pressure and Depth Pdepth h Pdepth 0 gh P0 h Where Pdepth h the p pressure at depth p h Pdepth 0 the pressure at depth 0 density of the liquid g 9 81 m s2 g 9 81 h depth P Pdepth 0 Patmospheric 1 013x10 1 013x105 Pa 1 atm 760 Torr From Pascal s principle If P0 changes then the pressures att all ll depths d th changes h with ith the th same value l PHY 231 7 A submarine A submarine is built in such a way that it can stand pressures of up to 3x106 Pa approx 30 times the atmospheric pressure How H d deep can it go Pdepth h Pdepth 0 g gh 3E 06 1 0E 05 1 0E 03 9 81 h h 296 m PHY 231 8 Does the shape of the container matter NO PHY 231 9 Pressure measurement The open tube manometer The pressure at A and B is the same P P0 gh so h P P h P P0 g If the pressure P 1 01 atm what i h the is h liquid li id iis water h 1 01 1 1 0E 05 1 0E 03 9 81 0 1 m PHY 231 10 Pressure Measurement the mercury barometer P0 mercuryygh mercuryy 13 6E 03 kg m3 mercury specific 13 6 PHY 231 11 Pressures at same heights are the same P0 P0 h P P0 gh P P h h h P P0 gh P P h P P0 gh PHY 231 12 P0 htop hbottom b Buoyant force B Ptop P0 wghtop Pbottom P0 wghbottom p wg htop h hbottom F A F B wg h wg hA g hA wgV wgV Mwaterg w Mobjg If the object is not moving B w B w so so wgV gV M Mobjg Archimedes 287 BC principle the magnitude of the buoyant f force is equall to the h weight h of f the h fluid fl d displaced d l d by the h object PHY 231 13 Archimedes ss Principle Archimedes THE MAGNITUDE OF THE BUOYANT FORCE IS THE WEIGTH OF THE FLUID DISPLACED BY THE OBJECT It is true whether the object is completely or partially submerged in the fluid PHY 231 14 Comparing densities B fluidgV Buoyant force w Mobjectg objectgV Stationary B w object fluid If object fluid the object goes down i k sink If object fluid the object j g goes up p float When the object sinks sinks the bottom of container provides an upward normal force N so that w B N PHY 231 15 Buoyant force For floating object object fluid Vdisplaced Mobject water Mobject objectVobject For submerged object object orr fluid Vdisplaced Vobject Vobject Mobject object PHY 231 16 A floating object A B w h w Mobjectg objectVobjectg B weight of the fluid displaced by the object Mwater displaced t di l dg waterVdisplacedg waterhAg h h height i ht of f th the object bj t under d water t The object is floating so there is no net force B w objectVobject waterVdisplaced h objectVobject waterA only y useable if part p of the object j is above the water PHY 231 17 A N An example B N 7 kg iron sphere of the same dimension as in A 1 kg of water inside thin hollow sphere Two weights h of f equall size and d shape h but b different d ff mass are submerged in water What are the weights read out B waterVdisplacedg w B w sphereVsphereg A B waterVsphereg w waterVsphereg so B w and 0 N is read out T w B 6 1 9 8 T w B 6 1 9 8 B B waterVsphereg Mwater sphereg g w ironVsphereg Miron sphereg 7Mwater sphereg 58 8 N 18 PHY 231 N Quiz A hollow sphere with negligible weight if not filled is filled with water and hung from a scale scale The weight is 10 N N It is then submerged What is the weight read from the scale 10N of water inside thin hollow sphere a b c d e 0N 5N 10 N 20 N impossible to tell PHY 231 19 question Imagine holding two bricks under water brick water Brick A is just beneath the surface of the water Brick B is i at a greater depth d h The Th force f needed d d to hold h ld brick b i k B in place is a larger g b the same as c smaller than the force required to hold brick A in place place Grav force is the same on both Buoyant force B weight of water displaced by brick Also same for both PHY 231 20 quiz extra credit A block of weight w is placed in water and found to stay submerged as shown i th in the picture i t The Th …
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