PHYSICS 231 Solids Fluids Flow gas liquid solid Remco Zegers PHY 231 1 States of matter Solid Liquid Gas Plasma difficult to deform easy to deform easy to deform easy to deform difficult to compress difficult to compress easy to compress easy to compress difficult to flow easy to flow easy to flow easy to flow not charged not charged not charged charged PHY 231 2 Phase transformations PHY 231 3 solids amorphous ordered PHY 231 crystalline 4 The deformation of solids Strain Constant Stress Constant elastic modulus stress Stress Tells something about the force causing the deformation Force per unit area causing the deformation Strain Measure of the degree of deformation Measure of the amount of deformation For small stress strain and stress are linearly correlated inelastic regime breaking point elastic limit elastic regime The elastic modulus depends on Material that is deformed strain Type of deformation a different modulus is defined for different types of deformations 5 PHY 231 The Young s modulus tensile stress Y tensile strain 2 tensile stress F A N m Pascal Pa tensile strain L L 0 FL0 F A Y L L0 A L Beyond the elastic limit an object is permanently deformed it does not return to its original shape if the stress is removed PHY 231 6 example An architect wants to design a 5m high circular pillar with a radius of 0 5 m that holds a bronze statue that weighs 1 0E 04 kg He chooses concrete for the material of the pillar Y 1 0E 10 Pa How much does the pillar compress F A Y L L0 2 M statueg R pillar L L0 R 0 5 m L0 5m Y 1 0E 10 Pa M 1 0E 04 kg 5m L 6 2E 05 m PHY 231 7 Ultimate strength Ultimate strength maximum force per unit area a material can withstand before it breaks or fractures Different for compression and tension material Tensile strength N m2 Compressive strength N m2 Steel 5 0x108 5 5x108 Bone 1 2x108 1 5x108 Concrete 2x106 2x107 PHY 231 8 example A builder is stacking 1 m3 cubic concrete blocks Each blocks weighs 5E 03 kg The ultimate strength of concrete for compression is 2E 07 Pa How many blocks can he stack before the lowest block is crushed The force on the low end of the lowest block is F Nmblockg N total number of blocks mblock mass of one block g 9 81 m s2 Ultimate strength 2E 07 F A Nmblockg 1 N 408 blocks PHY 231 9 The Shear Modulus x shear stress S shear strain 2 shear stress F A N m Pascal Pa shear strain x h F A Fh S x h A x PHY 231 10 Moving earth crust 100 m 30 m A tectonic plate in the lower crust 100 m deep of the earth is shifted during an earthquake by 30m What is the shear stress involved if the upper layer of the earth does not move S 1 5E 10 Pa shear stress F A S shear strain x h F A 4 5E 09 Pa PHY 231 11 Bulk Modulus volume stress B volume strain volume stress F A N m 2 Pascal Pa volume strain V V 0 F A P B V V0 V V0 P pressure Compressibility 1 Bulk modulus PHY 231 12 example What force per unit area needs to be applied to compress 1 m3 water by 1 B 0 21E 10 Pa F A B V V0 V V0 0 01 so F A 2 1E 07 Pa PHY 231 13 Some elastic moduli material Young s Modulus N m2 Shear modulus N m2 Bulk Modulus N m2 Steel 20x1010 8 4x1010 16x1010 Bone 1 8x1010 8 0x1010 aluminum 7x1010 2 5x1010 7x1010 water 0 21x1010 PHY 231 14 Density density M V specific density 3 kg m specific material water 4 material density kg m3 water 1 00x103 oxygen 1 43 lead 11 3x103 PHY 231 o C 15 Pressure Pressure F A N m2 Pa Same Force different pressure PHY 231 16 example A nail is driven into a piece of wood with a force of 700N What is the pressure on the wood if Anail 1 mm2 A person weighing 700 N is lying on a bed of such nails his body covers 1000 nails What is the pressure exerted by each of the nails Pnail F Anail 700N 1E 06m2 7E 08 Pa Pperson F 1000Anail 700 1E 03 7E 05 Pa about 7 times the atmospheric pressure PHY 231 17 question A object with weight of W in N is resting on a table with k legs each having a contact surface a m2 with the floor The weight of the table is V in N The pressure P exerted by each of the legs on the floor is a b c d e W V a W a W V ka W ka W V g a with g 9 81 m s2 P F A F V W A ka PHY 231 18 Force and pressure Air P 1 0E 5 Pa A P 0 Vacuum F What is the force needed to move the lit Force due to pressure difference Fpressure PA If A 0 01 m2 about 10 by 10 cm then a force F 1 0E 5 0 01 1000N is needed to pull the lit Fpressure difference PA PHY 231 19 Magdeburg s hemispheres Otto von Guericke Mayor of Magdeburg 17th century PHY 231 20 Solids General Previously FL0 F A Young s modulus Y L L0 A L F A Fh Shear modulus S x h A x F A P Bulk modulus B V V0 V V0 Also fluids P pressure P F A N m2 Pa M V kg m3 Fpressure difference PA Pascal s principle a change in pressure applied to a fluid that is enclosed is transmitted to the whole fluid and all the walls of the container that hold the fluid 21 PHY 231 Pascal s principle Pascal s principle a change in pressure applied to a fluid that is enclosed is transmitted to the whole fluid and all the walls of the container that hold the fluid HOLDS FOR A FLUID FULLY ENCLOSED ONLY PHY 231 22 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 P F1 A1 F2 A2 If A2 A1 then F2 F1 So if we apply a small force F1 we can exert a very large Force F2 Hydraulic press demo PHY 231 23 Pressure Depth water F1 surface Mg F2 PatmA Horizontal direction P1 F1 A P2 F2 A F1 F2 no net force So P1 P2 atm atmospheric A surface area M mass Vertical direction Ftop PatmA Fbottom PbottomA Mg PbottomA gAh Since the column of water is not moving Ftop Fbottom 0 PatmA PbottomA gAh PbottomA Pbottom Patm gh 24 PHY 231 Pressure and Depth Pdepth h Pdepth …
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