PHYSICS 231 Lecture 20 material science and pressure gas liquid solid PHY 231 1 quiz A child runs toward a merry go round and jumps on the edge As a results the merry go round starts to spin Next she moves towards the center of the merry go round If no net torque is applied to the child or merry go round merry go round then then a they will start to spin faster while she moves to the center b the rotational velocity will not change while she moves to the center c they will start to spin less fast while she moves to the the center PHY 231 2 Solid States of matter Liquid Gas Plasma difficult to deform difficult to compress difficult to flow easy to deform easy to deform easy to deform difficult to compress easy y to flow easy to easy to compress compress easy y to flow easy y to flow not charged h d not charged h d not charged h d charged PHY 231 3 Phase transformations PHY 231 4 solids amorphous h ordered PHY 231 crystalline 5 The deformation of solids Stress Tells something about the force causing the deformation Strain Measure of the degree of deformation For small stress strain and stress are linearly correlated Strain Constant Stress Constant elastic modulus The elastic modulus depends on Material that is deformed Type of deformation a different modulus is defined for diff different t ttypes of fd deformations f ti PHY 231 6 The Young s modulus tensile stress Y tensile strain tensile stress F A N m 2 Pascal Pa tensile strain L L0 F L0 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 7 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 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 statue g R ppillar L L0 R 0 5 m L0 5m Y 1 R 0 5 Y 1 0E 10 0E 10 Pa M 1 M 1 0E 04 0E 04 kg 5m L 6 2E 05 m PHY 231 8 question F A Given Y L L0 A rod with a cross section A of 1 cm2 is stretched by 1 mm if a force of 1000 N is applied If on a rod of the same material but which is 2x loner and has a cross section of 2 cm2 a force of 2000 N is applied it will stretch by a b c d 1 mm 2 mm 4 mm 8 mm Fx2 Ax2 L0x2 so L must be twice larger to keep Y constant PHY 231 9 Ultimate strength Ultimate strength maximum force per unit area a material can withstand before it breaks or fractures Different for compression and tension PHY 231 10 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 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 f one block bl k g 9 81 m s2 Ultimate strength g 2E 07 F A Nmblockg 1 N 408 blocks PHY 231 11 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 12 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 13 Bulk Modulus volume stress B volume strain volume stress F A N m 2 Pascal Pa volume strain V V0 F A P B V V0 V V0 P pressure Compressibility 1 Bulk modulus PHY 231 14 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 V V0 V V0 0 01 so F A 2 1E 07 Pa PHY 231 15 Some typical elastic moduli PHY 231 16 Density M V 3 kg m specific material water 4 PHY 231 o C 17 Pressure Pressure F A N m2 Pa Pascal Same Force different pressure PHY 231 18 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 i hi 700 N iis llying i on a bed b d of f such h nails his body covers 1000 nails What is the pressure exerted by y each of the nails Pnail F Anail 700N 1E 06m2 7E 08 Pa Pperson F 1000A F 1000Anail 700 1E 03 700 1E 03 7E 05 Pa about 7 times the atmospheric p pressure PHY 231 19 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 p 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 lit Fpressure pressure difference difference PA PHY 231 20
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