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PHYSICS 231 Lecture 20: material science and pressure gas liquid solid Remco Zegers Walk-in hour: Tue 4-5 pm Helproom 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 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) the 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 to flow easy to easy to compress compress easy to flow easy to flow not charged not charged not charged charged PHY 231 3 Phase transformations PHY 231 4 solids amorphous 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 different types of deformations) PHY 231 6 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 AL 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 kg. He chooses concrete for the material of the pillar (Y=1.0E+10 Pa). How much does the pillar compress? M statueg /(R F/A Y L / L0 L / L0 2 pillar ) R=0.5 m L0=5m Y=1.0E+10 Pa M=1.0E+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. 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 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 Ax 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 / 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) 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 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 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 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 20 Magdeburg’s hemispheres Otto von Guericke (Mayor of Magdeburg, 17th century) PHY 231 21