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PHYSICS 231 Lecture 20: material science and pressure

PHYSICS 231 Lecture 20: material science and pressure. liquid. solid. gas. Remco Zegers Walk-in hour: Tue 4-5 pm Helproom. 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

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PHYSICS 231 Lecture 20: material science and pressure

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  1. PHYSICS 231Lecture 20: material science and pressure liquid solid gas Remco Zegers Walk-in hour: Tue 4-5 pm Helproom PHY 231

  2. 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: • they will start to spin faster while she moves to the center • 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

  3. States of matter PHY 231

  4. Phase transformations PHY 231

  5. solids ordered crystalline amorphous PHY 231

  6. 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

  7. The Young’s modulus Beyond the elastic limit an object is permanently deformed (it does not return to its original shape if the stress is removed). PHY 231

  8. R=0.5 m L0=5m Y=1.0E+10 Pa M=1.0E+04 kg L=6.2E-05 m 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? 5m PHY 231

  9. Fx2, Ax2, L0x2 so L must be twice larger to keep Y constant question Given: • 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: • 1 mm • 2 mm • 4 mm • 8 mm PHY 231

  10. 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

  11. 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

  12. The Shear Modulus x PHY 231

  13. F/A=4.5E+09 Pa 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) PHY 231

  14. Bulk Modulus Compressibility: 1/(Bulk modulus) PHY 231

  15. V/V0=0.01 so, F/A=2.1E+07 Pa !!! example What force per unit area needs to be applied to compress 1 m3 water by 1%? (B=0.21E+10 Pa) PHY 231

  16. Some typical elastic moduli PHY 231

  17. Density PHY 231

  18. Pressure Pressure=F/A (N/m2=Pa) Same Force, different pressure PHY 231

  19. 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

  20. Force and pressure Air (P=1.0E+5 Pa) P=0 Vacuum A 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

  21. Magdeburg’s hemispheres Otto von Guericke (Mayor of Magdeburg, 17th century) PHY 231

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