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

2. 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: 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

3. PHY 231 3 States of matter

4. PHY 231 4 Phase transformations

5. PHY 231 5 solids amorphous ordered crystalline

6. 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)

7. 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).

8. PHY 231 8 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 R=0.5 m L 0 =5m Y=1.0E+10 Pa M=1.0E+04 kg  L=6.2E-05 m

9. PHY 231 9 question Given: A rod with a cross section A of 1 cm 2 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 cm 2 a force of 2000 N is applied, it will stretch by: a)1 mm b)2 mm c)4 mm d)8 mm Fx2, Ax2, L 0 x2 so  L must be twice larger to keep Y constant

10. 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.

11. PHY 231 11 example A builder is stacking 1 m 3 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=Nm block g. N: total number of blocks m block =mass of one block g=9.81 m/s 2 Ultimate strength: 2E+07=F/A =Nm block g/1 N=408 blocks.

12. PHY 231 12 The Shear Modulus xx

13. PHY 231 13 Moving earth crust 30 m 100 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) F/A=4.5E+09 Pa

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

15. PHY 231 15 example What force per unit area needs to be applied to compress 1 m 3 water by 1%? (B=0.21E+10 Pa)  V/V 0 =0.01 so,  F/A=2.1E+07 Pa !!!

16. PHY 231 16 Some typical elastic moduli

17. PHY 231 17 Density

18. PHY 231 18 Pressure Pressure=F/A (N/m 2 =Pa) Same Force, different pressure

19. 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 A nail =1 mm 2 ? 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? P nail =F/A nail =700N/1E-06m 2 =7E+08 Pa P person =F/(1000A nail )=700/1E-03= 7E+05 Pa (about 7 times the atmospheric pressure).

20. PHY 231 20 Force and pressure A P=0 Vacuum Air (P=1.0E+5 Pa) F Force due to pressure difference: F pressure =  PA If A=0.01 m 2 (about 10 by 10 cm) then a force F=(1.0E+5)*0.01=1000N is needed to pull the lit. What is the force needed to move the lit? F pressure-difference =  PA

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