1. Contact forces

2. “If, in some cataclysm ( 大灾难 ), all of scientific knowledge were to be destroyed, and only one sentence passed on to the next generations of creatures, what statement would contain the most information in the fewest words?...” Richard Feynman (1918 – 1988) Nobel prize winner

3. “I believe it is the atomic hypothesis (or atomic fact, or whatever you wish to call it) that all things are made of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another.” Richard Feynman (1918 – 1988) Nobel prize winner Read: “Surely You’re Joking, Mr Feynman!”

4. A cubic lattice of balls and springs is a good model for solid matter.

7. Scanning tunneling microscope (STM) images of a silicon ( 硅 ) surface.

8. Tension force

9. We can model a wire as a chain of balls and springs.

10. Our goal: Work out the stiffness of the “spring” connecting two copper atoms.

11. Your turn… Approximately what is the radius of a copper ( 铜 ) atom? 1) 1 e-15 m 2) 1 e-12 m 3) 1 e-10 m 4) 1 e-8 m 5) 1 e-6 m

12. Your turn… How does the diameter of one atom in a solid compare to the length of an interatomic bond? 1) The bond length is greater than the atomic diameter 2) The bond length is less than the atomic diameter 3) They are the same

15. 1 mol ( 摩尔 ) of Cu is 64 g Density ( 密度 ) is 8.94 g/cm 3 What is the volume of one atom? Diameter of a Cu atom:

16. Stretched copper wire

18. You hang a 1 kg mass from a spring, which stretches 0.4 m. You link the spring end to end with another identical spring, and hang a 1 kg mass from the linked springs. How much does this longer spring stretch? 1) 0.16 m 2) 0.2 m 3) 0.4 m 4) 0.8 m Your turn…

20. A short spring has a stiffness of 20 N/m. You link 4 of these springs end to end to make a longer spring. What is the stiffness of the longer spring? 1) 0.2 N/m 2) 5 N/m 3) 20 N/m 4) 80 N/m

21. Your turn… You hang a 1 kg mass from a spring, which stretches 0.4 m. You place a second identical spring beside the first, so the 1 kg mass is now supported by two springs. How much does each spring stretch? 1) 0.2 m 2) 0.4 m 3) 0.5 m 4) 0.8 m

22. Your turn… A short spring has a stiffness of 20 N/m. You use 4 of these springs side by side to support a mass. What is the stiffness of the 4 side-by- side springs, considered as one effective spring? 1) 0.2 N/m 2) 5 N/m 3) 20 N/m 4) 80 N/m

23. Springs in series: less stiff.Springs in parallel: more stiff.

24. 10 kg 2 m Stretch: 1.51 mm 1 mm Stretched copper wire

25. Cross-sectional area 横截面 Solve for the stiffness of one bond…

26. For copper,

27. Normal force When something compresses the springs, they push back with enough force to balance the compressing force.

28. ‘Normal’ is another word for ‘perpendicular’ ( 垂直 ). The direction of the normal force is normal to the surface. Normal force

29. Friction 摩擦力 Friction is caused by interactions between the atoms in two surfaces trying to slide past each other.

30. -Static friction: when the two surfaces do not slide -Kinetic friction: when the two surfaces do slide These formulas are approximations – friction is really very complicated!

31. μ s and μ k are called the ‘coefficients of friction’.

32. Your turn… You push a 100 kg mass on the floor with a horizontal force of 400 N. It doesn’t move. The coefficient of static friction is 0.6. What is the magnitude of the frictional force on the block by the floor? 1) 980 N 2) 588 N 3) 400 N 4) Can’t tell

33. Your turn… You push an initially stationary 100 kg mass on the floor with a horizontal force. The coefficient of static friction is 0.6. What is the minimum amount of force you need to exert on the mass in order to get it to move? 1) 980 N 2) 588 N 3) 400 N 4) Can’t tell

34. I push a book against the wall with a force of 30 N. The mass of the book is 3 kg. The coefficient of static friction for the book and the wall is 0.6. Will the book slide? Example