1. Chapter 11 Equilibrium and Elasticity

2. Equilibrium

3. Two Conditions for Equilibrium To motivate these, recall:

4. Defining Equilibrium Equilibrium = no net external force or torque = no change in translation or rotation) your text says L=0; others allow nonzero L:

5. Defining Static Equilibrium ‘Static’ Equilibrium = the special case of no translation or rotation at all

6. Two Conditions for Equilibrium When applying these, we must consider all external forces But the gravitational force is rather subtle

7. Center of Gravity (cg) Gravity acts at every point of a body Let  = the torque on a body due to gravity Can find  by treating the body as a single particle (the ‘cg’)

8. Center of Mass (cm) it can be shown: if g = constant everywhere, then: center of gravity = center of mass

9. Using the Center of Gravity Pressent some more explanatory notes

10. Solving Equilibrium Problems

11. Two Conditions for Equilibrium From now on, in this chapter/lecture: center of mass = center of gravity ‘equilibrium’ means ‘static equilibrium’ write:  F and  for  F ext and  ext

12. First Condition for Equilibrium

13. Second Condition for Equilibrium

14. Exercise 11-11 Work through Exercise 11-11

15. Exercise 11-14 Work through Exercise 11-14

16. A different version of Example 11-3 The ‘Leaning Ladder’ Problem Work through the variation the the text’s leaning ladder problem

17. Problem 11-62 ‘Wheel on the Curb’ Problem Work through Problem 11-62

18. Elasticity

19. Real bodies are not perfectly rigid They deform when forces are applied Elastic deformation: body returns to its original shape after the applied forces are removed

20. Stress and Strain stress: describes the applied forces strain: describes the resulting deformation Hooke’s Law: stress = modulus × strain modulus: property of material under stress (large modulus means small deformation)

21. Hooke’s Law and Beyond O to a : small stress, strain Hooke’s Law: stress=modulus×strain a < b : stress and strain are no longer proportional

22. Units stress = modulus × strain stress (‘applied force’): pascal= Pa=N/m 2 strain (‘deformation’): dimensionless modulus: same unit as stress

23. Types of Stress and Strain Applied forces are perpendicular to surface: tensile stress bulk (volume) stress Applied forces are parallel to surface: shear stress

24. Tensile Stress and Strain tensile stress = F/A tensile strain =  l/l 0 Young’s modulus = Y

25. Tensile Stress and Strain Work through Exercise 11-22

26. Compression vs. Tension tension (shown): pull on object compression: push on object (reverse direction of F shown at left) Y compressive = Y tensile Work through Exercise 11-26

27. Tension and Compression at once

28. Bulk Stress and Strain pressure: p=F/A bulk stress =  p bulk strain =  V/V 0 bulk modulus = B

29. Bulk Stress and Strain B > 0 negative sign above:  p and  V have opposite signs Work through Exercise 11-30

30. Shear Stress and Strain

31. shear stress = F 7 /A shear strain = x/h = tan  shear modulus = S

32. Shear Stress and Strain Do Exercise 11-32

33. Regimes of Deformation O to a : (small stress, strain) stress=modulus×strain elastic, reversible a < b : elastic, reversible but stress and strain not proportional

34. Regimes of Deformation From point O to b : elastic, reversible from point b to d: plastic, irreversible ductile materials have long c–d curves brittle materials have short c–d curves

35. Demonstation Tensile Strength and Fracture