Flashcards — Chapter 12 🃏

Static Equilibrium and Elasticity — forces and torques in balance, materials under stress! 🏗️

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📋 Card sets: key terms and formulas

Section §12.1 — Equilibrium Conditions

1. Static equilibrium — state where an object is at rest; requires two conditions: ΣF = 0 and Στ = 0
2. Net force condition — ΣF = 0 (sum of all forces equals zero); no acceleration
3. Net torque condition — Στ = 0 (sum of all torques equals zero); no rotational acceleration
4. Translational equilibrium — no linear acceleration; achieved when ΣF = 0
5. Rotational equilibrium — no angular acceleration; achieved when Στ = 0
6. Center of mass — point where total mass is concentrated for translational motion
7. Center of gravity — point where gravitational force acts; same as center of mass in uniform field
8. Simultaneous equilibrium — both translational and rotational equilibrium at once

Section §12.2 — Solving Equilibrium Problems

9. Force diagram — drawing showing all forces acting on an object; essential first step
10. Pivot point (torque reference) — arbitrary point chosen for summing torques; choose wisely to simplify calculations
11. Lever arm — perpendicular distance from pivot to line of force action
12. Torque balance — τ = r × F or τ = rF sin(θ) for single force; must sum to zero
13. Mechanical advantage — ratio of load to effort force; levers multiply force
14. Ideal pulley — massless, frictionless; tension same throughout rope
15. Inclined plane equilibrium — forces parallel and perpendicular to plane; component analysis crucial

Section §12.3 — Stability and Balance

16. Stable equilibrium — object at lowest potential energy; small perturbation → restoring force
17. Unstable equilibrium — object at highest potential energy; small perturbation → divergence
18. Neutral equilibrium — no change in potential energy with small displacement; no restoring force
19. Tipping condition — object tips when center of gravity moves outside base of support
20. Tipping angle — maximum angle of incline before object overturns; depends on geometry
21. Wide base is stable — wider base → larger restoring torque; harder to tip over
22. Pendulum analogy — hanging mass at lowest point is stable; any push → oscillates back

Section §12.4 — Stress and Strain

23. Stress — internal force per unit area; σ = F/A (Pa or N/m²)
24. Strain — fractional change in dimension; ε = ΔL/L₀ (dimensionless)
25. Tensile stress — pulling stress; material stretched along one axis
26. Tensile strain — fractional elongation; length increases under pulling stress
27. Compressive stress — pushing stress; material compressed along one axis
28. Compressive strain — fractional compression; length decreases under pushing
29. Shear stress — stress from sideways force; τ = F/A (force parallel to surface)
30. Shear strain — angular distortion; γ = Δx/h (change in angle, dimensionless)

Section §12.5 — Elastic Moduli

31. Young's modulus — E = (tensile stress) / (tensile strain) = σ / ε; measures resistance to length change
32. Units of Young's modulus — Pa (pascals) or GPa (gigapascals); steel ~200 GPa
33. Shear modulus (rigidity modulus) — G = (shear stress) / (shear strain) = τ / γ; measures resistance to shape change
34. Bulk modulus — K = (pressure) / (fractional volume change) = -P / (ΔV/V₀); resistance to compression
35. Hooke's law (for materials) — stress is proportional to strain (within elastic limit): σ = E·ε
36. Elastic limit — maximum stress before permanent deformation; material returns to original shape if below this
37. Elastic region — on stress-strain curve; linear relationship between stress and strain
38. Yield point — stress at which material begins permanent (plastic) deformation
39. Breaking point (ultimate strength) — stress at which material fractures and fails completely
40. Ductility — material's ability to deform plastically before breaking; high in copper, low in brittle materials

Section §12.6 — Deformation and Failure

41. Plastic deformation — permanent change in shape; material does not return to original form
42. Elastic deformation — temporary change; material returns when force is removed
43. Stress concentration — stress is higher near notches, cracks, or sharp corners
44. Safety factor — design margin; actual stress << yield stress; typically 2–5× for structures
45. Brittle materials — break with little plastic deformation (glass, ceramics); opposite of ductile
46. Ductile materials — exhibit large plastic deformation before breaking (metals like copper, aluminum)

Section §12.7 — Applications

47. Cantilever beam — beam fixed at one end, free at the other; deflects under load
48. Simply supported beam — beam resting on two supports; bends under distributed load
49. Thermal stress — stress due to temperature change; different materials expand differently
50. Column buckling — long, slender column under compression; fails by buckling, not crushing
51. Torsion — twisting deformation; related to shear modulus
52. Poisson's ratio — when material is stretched, it gets slightly thinner; dimensionless, ~0.3 for most metals

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📊 Topics covered

• Equilibrium conditions — force and torque balance
• Problem-solving strategies — free-body diagrams, pivot selection, simultaneous equations
• Stability types — stable, unstable, neutral
• Stress and strain — definitions and three types
• Elastic moduli — Young's, shear, bulk; Hooke's law
• Material properties — elastic vs. plastic, ductility, breaking strength
• Practical applications — beams, columns, safety design

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What comes next:

👉 §12.1–§12.3 — worked problems (step-by-step examples)
👉 §12.4–§12.5 — practice problems (exercises)
👉 §12.6–§12.8 — Q&A (answers to common misconceptions)

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