Equilibrium, Elasticity & Material Properties Explained | Chapter 11 of University Physics

Chapter 11 examines how rigid bodies remain in balance under forces and how materials deform under stress. You’ll learn the conditions for static equilibrium, locate the center of gravity, construct free-body diagrams, and explore stress-strain behavior including Young’s, shear, and bulk moduli, as well as elastic versus plastic deformation.

Conditions for Rigid-Body Equilibrium

For a rigid body to be in equilibrium (static or dynamic), two requirements must hold:

• ΣF = 0 — No net external force (no translation)
• Στ = 0 — No net external torque about any axis (no rotation)

These ensure the object remains at rest or moves with constant velocity without spinning.

Center of Gravity & Stability

The center of gravity is the point where an object’s weight can be assumed to act. Under uniform gravity, it coincides with the center of mass. Locating this point is crucial when calculating torques and assessing whether an object will tip or remain stable.

Solving Equilibrium Problems

Use a systematic approach:

• Draw a detailed free-body diagram isolating the body.
• Identify all forces (weight, normal, tension, etc.) and their lines of action.
• Select a convenient pivot point—forces through the pivot produce zero torque.
• Apply ΣF = 0 and Στ = 0 to solve for unknown forces or angles.

Stress, Strain & Elastic Moduli

Stress (σ) is force per unit area (Pa), and strain (ε) is fractional deformation (unitless). In the elastic limit, Hooke’s Law holds:

σ = Y ε (stress ∝ strain)

Key Elastic Moduli

• Young’s Modulus (Y): Tensile/compressive stress over axial strain.
• Shear Modulus (S): Shear stress over angular deformation.
• Bulk Modulus (B): Volumetric stress over fractional volume change.

Elastic vs. Plastic Behavior

Materials exhibit different regimes:

• Proportional Limit: End of linear σ–ε relationship.
• Elastic Limit: Maximum stress before permanent deformation.
• Plastic Deformation: Irreversible shape change beyond elastic limit.
• Breaking Stress: Stress at which material fails.
• Elastic Hysteresis: Energy loss during loading/unloading cycles.

Conclusion

By combining equilibrium conditions with material property insights, you can analyze structures and components under load, predict deformations, and design systems for stability. Master these principles to tackle real-world engineering and physics challenges.

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