Physics XI - Chapter 09: Mechanical Properties of Solids
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- Deforming Force: Force that changes the shape or size of a body.
- Restoring Force: Internal force that opposes deformation and tries to restore original shape.
- Stress: Restoring force per unit area (σ = F/A); SI unit: Pascal (Pa) or N/m².
- Strain: Ratio of change in dimension to original dimension (no unit).
- Hooke's Law: Within elastic limit, stress ∝ strain (σ ∝ ε).
- Young's Modulus (Y): Ratio of tensile stress to tensile strain; Y = (F/A)/(ΔL/L).
- Bulk Modulus (K): Ratio of volume stress to volume strain; K = -P/(ΔV/V).
- Modulus of Rigidity (η): Ratio of shearing stress to shearing strain; η = F/(Aθ).
- Poisson's Ratio (σ): Ratio of lateral strain to longitudinal strain; σ = -(ΔD/D)/(ΔL/L).
- Elastic Potential Energy: U = ½ × stress × strain × volume = ½ F ΔL.
- Elastic Limit: Maximum stress up to which body returns to original shape.
- Yield Point: Point beyond which strain increases rapidly without stress increase.
- Plastic Behavior: Permanent deformation beyond elastic limit.
- Ductility: Property of being drawn into wires (e.g., copper, gold).
- Malleability: Property of being hammered into sheets (e.g., silver, aluminum).
- Brittleness: Property of breaking without significant deformation (e.g., glass, ceramics).
- Elastic After-effect: Time lag in regaining original shape after removing stress.
- Relations between Moduli: Y = 3K(1 - 2σ) = 2η(1 + σ).
- Thermal Stress: Stress developed when expansion/contraction is prevented; σ = YαΔT.
- Energy Density: Energy stored per unit volume = ½ × stress × strain.
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Chapter Summary
This chapter explores how solid materials respond to external forces - a fundamental concept that explains why bridges don't collapse under traffic, why buildings withstand winds, and why springs bounce back. We begin by understanding that when external forces act on a solid, they cause deformation, and the solid develops internal restoring forces that oppose this deformation.
The core of this chapter revolves around stress and strain - the quantitative measures of deforming forces and the resulting deformations. Stress tells us how much force is applied per unit area, while strain measures how much deformation occurs relative to the original size. Hooke's Law establishes the crucial relationship that within the elastic limit, stress is directly proportional to strain, forming the basis of elastic behavior.
We study three important elastic moduli: Young's modulus for longitudinal deformation, bulk modulus for volume changes, and modulus of rigidity for shearing deformation. Each modulus characterizes a material's stiffness against specific types of deformation. Poisson's ratio beautifully connects longitudinal and lateral deformations, revealing how materials contract sideways when stretched lengthwise.
The chapter also covers practical aspects like stress-strain curves that show a material's behavior from elastic deformation through yielding to ultimate fracture. We learn about material properties like ductility, malleability, and brittleness that determine real-world applications. The concept of strain energy explains where the work done in deforming a material goes, and thermal stress calculations show why expansion joints are crucial in large structures.
This knowledge forms the foundation for material science and engineering design, helping us choose the right materials for specific applications - from flexible rubber bands to rigid steel beams - based on their mechanical properties.